Class 9

Punjab State Board PSEB 9th Class English Book Solutions English Grammar Non-Finites Exercise Questions and Answers, Notes.

PSEB 9th Class English Grammar Non-Finites

(a) Fill up the blanks, selecting suitable to-infinitives from the following list :

(to see, to implement, to do, to announce, to show, to join, to let, to waste, to play, to do, to go, to solve, to post, to ask, to remember)

1. It is time ………………
2. That was a sight …..
3. The judge has a judgement ………
4. That is something ………………..
5. I have a new plan ……………
6. I have a nice picture ……….
7. Have you any plan ……………… the college ?
8. I have some questions ……………… you.
9. Have you any work ……………. ?
10. I have a house 11. She has no problem ………………
12. I have no time …………….
13. Do you have any letters …………..
14. He has some homework …………..
15. Bedi has a match ……………… on Sunday.
Answer:
1. to go
2. to see
3. to announce
4. to remember
5. to implement
6. to show
7. to join
8. to ask
9. to do
10. to let
11. to solve
12. to waste
13. to post
14. to do
15. to play.

(b) Frame seven meaningful sentences from the table below :

I have

some letters some homework some good news a question some pictures a match no time

to ask you to waste to play on Sunday to show you to do to tell you to post

1. I have some letters to post.
2. I have some homework to do.
3. I have some good news to tell you.
4. I have a question to ask you.
5. I have some pictures to show you.
6. I have a match to play on Sunday.
7. I have no time to waste.

Fill up the blanks with the Present Participle form of the following Verbs :

(a) (smoke, look, spit, swim, read, wait, go, read, eat, see)

1. …………… is a very good exercise.
2. No …………….. in this compartment.
3. ……………. French is easier than to speak it.
4. ………….. after children requires patience.
5. ………….. between meals is bad.
6. No ……………….
7. He insisted on ……………. her.
8. I am quite used to ……………… in queues.
9. Do you feel like …………….. for a swim ?
10. I am looking forward to ……………… that book.
Answer:
1. Swimming
2. smoking
3. Reading
4. Looking
5. Eating
6. spitting
7. seeing
8. waiting
9. going
10. reading.

(b) (travel, talk, work, walk, ride, see, wait, steal, drop, smoke, cut)

1. He is used to …………….. at night.
2. Try to avoid ……………. in the rush hour.
3. There’s nothing here worth ………….
4. Stop ……..
5. Would you mind ……………… a moment ?
6. He prefers …………….. to …………
7. The grass needs …………..
8. I don’t allow ……………… here.
9. I heard the cork ………..
10. I caught him ……………… my apples.
Answer:
1. working
2. travelling
3. seeing
4. talking
5. waiting
6. walking, riding
7. cutting
8. smoking
9. dropping
10. stealing.

Put the – ing forms (Participles) of the following Verbs in the blanks in the following sentences :

(please, write, rise, run, tire, drip, bore, work, grow, amuse.)
1. I caught a …………….. dog.
2. It was a ……………… sight.
3. We had a …………….. journey.
4. Give him a …………… pad.
5. …………… crops need care.
6. I do not like ……………… taps.
7. Did you see the …………….. flames ?
8. It was a ……………….. play.
9. We had an ……………… talk.
10. The government is looking after the …………… classes.
Answer:
1. running
2. pleasing
3. tiring
4. writing
5. Growing
6. dripping
7. rising
8. boring
9. amusing
10. working.

Given below are some pairs of sentences. Combine them into single sentences, using the Participle Phrases :

1. I saw a thief.
He was running away towards the station.

2. You can see the child.
She is sleeping peacefully.

3. His brother came home.
He brought an English wife with him.

4. Kindly give something to the poor beggar.
He is crying for alms.

5. The prince slept soundly.
He dreamt of his bright future.

6. My father came back home.
He brought some fruit for use.

7. Ram killed the witness.
He was giving a statement.

8. A police officer came to my house today.
He brought my missing bicycle with him.

9. I can hear my son.
He is saying prayers.

10. Could you bring me a pen ?
It is lying on the shelf.
Answers
1. I saw a thief running away towards the station.
2. You can see the child sleeping peacefully.
3. His brother came home bringing an English wife with him.
4. Kindly give something to the poor crying beggar.
5. The prince slept soundly dreaming of his bright future.
6. My father came back home bringing some fruit for use.
7. Ram killed the witness giving a statement.
8. A police officer came to my house today bringing my missing bicycle with him.
9. I can hear my son saying prayers.
10. Could you bring me a pen lying on the shelf?

Fill in the blanks with correct Past Participle form of the given verbs :

(wound, cook, burn, break, write, build, rot, lose, unlock, fade, close, paint, translate, finish, fail)

1. I got my house ……………
2. He got the book …………
3. The …………… soldier was taken to the hospital.
4. The overseer is getting this house ……..
5. The ……………… rose was thrown out.
6. You must get the room ……………..
7. The …………….. food got spoilt.
8. Give a ……………… statement.
9. A ……………. child dreads the fire.
10. This college does not admit ……….. students.
11. He died of a …………….. heart.
12. The officer wants this work ………….. by today.
13. Who likes ……………. vegetables ?
14. That lady found her ……………… purse.
15. I found all the doors
Answer:
1. built
2. translated
3. wounded
4. unlocked
5. faded
6. painted
7. cooked
8. written
9. burnt
10. failed
11. broken
12. finished
13. rotten
14. lost
15. closed.

Combine the following sentences, using Participles or Gerunds or Infinitives :

1. I made a journey to Mumbai yesterday. I went there to get the best financial advice.
2. Your parcel never reached me. It had been addressed to the wrong place.
3. Turn to the right. You will find the office.
4. He drew his sword. He rushed at the king.
5. It was my purse. It had been lost.
6. He made a promise. He kept it also.
7. One must serve twenty years. After that one can retire.
8. He said he would come today. I was pleased at this.
9. I promise to help you in time of need. You can rely on this.
10. She was praised by all. She grew proud.
Answer:
1. I made a journey to Mumbai to get the best financial advice.
2. Having been addressed to the wrong place, your parcel never reached me.
3. Turning to the right, you will find the office.
4. Drawing his sword he rushed at the king.
5. It was my lost purse.
6. Having made a promise he kept it also.
7. After serving for twenty years one can retire.
8. I was pleased to hear of his coming today.
9. You can rely on my promise to help you in times of need.
10. Being praised by all, she grew proud.

The Infinitive

क्रिया के मूल रूप को Infinitive कहा जाता है। इस पर कर्ता के Number और Person का कोई प्रभाव नहीं होता है।
Infinitive दो प्रकार के होते हैं :
Bare Infinitive : यह क्रिया का वह मूल रूप होता है जिसके साथ to नहीं लगता है।
I saw her weep. — We made her sing.

To-Infinitive : यह क्रिया का वह मूल रूप होता है जिसके साथ to लगा होता है।
I want to go now. — We have to pay taxes.

The Use of Bare-Infinitive

Bare-Infinitive का प्रयोग निम्नलिखित हालतों में किया जाता है :

1. निम्नलिखित सहायक क्रथाओ के बाद
do, does, did, can, could, will, would, shall, should, may, might, need, must, dare.
1. I shall accompany you.
2. He may come today.
3. You need not do it.

2. निम्नलिखित सकर्मत (Transitive) कियाओं के बाद :

make, let, bid, feel, hear, see, watch, notice, observe, if I
1. ‘I heard him go up the stairs.
2. I saw him steal my pen.
3. I felt the cold air strike against my face.
4. He made her weep every day.

3. had और would वाले निम्नालिखित phrases के बाद :

had better, had rather, would rather, had sooner, would sooner.
1. I would rather die than beg.
2. You had better stop smoking.

4. than (conjunction) it but (preposition) etc are :

1. I would rather walk than ride your scooter.
2. He did nothing but laugh.
नोट : but के बाद ‘bare-infinitive’ का प्रयोग केवल तभी किया जाता है जब but से पूर्व मुख्य क्रिया के रूप में do, does, did का प्रयोग किया गया हो।

The Use of To-Infinitive.

To-infinitive का प्रयोग निम्नलिखित हालतों में किया जाता है :

1. ought और have के साथ to-infinitive का प्रयोग किया जाता है यदि इन शब्दों का प्रयोग किसी जिम्मेदारी (obligation) अथवा कर्त्तव्य को प्रकट करने के लिए किया गया हो।

1. You ought to respect your elders.
2. We ought to help the poor.
3. I have to support my family.
4. She has to live with her parents.
5. Boys had to pay their fees.

2. किसी कारण अथवा उद्देश्या के प्रकट करने के लिए भी to-invinitive का प्रयोग किया जाता ह

1. She came here to consult you.
2. I went to Delhi to meet my brother.
3. They stopped at the market to buy some apples.
4. We did not go there to earn money.

निम्नलिखित क्रियाओं के साथ to-infinitive लगाया जाता है यदि उनका प्रयोग किसी मनोरथ, इच्छा अथवा तत्परता को प्रकट करने के लिए किया गया हो :

want, hope, like, love, hate, promise, intend, propose, decide, swear, learn, remember, forget, agree, consent, neglect, refuse, attempt, fail, hesitate, prepare, care, pretend, determine, arrange, seem.
1. I want to go now.
2. She decided to marry him.
3. I forgot to answer this question.
4. They promised to pay all the taxes.

निम्नलिखित सकर्मक क्रियाओं के साथ कर्म (object) लगाने के बाद to-infinitive का प्रयोग किया जाता है :

ask, advise, allow, beg, compel, courage, force, instruct, invite, order, permit, request, tell, teach, warn, Bici
1. I begged him to help me.
2. My mother asked me to work hard.
3. The teacher allowed him to go.
4. The boys requested the teacher to forgive them.

Fill in the blanks with the correct form of the verbs given in brackets :

1. Mohan wants ………………. (swim) in the river.
2. The teacher asked him ……………….. (get) out of the room.
3. I forgot ……………….. (bring) my purse.
4. Let him ……………….. (go) now.
5. I have come ……………….. (see) the Principal.
6. It began ……………….. (rain) and we couldn’t go out.
7. We saw him ……………. (arrive) at the station.
8. The book was easy …………….. (read).
9. We didn’t expect Ram …………. (win).
10. They heard her ………………. (sing) a sweet song.
11. Mohan knows how ……………….. (answer) this question.
12. He was too tired ……………….. (walk).
13. He made me …………….. (do) it.
14. They stopped ……………… (have) some rest.
15. He is saving money ………….. (buy) a scooter.
16. Would you like …….. (have) dinner with us?

The Gerund

-ing प्रत्यय वाली ऐसी क्रिया जो Noun का काम कर रही हो उसे Gerund कहा जाता है। इसका प्रयोग निम्नलिखित स्थितियों में किया जा सकता है :

1. Subject to a Verb	1. Swimming improves one’s health. 2. Smoking causes cancer.
2. Object to a Verb	1. I dislike smoking. 2. I love swimming.
3. Object to a Preposition	1. He is fond of playing. 2. She was fined for coming late.
4. Complement to a Linking Verb	1. His only aim was cheating. 2. My favourite hobby is gardening.
5. In apposition to a Pronoun	1. It is no use crying. 2. It is foolish saying that.

Gerunds के प्रयोग के सम्बन्ध में ध्यान रखने योग्य बातें :

1. निम्नलिखित क्रियाओं के साथ कर्म (object) के रूप में to-infinitive तथा gerund में से किसी का भी प्रयोग किया जा सकता है।
advise, allow, attempt, begin, continue, hate, intend, learn, like, love, remember, start.

To-infinitive	Gerund
1. He intends to live here. 2. I love to hear this song. 3. I remembered to see him. 4. We prefer to travel by air. 5. He continued to write letters.	1. He intends living here. 2. Move hearing this song. 3. I remembered seeing him. 4. We prefer travelling by air. 5. He continued writing letters.

2. अनुभूति सम्बन्धी निम्नलिखित क्रियाओं के साथ bare-infinitive अथवा gerund में से किसी का भी प्रयोग किया जा सकता है :
feel, hear, notice, observe, see, watch.

Bare-Infinitive	Gerund
1. I heard her come in. 2. She saw me cross the road. 3. I heard you shout in the class.	1. I heard her coming in. 2. She saw me crossing the road. 3. I heard you shouting in the class.

3. निम्नलिखित क्रियाओं के साथ केवल gerund का ही प्रयोग किया जा सकता है। इनके साथ infinitive का प्रयोग कभी नहीं किया ‘
जाना चाहिए।
avoid, delay, deny, dislike, enjoy, finish, forget, imagine, keep (जारी रखना), mind (बुरा मनाना), pardon, postpone, risk, stop, suggest, try (परखना), understand.

4. निम्नलिखित क्रियाओं के साथ भी gerund का ही प्रयोग किया जाता है :

be worth, can’t bear, be no use, can’t stand, be no good, can’t help.

1. This table is worth buying.
2. It is no use crying over spilt milk.
3. It is no good imitating others.
4. She can’t bear living away from her children.
5. I can’t stand smoking in my room.
6. We couldn’t help laughing at him.

5. यदि किसी gerund से पूर्व कोई संज्ञा अथवा सर्वनाम लगा हो, तो यह अवश्य ही सम्बन्धवाचक रूप में होना चाहिए, जैसे

1. I dislike Mohan’s coming late daily.
2. Your father depends on your working hard.
3. Do you mind my smoking here?

Fill in the blanks with the correct form of the given verbs (Gerund or Infinitive) :

1. I don’t mind …………. (give) my book to you.
2. My father has stopped ………… (talk) to him.
3. We enjoyed …………… (swim) in the river.
4. She likes …………. (walk) in her garden.
5. He has given up …………. (smoke).
6. The tailor has completed ………….. (sew) the shirt.
7. He refused ………….. (accept) my advice.
8. When the bell rang, the students came
9. I decided ………. (see) the Principal.
10. She offered …………… (bring) flowers for me.
11. I want …………… (play) cricket.
12. Do you really enjoy …………. (play) football ?
13. My father can’t afford ………….. (buy) a T.V. set.
14. They will not permit you …………… (talk) in the library.
15. I advised my brother ………….. (work) hard for the test.

The participle

क्रिया के जिस रूप में Verb तथा Adjective दोनों के ही गुण हों, उसे Participle कहा जाता है। Participle तीन प्रकार के होते हैं :

Present Participle	Past Participle	Perfect Participle
Drowning	Drowned	Having drowned
Seeing	Seen	Having seen
Finishing	Finished	Having finished

1. Present Participle के कुछ उदाहरण

• A drowning man catches at a straw.
• The results were encouraging.
• Taking a walking stick, the old lady came out of the cottage.
• Seeing the police, the thief ran away.
• Naresh went into the bathroom singing.

2. Past Participle के कुछ उदाहरण

• His spoken English is much better than yours.
• These solved papers are very helpful.
• I boarded a crowded bus.
• I saw a faded rose.

3. Perfect Participle के कुछ उदाहरण

• Having bought a book, I came back from the market.
• Having done his homework, John went out to play.
• Having attended a meeting of the club, I came back.
• Having won a prize, Neelu felt happy.

4. Participle Phrases के कुछ उदाहरण
याद रखिए कि
(1) जब कोई क्रिया वाक्य की मुख्य क्रिया के समय पर ही हो रही हो तो उसके लिए Present Participle (V₁-ing) का प्रयोग किया जाना चाहिए :
I looked through some old papers and came across this letter.
= Looking through some old papers, I came across this letter.

The students saw the Headmaster and they stopped talking.
= Seeing the Headmaster, the students stopped talking.

(2) जब कोई क्रिया वाक्य की मुख्य क्रिया से पहले हो चुकी हो, तो उसके लिए Past Participle (having + V₃) का प्रयोग किया जाता है :
I met my friend and went back with him to his house.
= Having met my friend, I went back with him to his house.

The match ended and the spectators went away.
= The match having ended, the spectators went away.

Fill in the blanks with the correct non-finite form (Infinitive, Gerund or Participle) of the verbs given in the brackets :

1. The rice will grow well in the ………… (come) rains.
2. We heard of his ………… (come) back today.
3. We hope …………… (see) him back soon.
4. …………… (Believe) him to be right, I trusted him.
5. Night ………….. (come) on, the men went home.
6. Did you hear of his ………. (win) a prize ?
7. I am tired of …………. (do) this work.
8. Generally ……… (speak), we get what we deserve.
9. We saw him …………( leave) the house.
10. I was very happy ………… (see) you.
11. I shall be glad …….. (help) you.
12. My wife ……………… (expect) my return, did not leave the house.
13. ………….. (Spelt) is more difficult than …………. (write).
14. I am …………… (blame), not you.
15. The coach made us … (run).

Miscellaneous Sentences For Practice

Use the proper form of Non-finites in the following sentences

I.

1. ………………. (Teach) correct English needs great care.
2. People assembled ………………. (hear) the Minister.
3. I saw him ………………. (leave) his house.
4. Some people love ……………….(climb) mountains.
5 ……………….(Walk) is a good exercise.
6. It is easy ………………. (advise) others.
7. People worship the ………………. (rise) sun.
8. I made him ………………. (laugh).
9. A ………………. (drown) man catches at a straw.
10. I intend ……………….(spend) my vacation with my uncle.

II.

1. We are busy ………………. (pack).
2. He refused ………………. (obey) me orders.
3. I hope ………………. (succeed) in my plans.
4. The ………………. (steal) money did not last long.
5. He insisted on ………………. (see) him.
6. These days it is not easy ………………. (get) a job.
7. We were too ……………….(tire) to work.
8. I enjoy ………………. (piny) with small children.
9. ………………. (Smoke) is injurious to health.
10. She agreed ………………. (marry) the poor shepherd.

III.

1. They all heard him ………………. (sing).
2. The runner is ………………. (exhaust).
3. It is no use ………………. (wait) here now.
4. Are you interested in ………………. (paint) ?
5. Dogs are not allowed ………………. (enter) the garden.
6. ………………. (Swim) is a good exercise.
7. I heard him ………………. (cry) for help. .
8. Are you interested in ………………. (boat) ?
9. She was too tired ………………. (walk).
10. No ………………. (park) here.

IV.

1. I wonder why he avoids ………………. (meet) me.
2. It is no use ………………. (argue) with him.
3. I made him ………………. (feel!) sorry.
4. ………………. (Drink) ruins our health.
5. I don’t mind ………………. (wait).
6. He did not let me ………………. (play) in his garden.
7. I hope ………………. (get) first division in the examination.
8. I don’t want ………………. (swim) in the river.
9. I enjoy ………………. (sing) patriotic songs.

V.

1. His story made the listeners ………………. (weep).
2. Dancing is difficult ………………. (learn).
3. We enjoyed ………………. (boat) in the lake.
4. I saw the ball ………………. (roll) into the well.
5. We are looking forward to ………………. (see) her.
6. He used ………………. (smoke) in his youth.
7. How dare you ………………. (talk) like that ?
8. They found her ………………. (sleep).
9. They made her ………………. (sing) a song.
10. She refused ………………. (help).

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 8 Quadrilaterals Ex 8.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.1

Question 1.
The angles of a quadrilateral are in the ratio 3: 5 : 9: 13. Find all the angles of the quadrilateral.
Answer:
Let, ABCD be a given quadrilateral.
∴ ∠A : ∠B : ∠C : ∠D = 3 : 5 : 9 : 13
Sum of ratios = 3 + 5 + 9 + 13 = 30
In quadrilateral ABCD, ∠A + ∠B + ∠C + ∠D = 360°
∴ ∠A = \(\frac{3}{30}\) × 360° = 3 × 12 = 36°
∴ ∠B = \(\frac{5}{30}\) × 360° = 5 × 12 = 60°
∴ ∠C = \(\frac{9}{30}\) × 360° = 9 × 12 = 108°
∴ ∠D = \(\frac{13}{30}\) × 360° = 13 × 12 = 156°
Thus the angles of the given quadrilateral are 36°, 60°, 108° and 156°.

Question 2.
If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Answer:
In parallelogram ABCD, diagonals are equal.
∴ AC = BD.
In ∆ DAB and ∆ CBA.
DA = CB (Theorem 8.2)
AB = BA (Common)
DB = CA (Given)
∴ ∆ DAB ≅ ∆ CBA sss rule)
∴ ∠ DAB = ∠CBA (CPCT)
In parallelogram ABCD, AD || BC and AB is their transversal.
∴ ∠ DAB + ∠ CBA = 180°
(Interior angles on the same side of transversal)
Thus, in parallelogram ABCD, two angles ∠A and∠B are right angles. Hence, all the angles are right angle.
Hence, the parallelogram ABCD having equal diagonals is a rectangle.

Question 3.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Answer:
In quadrilater ABCD. diagonals AC and BD bisect each other at M at right angles.
∴ AM = CM, BM = DM and
∠AMB = ∠CMB = ∠CMD = ∠AMD = 90°.
In ∆ AMB and ∆ CMB,
AM = CM
∠ AMB = ∠CMB
BM = BM (Common)
∴ ∆ AMB ≅ ∆ CMB (SAS rule)
∴ AB = CB (CPCT)
Similarly, proving ∆ BMC ≅ ∆ DMC and ∆ DMA ≅ ∆ BMA, we get BC = DC and DA = BA.
Thus, in quadrilateral. ABCD.
AB = BC CD = DA.
Therefore, quadrilateral ABCD is a rhombus.
Thus, if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Question 4.
Show that the diagonals of a square are equal and bisect each other at right angles.

Answer:
ABCD is a square in which diagonals AC and BD intersect at M.
Every square is a parallelogram.
∴ AC and BD bisect each other. …………… (1)
In ∆ DAB and ∆ CBA,
DA = CB (Sides of a square)
∠ DAB = ∠ CBA (Right angles in a square)
AB = BA (Common)
∴ ∆ DAB ≅ ∆ CBA (SAS rule)
∴ BD = AC (CPCT) ……………….. (2)
Now, in ∆ AMB and ∆ CMB,
AM = CM (BD bisects AC at M).
BM = BM (Common)
AB = CB (Sides of a square)
∴ ∆ AMB ≅ ∆ CMB (SSS rule)
∴ ∠ AMB = ∠CMB (CPCT)
But, ∠ AMB and ∠ CMB form a linear pair.
∴ ∠ AMB + ∠ CMB = 180°
Hence, ∠AMB = ∠ CMB = 90° (3)
(1), (2) and (3) taken together proves that the diagonals of a square are equal and bisect each other at right angles.

Question 5.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Answer:
In quadrilateral ABCD, diagonals AC and BD are equal and bisect each other at right angles.
∴ AC = BD,
MA = MC = MB = MD = \(\frac{1}{2}\)AC = \(\frac{1}{2}\)BD and
∠AMB = ∠CMB= ∠DMC = ∠DMA= 90°.
In ∆ AMB and ∆ CMB,
AM = CM
∠ AMB = ∠ CMB (Right angles)
BM = BM (Common)
∴ ∆ AMB ≅ ∆ CMB (SAS rule)
∴ AB = CB (CPCT)
Similarly, we can prove that BC = DC and
DA = BA.
Thus, in quadrilateral ABCD,
AB = BC = CD = DA …………… (1)
Now, in ∆ DAB and ∆ CBA,
DA = C B
BD = AC (Given)
AB = BA (Common)
∴ ∆ DAB ≅ ∆ CBA (SSS rule)
∴ ∠DAB = ∠CBA (CPCT)
Thus, in quadrilateral ABCD, ∠A = ∠B.
Similarly, we can prove that ∠B = ∠C and ∠C = ∠D.
Thus, in quadrilateral ABCD,
∠A = ∠B = ∠C = ∠D.
Moreover. In quadrilateral ABCD,
∠A + ∠B + ∠C + ∠D = 360°
∴ ∠A = ∠B = ∠C = ∠D = \(\frac{360^{\circ}}{4}\) = 90° ……………… (2)
Thus, (1) and (2) taken together proves that in quadrilateral ABCD, all the sides are equal and all the angles are equal.
Therefore, quadrilateral ABCD is a square.
Thus, if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Question 6.
Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus.

Answer:
Diagonal AC of parallelogram ABCD bisects ∠A.
∴ ∠DAC = ∠BAC …………… (1)
Now, ∠BAC and ∠DCA are alternate angles formed by transversal AC of AB || CD.
∴ ∠BAC = ∠DCA …………… (2)
Similarly, ∠DAC and ∠BCA are alternate angles formed by transversal AC of AD || BC.
∴ ∠DAC = ∠BCA ……………… (3)
From (1), (2) and (3),
∠DCA = ∠BCA.
But, ∠DCA + ∠BCA = ∠BCD (Adjacent angles)
∴ AC bisects ∠C also.
In parallelogram ABCD,
∠A = ∠C (Theorem 8.4)
∴ \(\frac{1}{2}\)∠A = \(\frac{1}{2}\)∠C
∴ ∠ DAC = ∠ DCA
∴ In ∆ DAC, DA = DC (Sides opposite to equal angles)
Moreover, in parallelogram ABCD,
AB = CD and BC = DA (Theorem 8.2)
∴ AB = BC = CD = DA
Thus. In parallelogram ABCD, all the sides are equal.
Hence, ABCD is a rhombus.

Question 7.
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
Answer:

ABCD is a rhombus
∴ AB || DC, BC || AD and AB = BC = CD = DA.
AB || DC and AC is their transversal.
∴ ∠CAB = ∠ACD (Alternate angles)
In, ∆ DAC, CD = DA
∴ ∠ACD = ∠CAD
Then, ∠CAB = ∠CAD
But, ∠CAB + ∠CAD = ∠ DAB (Adjacent angles)
∴ ∠ CAB = ∠CAD = \(\frac{1}{2}\) ∠DAB
This shows that AC bisects ∠A.
Again, BC || AD and AC is their transversal.
∴ ∠ BCA = ∠ DAC (Alternate angles)
In, ∆ DAC, DA = DC
∴ ∠ DAC = ∠ DCA
Then, ∠BCA = ∠DCA
But, ∠ BCA + ∠ DCA = ∠ DCB (Adjacent angles)
∴ ∠ BCA = ∠ DCA = \(\frac{1}{2}\)∠ DCB
This shows that AC bisects ∠C.
Thus, AC bisects ∠A as well as ∠C.
Similarly, taking BD as transversal of AB || DC, and BC || AD, it can be proved that BD bisects ∠B as well as ∠D.

Question 8.
ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square. (ii) Diagonal BD bisects ∠B as well as ∠D.
Answer:

In rectangle ABCD, AB = CD, BC = AD, AB || CD and BC || AD.
AC bisects ∠A as well as ∠C.
∴ ∠DAC = ∠BAC = \(\frac{1}{2}\)∠A and
∠ DCA = ∠ BCA = \(\frac{1}{2}\)∠C
Now, AB || CD and AC is their transversal.
∴ ∠ BAC = ∠ DCA (Alternate angles)
∴ ∠ DAC = ∠ DCA
Thus, in ∆ DAC, ∠DAC = ∠DCA
∴ AD = CD (Sides opposite to equal angles)
From this, we get AB = BC = CD = DA.
Also, in rectangle ABCD,
∠A = ∠B = ∠C = ∠D = 90°
Hence, ABCD is a square. …..Result (i)
In ∆ BCD, BC = CD
∴ ∠ CBD = ∠ CDB
Moreover, AB || CD and BD is their transversal.
∴ ∠ CDB = ∠ ABD (Alternate angles)
∴ ∠ CBD = ∠ ABD
Now, ∠ CBD + ∠ ABD = ∠ ABC
∴ ∠ CBD = ∠ ABD = \(\frac{1}{2}\) ∠ ABC
Thus, BD bisects ∠B.
Similarly, diagonal BD bisects ∠ D.
Hence, diagonal BD bisects ∠B as well as ∠D …….. Result (ii)

Question 9.
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see the given figure). Show that:
(i) ∆ APD ≅ ∆ CQB
(ii) AP = CQ
(iii) ∆ AQB ≅ ∆ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram.
Answer:

ABCD is a parallelogram.
∴ AD || BC and BD is their transversal.
∴ ∠ADB = ∠CBD (Alternate angles)
∴ ∠ADP = ∠CBQ …………… (1)
Similarly, CD || BA and BD is their transversal.
∴ ∠ ABD = ∠ CDB (Alternate angles)
∴ ∠ABQ = ∠CDP ……………… (2)
In ∆ APD and ∆ CQB,
AD = CB (Opposite sides of a parallelogram)
∠ ADP = ∠ CBQ [by (1)]
DP = BQ (Given)
∴ ∆ APD ≅ ∆ CQB (SAS rule) ……. Result (i)
∴ AP = CQ (CPCT) …… Result (ii)
In ∆ AQB and ∆ CPD,
AB = CD (Opposite sides of a parallelogram)
∠ ABQ = ∠ CDP [by (2)]
BQ = DP (Given)
∴ ∆ AQB ≅ ∆ CPD (SAS rule) …….. Result (iii)
∴ AQ = CP (CPCT) ………….. Result (iv)
Now, in quadrilateral APCQ, AP = CQ and AQ = CP
Hence, by theorem 8.3, APCQ is a parallelogram. ………. Result (v)

Question 10.
ABCD is a parallelogram and AP and Cg are perpendiculars from vertices A and C on diagonal BD (see the given figure). Show that
(i) ∆ APB ≅ ∆ CQD
(ii) AP = CQ

Answer:
In parallelogram ABCD, AB || CD and BD is their transversal.
∴ ∠ ABD = ∠ CDB (Alternate angles)
∴ ∠ABP = ∠CDQ ……………. (1)
Now, in ∆ APB and ∆ CQD,
AB = CD (Opposite sides of a parallelogram)
∠ ABP = ∠ CDQ [by (1)]
∠ APB = ∠ CQD (Right angles)
∆ APB ≅ ∆ CQD (AAS rule) ………… Result (i)
∴ AP = CQ (CPCT) ……….. Result (ii)

Question 11.
In ∆ ABC and ∆ DBF, AB = DE, AB || DE, j BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that:
(i) Quadrilateral ABED is a parallelogram
(ii) Quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) Quadrilateral ACFD is a parallelogram
(v ) AC = DF
(vi) ∆ ABC ≅ ∆ DEF.

Answer:
In quadrilateral ∆ BED, AB = DE and AB || DE. Thus, in quadrilateral ABED, sides in one s pair of opposite sides are equal and parallel. Hence, by theorem 8.8, quadrilateral ABED is a parallelogram. …… Result (i)
Similarly, in quadrilateral BEFC, BC = EF and BC || EF.
Hence, by theorem 8.8, quadrilateral BEFC is a parallelogram. …………. Result (ii)
In parallelogram ABED, AD || BE and in parallelogram BEFC, BE || CE Thus, AD and CF both are parallel to BE.
∴ AD || CF ……….(1)
In parallelogram ABED, AD = BE and in parallelogram BEFC, BE = CF.
∴ AD = CF ……… (2)
Taking (1) and (2) together, we get
AD || CF and AD = CF ………. Result (iii)
In quadrilateral ACFD, AD || CF and AD = CF. Hence, by theorem 8.8, quadrilateral ACFD is a parallelogram. ………. Result (iv)
AC and DF are opposite sides of parallelogram ACFD.
∴ AC = DF ………….. Result (v)
Now, in ∆ ABC and ∆ DEF,
AB = DE (Given)
BC = EF (Given)
AC = DF [by result (v)l
∴ ∆ ABC ≅ ∆ DEF (SSS rule) …… Result (vi)

Question 12.
ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that:
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ ABC ≅ ∆ BAD
(iv) diagonal AC = diagonal BD
[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.)

Answer:
AB is extended to E, and AB || CD.
∴ AE || CD
In quadrilateral ADCE, AE || CD and by consturction CE || DA.
∴ Quadrilateral ADCE is a parallelogram.
∴ AD = CE
Moreover, AD = BC (Given)
∴ BC = CE
In ∆ BCE, BC = CE
∴ ∠CBE = ∠CEB
∴ ∠CBE = ∠CEA ………….. (1)
In parallelogram ADCE, AD || CE and AE is their transversal.
∴ ∠ DAE + ∠ CEA = 180° (Interior angles on the same side of transversal)
∴ ∠ DAE + ∠ CBE = 180° [by (1)]
∴ ∠ DAE = 180° – ∠ CBE …………… (2)
Moreover, ∠ ABC + ∠ CBE = 180° (Linear pair)
∴ ∠ ABC = 180° – ∠ CBE …………. (3)
From (2) and (3),
∠ DAE = ∠ ABC
∴ ∠A = ∠B ……… Result (i)
AB || CD and AD is their transversal.
∴ ∠A + ∠D = 180°
∴ ∠D = 180°- ∠A ………….. (4)
AB || CD and BC is their transversal.
∴ ∠B + ∠C = 180°
∴ ∠C = 180°- ∠B
∴ ∠C = 180° – ∠ A [by result (i)] ……… (5)
From (4) and (5),
∠C = ∠D …….. Result (ii)
Draw diagonals AC and BD.
In ∆ ABC and ∆ BAD,
BC = AD (Given)
∠ ABC = ∠ BAD [by result (i)]
AB = BA (Common)
∴ ∆ ABC ≅ ∆ BAD (SAS rule) ………. Result (iii)
∴ AC = BD (CPCT)
Thus, diagonal AC = diagonal BD … Result (iv)
Note: A trapezium in which non-parallel sides are equal is called an isosceles trapezium. As proved above, in an isosceles trapezium, the diagonals are equal and the angles on each parallel side are equal.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.5 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5

Question 1.
ABC is a triangle. Locate a point in the interior of ∆ ABC which is equidistant from all the vertices of ∆ ABC.
Answer:

In ∆ ABC, draw l, the perpendicular bisector of side AB and m, the perpendicular bisector of side BC. Name the point of intersection of l and m as P.
P is a point on the perpendicular bisector of AB. Hence, P is equidistant from A and B.
∴ PA = PB
P is a point on the perpendicular bisector of BC. Hence, P is equidistant from B and C.
∴ PB = PC
Thus, PA = PB = PC
Hence, P is the required point which is equidistant from all the vertices of ∆ ABC.
Note: Since ∆ ABC given here is an acute angled triangle, point P lies in the interior of ∆ ABC. If ∆ ABC is a right angled Mangle, point P lies on the hypotenuse. Actually, in that case, point P will be the midpoint of the hypotenuse. Lastly, if ∆ ABC is an obtuse angled triangle, point P lies in the exterior of ∆ ABC. This point P is called the circumcentre of ∆ ABC.

Question 2.
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Answer:
In ∆ ABC, draw the bisectors of ∠B and ∠C to intersect each other at point I.
I is a point on the bisector of ∠ B. Hence, I is equidistant from sides BA and BC. Similarly, I is a point on the bisector of ZC. Hence, I is equidistant from sides BC and CA.
Thus, point I is the required point which is equidistant from all the three sides AB, BC and CA of ∆ ABC.
This point I is called the incentre of ∆ ABC. It always lies in the interior of ∆ ABC irrespective of the type of ∆ ABC.

Question 3.
In a huge park, people are concentrated at three points (see the given figure):

A: where there are different slides and swings for children.
B: near which a man-made lake is situated.
C: which is near to a large parking and exit.
Where should an ice cream parlour be set up so that maximum number of persons can approach it ?
(Hint: The parlour should be equidistant from A, B and C.)
Answer:
First of all, construct ∆ ABC with the given points A, B and C as vertices. Then, as shown in example 1, draw the perpendicular s bisectors of any two sides of ∆ ABC and name their point of intersection as P.

Now, the ice cream parlour should be set up at the location given by point P as it is equidistant from all the three places (points) A, B and C.

Question 4.
Complete the hexagonal and star shaped < Rangolies [see figure (1) and (2)] by filling them with as many equilateral triangles of > side 1 cm as you can. Count the number < of triangles in each case. Which has more triangles?

Answer:
In figure (1), if we join the opposite vertices, we get three longest diagonals of hexagon ABCDEE By the intersection of these diagonals we get point O and six equilateral triangles – ∆ OAB, ∆ OBC, ∆ OCD, ∆ ODE, ∆ OEF and ∆ OFA. Each side of all these equilateral triangles will measure 5 cm. In each of these six triangles, we can fill 25 (1 + 3 + 5 + 7 + 9) equilateral triangles with side 1 cm each. Hence in the hexagonal Rangoli ABCDEF, we can fill 25 × 6 = 150 triangles.

Similarly, in figure (2), we can fill 150 triangles in the inner hexagon and 150 triangles in the six triangles on the boundary of the hexagon. Thus, in figure (2), 150 + 150 = 300 triangles can be filled.
Hence, more triangles can be filled in figure (2).

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4

Question 1.
Show that in a right angled triangle, the hypotenuse is the longest side.
Answer:

In ∆ ABC, ∠ B is a right angle.
∴ ∠ B = 90° and AC is the hypotenuse.
In ∆ ABC,
∠A + ∠B + ∠C = 180°
∴ ∠ A + 90° + ∠ C = 180°
∴ ∠ A + ∠ C = 90°
Now, ∠ A and ∠ C are both positive (in degrees) and their sum is 90°.
∴ ∠ A < 90° and ∠ C < 90°
∴ ∠ A < Z B and ∠ C < ∠ B
∴ BC < AC and AB < AC (Theorem 7.7)
Hence, hypotenuse AC is greater than each of the other two sides BC and AB. Thus, the hypotenuse is the longest side in a right angled triangle.

Question 2.
In the given figure, sides AB and AC of ∆ ABC are extended to points P and Q respectively. Also, ∠PBC < ∠ QCB. Show that AC > AB.

Answer:
∠ PBC < ∠ QCB (Given)
∴ – ∠ PBC > – ∠ QCB (Multiplying an inequality by (-1), it reverses)
∴ 180° – ∠ PBC > 180° – ∠ QCB (Adding 180° on both the sides) …………. (1)
Now, ∠ ABC and ∠ PBC as well as ∠ ACB and ∠ QCB from a linear pair.
∴ ∠ ABC = 180° – ∠ PBC and
∠ ACB = 180° – ∠ QCB
Substituting these values in (1), we get
∠ ABC > ∠ ACB
Now, in ∆ ABC, ∠ ABC > ∠ ACB A
∴ AC > AB (Theorem 7.7)

Question 3.
In the given figure, ∠ B < ∠ A and ∠ C < ∠ D. Show that AD < BC.

Answer:
In ∆ OAB, ∠ B < ∠ A
∴ OA < OB (Theorem 7.7) …………….. (1)
In ∆ OCD, ∠ C < ∠ D
∴ OD < OC (Theorem 7.7) ……………… (2)
Adding (1) and (2),
OA + OD < OB + OC
∴ AD < BC (As O is the point of intersection of AD and BC, it lies on both the line segments.)

Question 4.
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD ,(see the given figure). Show that ∠A > ∠C and ∠B > ∠D.

Answer:

Construction: In quadrilateral ABCD, draw diagonal AC.
AB is the smallest side of ABCD and CD is the longest side of ABCD.
∴ AB < BC and AD < CD.
In ∆ ABC, AB < BC
∴ ∠ ACB < ∠ BAC …… (1)
In ∆ CDA, AD < CD
∴ ∠ DCA < ∠ DAC ……… (2)
Adding (1) and (2),
∠ ACB + ∠ DCA < ∠ BAC + ∠ DAC
∴ ∠ BCD < ∠ BAD
∴ ∠ BAD > ∠ BCD
Thus, in quadrilateral ABCD, ∠ A > ∠ C. Similarly, after constructing diagonal BD and using the inequalities in A ABD and A CBD, it can be proved that ∠ B > ∠ D.

Question 5.
In the given figure, PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

Answer:
PS is the bisector of ∠QPR.
∴ ∠QPS = ∠RPS = \(\frac{1}{2}\) ∠QPR ……………. (1)
∠ PSR is an exterior angle of A PQS and ∠ PSQ is an exterior angle of A PRS.
∴ PSR = ∠ Q + ∠QPS and
∠PSQ = ∠R + ∠RPS …………….. (2)
Now, in A PQR, PR > PQ
∴ ∠ Q > ∠ R
∴ ∠Q + \(\frac{1}{2}\) ∠ QPR > ∠R + \(\frac{1}{2}\) ∠ QPR
∴ ∠Q + ∠QPS > ∠R + ∠RPS [from (1)]
∴ ∠PSR > ∠PSQ

Question 6.
Show that of all line segments drawn from a given point not on a given line, the perpendicular line segment is the shortest.
Answer:

AB is a line and P is a point not on AB.
PM is the perpendicular line segment drawn from P to line AB.
N is any point on AB, other than M.
In ∆ PMN, ∠ M = 90°
∴ ∠ N < 90°
Thus, in ∆ PMN, ZN < ZM.
∴ PM < PN
This is true for any location of point N.
Hence, of all the line segments drawn from a point not on a given line, the, perpendicular line segment is the shortest.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles MCQ Questions with Answers.

PSEB 9th Class Maths Chapter 7 Triangles MCQ Questions

Multiple Choice Questions and Answer

Answer each question by selecting the proper alternative from those given below each question to make the statement true:

Question 1.
In ∆ ABC, ∠A = ∠C, AC = 5 and BC = 4. Then, the perimeter of ∆ ABC is ……………. .
A. 9
B. 14
C. 13
D. 15
Answer:
C. 13

Question 2.
In ∆ PQR, PQ = PR, QR is extended to S and ∠PRS = 110°. Then, ∠PQR = ……………… .
A. 30°
B. 50°
C. 80°
D. 70°
Answer:
D. 70°

Question 3.
In ∆ ABC and ∆ DEF, AB = DE, BC = EF and ∠B = ∠E. If the perimeter of ∆ ABC is 20, then the perimeter of ∆ DEF is ……………. .
A. 10
B. 20
C. 15
D. 40
Answer:
B. 20

Question 4.
In ∆ ABC and ∆ PQR, AB = PQ, ∠A = ∠P and ∠B = ∠Q. If ∠A + ∠C = 130°, then ∠Q = …………….. .
A. 65°
B. 130°
C. 50°
D. 100°
Answer:
C. 50°

Question 5.
In ∆ PQR, ∠P = ∠Q = ∠R. If PQ = 6, then the perimeter of ∆ PQR is ………………. .
A. 12
B. 9
C. 18
D. 24
Answer:
C. 18

Question 6.
In ∆ ABC, AB < AC. Then …………… holds good.
A. ∠A < ∠B
B. ∠B < ∠C
C. ∠C < ∠A
D. ∠C < ∠B
Answer:
D. ∠C < ∠B

Question 7.
In ∆ PQR, ∠R > ∠Q. Then, ………………. holds good.
A. PQ > PR
B. QR > PQ
C. PR > PQ
D. PQ > QR
Answer:
A. PQ > PR

Question 8.
In ∆ ABC, AB > BC and BC > AC. Then, the smallest angle of ∆ ABC is …………………. .
A. ∠A
B. ∠C
C. ∠B
D. ∠A or ∠C
Answer:
C. ∠B

Question 9
………………….. cannot be the measures of the sides of a triangle.
A. 10, 12, 14
B. 2, 3, 4
C. 8, 9, 10
D. 2, 4, 10
Answer:
D. 2, 4, 10

Question 10.
In ∆ PQR, PQ = 4, QR = 6 and PR = 5. Then, …………….. is the angle with greatest measure in ∆ PQR.
A. ∠P
B. ∠Q
C. ∠R
D. ∠QRP
Answer:
A. ∠P

Question 11.
In ∆ XYZ, ∠X = 45° and ∠Z = 60°. Then, …………….. is the longest side of ∆ XYZ.
A. XY
B. YZ
C. XZ
D. XY or YZ
Answer:
C. XZ

Question 12.
In ∆ ABC, ∠B = 30° and BC is extended to D. If ∠ACD = 110°, then the longest side of ∆ ABC is ………………. .
A. AB
B. BC
C. CA
D. AB or AC
Answer:
B. BC

Question 13.
In ∆ ABC, AB = 4 and BC = 7, Then, ……………… holds good.
A. AC < 7
B. AC > 4
C. 4 < AC < 7
D. 3 < AC < 11
Answer:
D. 3 < AC < 11

Question 14.
In ∆ PQR, PQ = 3 and QR = 7. Then, …………….. holds good.
A. PR = 4
B. PR = 10
C. 10 > PR > 4
D. 7 > PR > 3
Answer:
C. 10 > PR > 4

Question 15.
In ∆ ABC, the bisectors of ∠B and ∠C intersect at I. If ∠A = 70°, then ∠BIC = ………………… .
A. 35°
B. 75°
C. 100°
D. 125°
Answer:
D. 125°

Punjab State Board PSEB 9th Class English Book Solutions English Grammar Narration Exercise Questions and Answers, Notes.

PSEB 9th Class English Grammar Narration

Change the following into Indirect Speech :

1. He says, “My brother likes apples.”
2. He says to me, “I do not live here.”
3. You say to Gagan, “You like English, but I like Hindi.”
4. They say to us, “We are not well today.”
5. Harpreet said, “I shall talk to you tomorrow.
6. Ram will say, “I have done my work.”
7. Mohan will say to her, “You can do this thing tonight.”
8. My sister said to me, “I will visit my friend next week.”
9. Mrs Sharma said, “I am teaching my son English.”
10. The teacher said to us, “Slow and steady wins the race.”
11. My father said, “Your friend met me yesterday.”
12. You said to Asha, “You had already done your work.”
13. My mother said, “I shall go to your school today.”
14. I said to her, “The English defeated the French in India.”
15. Mother said to me, “I shall wait for you here.”
Answer:
1. He says that his brother likes apples.
2. He tells me he does not live there.
3. You tell Gagan that he likes English, but you like Hindi.
4. They tell us that they are not well today.
5. Harpreet said that she would talk to me the next day.
6. Ram will say that he has done his work.
7. Mohan will tell her that she can do this thing tonight.
8. My sister told me that she would visit her friend the coming week.
9. Mrs. Sharma said that she was teaching her son English.
10. The teacher told us that slow and steady wins the race.
11. My father said that my friend had met him the previous day.
12. You told Asha that she had already done her work.
13. My mother said that she would go to my school that day.
14. I told her that the English defeated the French in India.
15. Mother told me that she would wait for me there.

Change the following into Indirect Speech :

1. Father said to me, “Mohan was playing while I was reading my newspaper.”
2. The man said, “I do not know what to do now.”
3. He said, “Two and two make four.”
4. “I may not come tomorrow,” said Mohan to me.
5. Her brother said, “The sun rises in the east.”
6. We said to her, “India won freedom in 1947.”
7. The teacher said to us, “I am doing register work.”
8. I said, “It has been raining since last week.”
9. The teacher said, “If you work hard, you will get a prize.”
10. The thief promised, “I will never steal again.’
Answer:
1. Father told me that Mohan was playing while he was reading his newspaper.
2. The man said that he did not know what to do then.
3. He said that two and two make four.
4. Mohan told me that he might not come the next day.
5. Her brother said that the sun rises in the east.
6. We told her that India won freedom in 1947.
7. The teacher told us that she was doing register work.
8. I said that it had been raining since the previous week.
9. The teacher said that if I worked hard, I would get a prize.
10. The thief promised that he would never steal again.

Change the following into Direct Speech :

1. She told me that she had got a good grade in the examination.
2. Ram promised that he would help me with money.
3. The player said that he was quitting cricket for good.
4. The leader asserted that his party would do anything to uplift the poor.
5. The Principal said that truth wins in the end.
6. My sister said that she could not lift that box.
7. You said that you had not heard the news.
8. They told us that they liked oranges better than bananas.
9. The poor man said that he did not know what to do.
10. The D.C. assured us that he would look into the matter.
Answer:
1. She said to me, “I have got a good grade in the examination.”
2. Ram promised, “I will help you with money.”
3. The player said, “I am quitting cricket for good.”
4. The leader asserted, “My party will do anything to uplift the poor.”
5. The Principal said, “Truth wins in the end.”
6. My sister said, “I cannot lift this box.”
7. You said, “I have not heard the news.”
8. They said to us, “We like oranges better than bananas.”
9. The poor man said, “I do not know what to do.”
10. The D.C. said to us, “I will look into the matter.’

Correct the errors in the following sentences :

1. The man asked me what I want.
2. I told to her that Mohan had eaten his lunch.
3. She was telling that she would not eat rice.
4. Ram suggested that let us go for a picnic.
5. The teacher said that two and two made four.
6. My sister asked when I have arrived.
7. I told her to wait until Mohan comes back.
8. He told me that the earth moved around the sun.
9. She said that she lives in Ludhiana.
10. I said that she looks very ugly in this dress.
Answer:
1. The man asked me what I wanted.
2. I told her that Mohan had eaten his lunch.
3. She was saying that she would not eat rice.
4. Ram suggested that we should go for a picnic.
5. The teacher said that two and two make four.
6. My sister asked when I had arrived.
7. I told her to wait until Mohan came back.
8. He told me that the earth moves around the sun.
9. She said that she lived in Ludhiana.
10. I said that she looked very ugly in that dress.

Fill the empty bubbles in Column C with what was said in Column A as shown in the example :

Answers
1. She ordered him to go away.
2. She regretted that she had been so rude to Meena.
3. She warned you not to touch that wire.
4. She persuaded you to go ahead, saying that you could do well in the competition.
5. She refused to go to the picnic.

Change the following into Indirect Speech :

1. He said to the teacher, “Please do not mark me absent.”
2. I said to the driver, “Drive as fast as you can.”
3. The teacher said to the students, “Imitate my pronunciation if you want to speak well.”
4. The doctor said to me, “Take a cold shower before breakfast if you want to keep fit.”
5. She said to me, “Kindly excuse me for coming late this time.”
6. Mother said to me, “Never cheat in the examination.”
7. Ram said to his friends, “Never tell a lie.”
8. The servant said to the master, “Pardon me this time, please.”
9. She said to her mother, “Let me join IAF.”
10. He said to me, “Let Tinkle try ever so hard, she will not reach the goal.”
Answer:
1. He requested the teacher not to mark him absent.
2. I asked the driver to drive as fast as he could.
3. The teacher advised the students to imitate his pronunciation if they wanted to speak well.
4. The doctor advised me to take a cold shower before breakfast if I wanted to keep fit.
5. She requested me to excuse her for coming late that time.
6. Mother advised me never to cheat in the examination.
7. Ram advised his friends never to tell a lie.
8. The servant requested his master to pardon him that time.
9. She asked her mother to let her join IAF.
10. He told me that Tinkle would not reach the goal however hard she tried.

Read the following dialogue and report it by filling up the blanks in the paragraph that follows :

Ram : I have invited three friends to dinner today.
Mohan : It is a very good thing.
Ram : The guests will come at 7 p.m.
Mohan : Then we will have to buy everything before going to office.
Ram : Let’s go to the supermarket to buy the things required.

Ram told Mohan that (a) …………
Mohan replied that (b) ……………..
Ram said further that the guests (c) …….
Mohan replied that then they would (d) …………..
Ram suggested that they should (e) ………..
Answer:
(a) he had invited three friends to dinner that day.
(b) it was a very good thing.
(c) would come at 7 p.m.
(d) have to buy everything before going to office.
(e) go to the supermarket to buy the things required.”

Read the following dialogue and report it by filling up the blanks in the paragraph that follows:

Wife : Our servant has run away.
Husband : Is anything missing?
Wife : Yes, my gold watch.
Husband : Where did you keep it ?
Wife : On the dressing table, as usual.
Husband : I am going to the police to report.

The wife told her husband that (a) ………. The husband asked the wife (b) ………. The wife told him that (c) ……… The husband then asked her where she (d) ……….. She replied that (e) ……… The husband told her that (f) ……….
Answer:
(a) their servant had run away.
(b) if there was anything missing.
(c) her gold watch was missing.
(d) had kept it.
(e) she had kept it on the dressing table as usual.
(f) he was going to the police to report.

Given below, you can see a picture. Complete the following paragraph reporting what happened in the picture :

A customer went to a shopkeeper and (a) ……………………. The shopkeeper took out one and told him (b) …………………. . The customer told him (c) ………….. as it was costly. The shopkeeper told him ,(d) ………..
Answer:
(a) asked him to show him a quality hanger
(b) to look at it. It would cost him five rupees
(c) to show him a cheaper one
(d) to take that nail instead.

Change the Narration :

1. Ram told me that the window went to the hospital because it had panes in its sides.
2. My brother said, “The traffic policeman is the strongest man because he can stop a speeding truck with one hand.”
3. She told me that SMILES is the longest word in English because there is a mile between the first S and the last S.
4. The teacher said, “An island and the letter t are alike because they are both in the middle of WATER.”
5. She said, “A bald man has no use of keys because he has lost his locks.”
Answer:
1. Ram said to me, “The window goes to the hospital because it has panes in its sides.”
2. My brother said that the traffic policeman is the strongest man because he can stop a speeding truck with one hand.
3. She said to me, “SMILES is the longest word in English because there is a mile between the first S and the last S.”
4. The teacher said that an island and the letter t are alike because they are both in the middle of WATER.
5. She said that a bald man has no use of keys because he has lost his locks.

Change the Narration :

1. The teacher told me to do up my buttons.
2. She informed us that the film had already started.
3. The teacher said, “The earth pulls everything towards it.”
4. “Shoot the prisoner,” said the chief to his men.
5. Maya said, “India became a Republic on 26th January.”
6. The doctor advised him to remain away from hurry, worry and curry.
7. He requested me to let him use my scooter.
8. My sister said, “I cannot lift this box.”
9. I told my father that I was too young to marry.
10. The police informed us that they had arrested the thief.
Answer:
1. The teacher said to me, “Do up your buttons.”
2. She said to us, “The film has already started.”
3. The teacher said that the earth pulls everything towards it.
4. The chief ordered his men to shoot the prisoner.
5. Maya said that India became a Republic on 26th January.
6. The doctor said to him, “Remain away from hurry, worry and curry.”
7. He said to me, “Let me use your scooter, please.”
8. My sister said that she could not lift that box.
9. I said to my father, “I am too young to marry.”
10. The police said to us, “We have arrested the thief.”.

Change the following sentences into the Indirect form of speech :

1. I said to him, “Will you return tomorrow?”
2. She said to me, “Will you come to the party ?”
3. She said to the fox, “Are the grapes sour ?”
4. He said to me, “Do you like sweets ?”
5. I said to him, “Do you like apples ?”
6. He said to me, “Do you like apples ?”
7. I said to him, “Should I depend on you for help ?”
8. Rama said to Sohani, “Are you angry with me?”
9. Ritu said to Gurvir, “Are you happy with my performance ?”
10. I said to him, “Did you like my new suit ?”
Answer:
1. I asked him if he would return the next day.
2. She asked me if I would come to the party.
3. She asked the fox if the grapes were sour.
4. He asked me if I liked sweets.
5. I asked him if he liked apples.
6. He asked me if I liked apples.
7. I asked him if I should depend on him for help.
8. Rama asked Sohani if she was angry with her.
9. Ritu asked Gurvir if he was happy with her performance.
10. I asked him if he had liked my new suit.

Change the Narration :

1. He said, “May you live long !”
2. He said, “Alas ! I have failed.”
3. He said, “Would that I were rich !”
4. He said, “Goodbye ! My friends !”
5. He said, “O for a glass of water !”
6. The captain said, “Bravo ! A good shot.”
7. He said, “Alas ! I have been ruined.”
8. The old man said, “May God bless you !”
9. “May you prosper in life !” said my mother to me.
10. “Pooh ! Go to hell,” said the old lady to her son.
Answer:
1. He prayed for my long life.
2. He exclaimed with sorrow that he had failed.
3. He wished that he had been rich.
4. He bade goodbye to his friends.
5. He longed for a glass of water.
6. The captain applauded him, saying that it was a good shot.
7. He exclaimed with sorrow that he had been ruined.
8. The old man prayed that God would bless him.
9. My mother prayed for my prosperity in life.
10. The old lady cursed her son, saying that he would go to hell.

Change the Narration :

1. The traveller said, “Can you tell me the way to the nearest inn ?” “Yes,” said the peasant. “Do you want one in which you can spend the night ?” “No,” replied the traveller, “I only want a meal.”
2. He said to me, “Hello, is it you ? Come in, take a seat. I have heard of your distress. But why do you look so forlorn? I shall do all I can to help you.”
Answer:
1. The traveller asked the peasant if he could tell him the way to the nearest inn. The peasant replied in the affirmative. He asked the traveller if he wanted one in which he could spend the night. The traveller replied in the negative. He said that he only wanted a meal.

2. He asked me if it was I and then asked me to come in and take a seat. He told me that he had heard of my distress. He asked me why I looked so forlorn. He assured me that he would do all he could to help me.

Read the following dialogue :

Raghav : I think one of my snakes has escaped.
Sheela : Isn’t it dangerous ? You really must stop collecting snakes, Raghav.
Raghav : But I like snakes – they are unusual pets.
Sheela : But I think it’s a dangerous thing to keep such pets.
Raghav : No, they’re not, they are really….er – quite friendly.
Sheela : Huh ! Snakes require a great deal of careful handling and are still a risk.
Raghav : I don’t mind. What matters is that I like them.
Sheela : Well, quite frankly, I hate them. They are awfully frightening to look at.
Raghav : Look, I am very careful and I handle them very gently. In fact, I don’t have many.
Sheela : Have you ever been bitten ?
Raghav : Well, its true. I’ve been bitten once or twice, but —

You have overheard the conversation between Raghav and Sheela. Write to your sister, Madhu, reporting the whole account in your own words. Give the conversation an interesting, unexpected or humorous ending.

449/2 Civil Lines
Ludhiana
26 January 20- –
Dear Madhu

As I know, you’re very interested in Raghav and his snakes. I thought I’d tell you about a conversation I’ve just heard between him and sheela.
He told her that he thought one of his snakes had escaped and, as usual, she told him to stop collecting them because they were dangerous. (Typical of sheela ! Don’t you think so ?)

she is so scared of snakes that she can’t bear even seeing one. The other day, she saw Raghav playing with a snake. Suddenly, the snake bit Raghav on his face. When sheela saw this, she gave a loud cry and fell down unconscious. She took an hour to come to herself. But then what a wonder for her to see ! The snake had died and no harm had come to Raghav. Can you tell why ? Waiting for your letter.

Your loving brother
Arun.

आरम्भिक ज्ञान की बातें

किसी व्यक्ति द्वारा कहे गये शब्दों को दो ढंगों से व्यक्त किया जा सकता है, जो कि नीचे दिए गए उदाहरणों से स्पष्ट है
1. She said to him, “You are a fool.”
2. She told him that he was a fool.

ऊपर दिए पहले वाक्य में वक्ता के वास्तविक शब्द ज्यों के त्यों दिए गए हैं।
कोई बात कहने के इस ढंग को Direct Speech या Direct Narration कहते हैं।
इसके विपरीत दूसरे वाक्य में वक्ता के शब्दों में परिवर्तन कर दिया गया है अर्थात् उसकी बात को अपने शब्दों में कहा गया है।
कोई बात कहने के इस ढंग को Indirect Speech या Indirect Narration कहते हैं।

A. Rules For Change Of Tenses

Direct Speech को Indirect Speech में बदलते समय Reported Speech की क्रिया (Verb) के tense में आगे लिखे नियमों के अनुसार परिवर्तन होता है|

Rule 1:
यदि Reporting Verb वर्तमान काल (Present Tense) या भविष्यत् काल (Future Tense) में हो, तो Reported Speech की क्रिया का Tense कभी नहीं बदला जाता।

Direct	Indirect
1. Hari says, “Mohan walks very fast.”	Hari says that Mohan walks very fast.
2. Mohan says, “Sohan plays well.”	Mohan says that Sohan plays well.
3. He says, “Renu needs money.”	He says that Renu needs money.
4. The teacher will say, “Gopal was never late.”	The teacher will say that Gopal was never late.
5. Anil will say, “Sham broke Mohan’s slate.”	Anil will say that Sham broke Mohan’s slate.

Rule 2:
यदि Reporting Verb भूत काल (Past Tense) में हो, तो Reported Speech की क्रिया को निम्नलिखित ढंग से बदला जाता है

(i) Present Indefinite Tense को Past Indefinite Tense में बदल दिया जाता है।

Direct	Indirect
1. Mohan said, “Ramesh works hard.” 2. He said, “The girl sings a song.”	Mohan said that Ramesh worked hard. He said that the girl sang a song.

(ii) Present Continuous Tense को Past Continuous Tense में बदल दिया जाता है।

Direct	Indirect
1. He said, “The teacher is teaching.” 2. Sohan said, “Ram is singing a song.”	He said that the teacher was teaching. Sohan said that Ram was singing a song.

(iii) Present Perfect Tense को Past Perfect Tense में बदल दिया जाता है।

Direct	Indirect
1. The teacher said, “Mohan has written a book.” 2. She said, “Sheela has won the race.”	The teacher said that Mohan had written a book. She said that Sheela had won the race.

(iv) Present Perfect Continuous Tense को Past Perfect Continuous Tense में बदल दिया जाता है।

Direct	Indirect
1. The mother said, “The children have been playing for two hours.” 2. Sant said, “Kishore has been living in this house since 1970.”	The mother said that the children had been playing for two hours. Sant said that Kishore had been living in that house since 1970.

(v) Past Indefinite Tense को Past Perfect Tense में बदला जाता है।

Direct	Indirect
1. Raju said, “Meena stood first in the test.” 2. They said, “The police did not arrest the thief.”	Raju said that Meena had stood first in the test. They said that the police had not arrested the thief.

(vi) Past Continuous Tense को Past Perfect Continuous Tense में बदला जाता है।

Direct	Indirect
1. Ashok said, “Manu was telling a lie.” 2. I said, “The girls were not singing.”	Ashok said that Manu had been telling a lie. I said that the girls had not been singing.

(vii) Shall / will, can तथा may को क्रमशः would, could तथा might में बदल दिया जाता है।

Direct	Indirect
1. The teacher said, “Mohan will read it.” 2. I said, “I shall be writing a letter.” 3. The old man said, “It may rain any time. 4. Sham said, “Mohan will have written a letter.” 5. They said, “She will have been washing the clothes for two hours.”	The teacher said that Mohan would read it. I said that I would be writing a letter. The old man said that it might rain any time.” Sham said that Mohan would have written a letter. They said that she would have been washing the clothes for two hours.

(viii) Must और needn’t को क्रमशः had to और did not have to में बदल दिया जाता है। यदि must और needn’t भविष्य की तरफ़ संकेत कर रहे हों, तो इन्हें क्रमशः would have to और would not have to बदल दिया जाता है।

Direct	Indirect
1. I said to my father, “I must go at once.” 2. My teacher said to me, “You needn’t go 3. I said to my host, “I must meet your son next week.” 4. I said to my host, “I needn’t meet your son next week.” 5. My father said to me, “You must obey your teachers.”	I told my father that I had to go at once. My teacher told me that I did not have to go. I told my host that I would have to meet his son next week. I told my host that I wouldn’t hats to meet his son next week. My father told me that I must obey my teachers.

Note 1. पहले वाक्य में must वर्तमान में विवशता या आवश्यकता को प्रकट करता है। इसलिए इसे ‘have to’ समझ कर had to में बदला गया है।

Note 2: तीसरे वाक्य में must भविष्य काल में विवशता को प्रकट करता है और इसे ‘shall have to’ के भाव में प्रयोग किया गया है। इसलिए इसे would have to में बदला गया है।

Note 3: पांचवें वाक्य में must का प्रयोग किसी स्थायी बात के लिए किया गया है। इसलिए इसे बदला नहीं गया है।

Change the form of Narration :

1. Geeta said, “Rakesh can swim across the river.”
2. Mohan said, “The girl is singing a song.”
3. Ravi said, “Mohinder has written a poem.”
4. Rohit said, “Rahul told a lie.”
5. Sohan said, “Mona was reading a book.”
6. Prem said, “Sheela may win the race.”
7. Prema said, “Sunita’s nose is running.”
8. Poonam said, “Sham has been running for two hours.”
9. Sumit said, “Preeti was making a noise.”
10. Sarita said, “Kavita will win a scholarship.”

Table of Rules for the Change of Verbs

Direct	Indirect
1. Present Indefinite    (sing) 2. Present Continuous   (is singing) 3. Present Perfect   (has sung) 4. Present Perfect Continuous    (has been singing) 5. Past Indefinite   (sang) 6. Past Continuous   (was singing) 7. Past Perfect    (had sung) 8. Past Perfect Continuous   (had been singing) 9. 1st form 10. Is, am, are 11. Was, were 12. Has, have 13. Do not, does not 14. Shall, will 15. Can, may	Past Indefinite (sang) Past Continuous (was singing) Past Perfect (had sung) Past Perfect Continuous (had been singing) Past Perfect (had sung) Past Perfect Continuous (had been singing) Unchanged (had sung) Unchanged  (had been singing) And form Was, were had been Had Did not Would Could, might

Exception to Rule -2

यदि Reported Speech में किसी स्थायी सत्य (universal truth) या पक्की आदत (habitual fact) का वर्णन हो, तो Reported Speech की क्रिया (Verb) का Tense नहीं बदला जाता, यद्यपि Reporting Verb भूतकाल (Past Tense) में ही क्यों न हो। इस तरह के वाक्य प्राय: Present Indefinite Tense में होते हैं।

Direct	Indirect
1. She said, “Honesty is the best policy.” 2. He said, “The sun rises in the east.” 3. The teacher said, “Unity is strength.” 4. Mohan said, “Two and two make four.” 5. Reena said, “Heavy rains bring floods.”	She said that honesty is the best policy. He said that the sun rises in the east. The teacher said that unity is strength. Mohan said that two and two make four. Reena said that heavy rains bring floods.

Change the form of Narration :

1. He said, “Man has two hands.”
2. He said, “The earth moves round the sun.”
3. The boy said, “All that glitters is not gold.”
4. Ram said, “The Hindus burn their dead.”
5. The teacher said, “God is everywhere.”
6. We said, “Work is worship.” ’
7. My granny said, “Hard work is the key to success.”
8. He said, “My mother gives alms to the poor every morning.”
9. My teacher said, “India became free on 15th August, 1947.”
10. Our science teacher said, “Light travels in a straight line.”

B. Rules For Change Of Pronouns

Rule -1 :
Reported Speech में First Person के Pronouns जैसे – I, my, me, we, our, us को | Reporting Verb के कर्ता (Subject) के अनुसार बदला जाता है।

Direct	Indirect
1. He said, “I am a teacher.” 2. She said, “I have played a match.” 3. You Said, “I did not receive the letter.” 4. Ram said, “I suffer from fever.”	He said that he was a teacher. She said that she had played a match. You said that you had not received the letter. Ram said that he suffered from fever.                      ’

Rule 2 :
Reported Speech में Second Person को Pronouns जैसे – you, your के Reporting Verb के कर्म (Object) के अनुसार
बदला जाता है।

Direct	Indirect
1. I said to him, “You are a nice boy.” 2. Ram said to me, “You cannot do it.” 3. I said to her, “You have been marked absent”. 4. Ram said to me, “You did not return the books.”	I told him that he was a nice boy. Ram told me that I could not do it. I told her that she had been marked absent. Ram told me that I had not returned the books.

Rule 3:
Reported Speech में Third Person के Pronouns जैसे – he, she, it, they और इनके विभिन्न रूप कभी नहीं बदले जाते हैं।

Direct	Indirect
1. Mohan said, “She is a good girl.” 2. I said, “He is not doing his duty.” 3. Raj said, “It is a beautiful sight.” 4. Ram said, “They have broken his leg.”	Mohan said that she was a good girl. I said that he was not doing his duty. Raj said that it was a beautiful sight. Ram said that they had broken his leg.

Change the form of Narration :

1. Sanjiv said, “He has sold his watch.”
2. Mohan said, “I have read all the stories.”
3. She said, “I know the rules of the game.”
4. He said to me, “I am waiting for you.”
5. You said to me, “You can solve all the sums.”
6. I said to him, “You have wasted your time.”
7. Sohan said, “Sheela was running a race.”
8. You said, “I am doing my work.”
9. I said to her, “You did your best for me.”
10. I said to Mohan, “It is a beautiful sight.”

C. Rules For Change Of Words Showing Nearness

जिन शब्दों से समय तथा स्थान की समीपता प्रकट हो, उनके स्थान पर ऐसे शब्दों का प्रयोग किया जाता है जिनसे समय तथा स्थान की दूरी प्रकट हो।

Direct	Indirect	Direct	Indirect       ‘
Here	There	Ago	Before
This	That	Tomorrow	The next day
These	Those	Today	That day
Now	Then	Yesterday	The previous day
Thus	So	Last night	The previous night
Hence	Thence	Last week	The previous week
Hither	Thither	The next day	The following day

Examples:

Direct	Indirect
1. He said to me, “I shall meet you tomorrow. 2. Mohan said, “I shall do it now.” 3. I said to him, “I bought this book yesterday.” 4. She said to me, “My uncle visited the Taj Mahal last year.” 5. Hari said, “Mohan would buy these oranges the next day.”	He told me that he would meet me the next day. Mohan said that he would do it then. I told him that I had bought that book the previous day. She told me that her uncle had visited the Taj Mahal the previous year. Hari said that Mohan would buy those oranges the following day.

Change the form of Narration :

1. The teacher said to the boys, “I shall finish this lesson tomorrow.”
2. You said to me, “I shall do it today.”
3. She said to me, “You cannot live here.”
4. The boy said, “I shall tell you the truth now.”
5. I said, “It may rain tomorrow.”
6. They said, “We went to the zoo yesterday.”
7. She said to her father, “I bought this pen last month.”
8. Ram said to you, “I will leave this place tomorrow.”
9. You said to Sheela, “I like these mangoes.”
10. I said to my sister, “You should go to school now.”

D. Rules For Change Of Different Types Of Sentences

Assertive Sentences:

यदि Reported Speech का वाक्य Assertive हो तो Indirect में बदलते समय निम्नलिखित परिवर्तन किये जाते हैं-
1. यदि say, says, will say, said के बाद to का प्रयोग न किया गया हो तो इन्हें ऐसे ही रहने दिया जाता है। इन्हें tell, tells, will tell अथवा told में नहीं बदला जाता है।

2.

• say to को tell में बदला जाता है।
• says to को tells में बदला जाता है।
• will say to को will tell में बदला जाता है।
• said to को told में बदला जाता है।

3. Reporting Verb के बाद लगे comma (,) तथा inverted commas (” “) को हटाकर that लगाया जाता है।

4. Reported Speech की क्रिया (Verb) को नियमों के अनुसार बदल दिया जाता है।

5. Reported Speech के Pronouns को भी नियमानुसार बदला जाना चाहिए। वाक्य के अन्त में Full stop (.) लगाया जाना चाहिए।

Direct

Indirect

1. He says, “I need money.” 2. The teacher will say, “Shashi was never late.” 3. Ram said to me, “You did not return my books.” 4. The officer said, “I am busy now.” 5. I said, “Ravi may stand first in the class.” 6. He said to the host, “I must go now.” 7. The teacher said, “Boys, I shall go with you.” 8. The teacher said, “The earth revolves round the sun.” 9. He said, “My mother gives alms to the poor every morning.” 10. You said to Sham, “You are telling a lie now.”

He says that he needs money. The teacher will say that Shashi was never late. Ram told me that I had not returned his books. The officer said that he was busy then. I said that Ravi might stand first in the class. He told the host that he had to go then. The teacher told the boys that he would go with them. The teacher said that the earth revolves round the sun. He said that his mother gives alms to the poor every morning. You told Sham that he was telling a lie then.

Interrogative Sentences

यदि Reported Speech का पहला अक्षर कोई Helping verb अथवा Question word (who, what, when, where, why, how, आदि) हो तो निम्नलिखित परिवर्तन किये जाते हैं
1.

• say या say to को ask में बदला जाता है।
• says या says to को asks में बदला जाता है।
• said या said to को asked में बदला जाता है।

2. Helping verb को Subject के बाद लगा कर वाक्य को साधारण बनाया जाता है।
3. प्रश्न-वाचक चिह्न हटा कर Full Stop (.) लगाया जाता है।
4. Reporing verb के बाद के लगे हुए comma (,) तथा inverted commas (” “) को हटा कर if अथवा whether लगाया जाता है।
5. परन्तु यदि वाक्य (who, whom, what, when, where, how, why आदि) किसी प्रश्न-वाचक शब्द से आरम्भ हो तो if नहीं लंगाया जाता है, अपितु उसी प्रश्न-वाचक शब्द को small letter से आरम्भ करके Reporting Verb के साथ जोड़ दिया जाता है।
6. Verbs तथा Pronouns को नियमों के अनुसार बदला जाता है।
7.

• Do, does को हटाकर verb की दूसरी फार्म लगाई जाती है।
• Did को हटाकर had + III form लगाई जाती है।

8. यदि Reported Speech में sir शब्द का प्रयोग किया गया हो तो, उसे हटा कर asked से पहले respectfully शब्द का प्रयोग किया जाता है।

Direct

Indirect

1. They said to me, “Are the grapes sour ?” 2. She said, “Shall I enjoy the party ?” 3. He said, “Shall I open the window ?” 4. He said to me, “Do you need money ?” 5. He said to me, “Did you know the truth ?” 6. He said to the officer, “May I use your telephone, Sir? 7. He said to her, “Where do you live ?” 8. The teacher said to the boys, “Why do you make a noise ?” 9. She said to you, “Who teaches you English ?” 10. I said to Mohan, “Will you company me to Delhi ?”

They asked me if the grapes were sour. She asked whether she would enjoy the party. He asked if he should open the window. He asked me if I needed money. He asked me if I had known the truth. He respectfully asked the officer if he might use his telephone. He asked her where she lived. The teacher asked the boys why they made a noise. She asked you who taught you English. I asked Mohan if he would accompany me to Delhi.

Exercise For Practice

Change the form of Narration :
1. I said to him, “Will you return tomorrow ?”
2. She said to the fox, “Are the grapes sour ?”
3. He said to me, “Do you like sweets ?”
4. I said to him, “Should I depend on you for help ?”
5. Rama said to Sohani, “Are you angry with me ?”
6. I said to him, “Do you like my new suit ?”
7. Ravi said to me, “Do you have a severe headache ?”
8. Neelu said to Ravi, “When can you come ?”
9. Kulwant said to Manjit, “Why ate you so happy today ?”
10. She said to the boy, “What do you want from me ?”

Imperative Sentences

जो वाक्य verb की पहली फार्म अथवा Don’t + V₁ या Never + V₁ या Please + V, से आरम्भ हों, उन्हें Imperative वाक्य कहा जाता है। ऐसे वाक्यों को Indirect में बदलते समय अग्रलिखित परिवर्तन किए जाते हैं
1. Reporting Verb अर्थात् said या said to को Reported Speech के भाव के अनुसार बदला जाता है.
(i) Please अथवा Kindly वाले वाक्यों में said या said to को requested में बदला जाता है।
(ii) उपदेश वाले वाक्यों में advised का प्रयोग किया जाता है।
(iii) आदेश वाले वाक्यों में ordered का प्रयोग किया जाता है।
(iv) जब कोई साधारण बात पूछी गई हो तो asked का प्रयोग किया जाता है।
(v) निषेधवाचक वाक्यों में forbade का प्रयोग किया जाता है।
(vi) यदि निषेधवाचक वाक्यों में asked का प्रयोग करना हो तो Don’t को not to में और never को never to में बदल देना चाहिए।

2. Comma तथा inverted commas हटा कर क्रिया से पूर्व to का प्रयोग किया जाता है और क्रिया की फार्म को नहीं बदला जाता है।
3. Pronouns को नियमों के अनुसार बदला जाता है।

Direct

Indirect

1. He said to me, “Do it.” 2. He said to me, “Don’t do it.” 3. He said to the peon, “Open the door. 4. I said to him, “Please sit down.” 5. She said to them, “Respect your elders.” 6. The teacher said to the boys, “Don’t waste your time in idle gossip.” 7. The lawyer said to the witness,“Speak as I tell you.” 8. The Commander said to his men,“Attack the enemy.” 9. The teacher said to students,“Never tell lies.” 10. The General said to the soldiers,“March quickly.”

He asked me to do it. He asked me not to do it. He ordered the peon to open the door.” I requested him to sit down. She advised them to respect their elders. The teacher advised the boys not to waste their time in idle gossip. The lawyer directed the witness to speak as he told him. The Commander commanded his men to attack the enemy. The teacher advised the students never to tell lies. The General ordered the soldiers to march quickly.

Change the form of Narration :

1. Father said to me, “Avoid bad company.”
2. The headmaster said to the peon, “Ring the bell.”
3. I said to Ganesh, “Please lend me fifty rupees.”
4. The beggar said, “Kindly give me food.”
5. The teacher said to the students, “Stop making noise.”
6. The teacher said to me, “Dare to be true.”
7. I said to my servant, “Bring me a glass of water.”
8. The mother said to her daughter, “Do not waste your time.”
9. The teacher said to the boys, “Never come late.”
10. The Principal said to the visitor, “Do not disturb me, please.”

The Use Of Let

Rule 1 :
जो वाक्य Let us से आरम्भ हों, उनमें Let किसी ‘सुझाव’ को व्यक्त करता है। ऐसे वाक्यों में said to को proposed to अथवा suggested to में बदला जाता है; और Let us के स्थान पर should लगाकर इसे साधारण वाक्य बना दिया जाता है।

Rule 2 :
Let me वाले वाक्य किसी ‘प्रार्थना’ का भाव प्रकट करते हैं। ऐसे वाक्यों में said to को told में बदला जाता है; और Let me को I may be allowed या to let में बदल दिया जाता है। ऐसे वाक्यों में said to को requested में भी बदला जा सकता है।

Rule 3:
Let him / her, आदि वाले वाक्य ‘आदेश’ को व्यक्त करते हैं। इनमें said to को ordered में बदल दिया जाता है, और let को to let में बदल दिया जाता है।’

Direct	Indirect
1. He said to his friend, “Let us dine out today.” 2. My father said to me, “Let him revise the lesson.” 3. She said to him, “Let us sit in the sun. 4. Mohan said to his friend, “Let me go home now.” 5. The headmaster said to the peon,“Let the boy come in.”	He proposed to his friend that they should dine out that day. My father ordered me to let him revise the lesson. She proposed to him that they should sit in the sun. Mohan requested his friend to let him go home then. The headmaster ordered the peon to let the boy come in.

Change the form of Narration :

1. Hari said to me, “Let us go out for a walk.”
2. He said to his friend, “Let us sit here.”
3. He said to me, “Let the child play.”
4. He said to his friends, “Let us dine out today.”
5. He said to the waterman, “Let me have a glass of water, please.”
6. The principal said to the peon, “Let the boys see these pictures.”
7. The hare said to the tortoise, “Let us run a race.”
8. I said to my brother, “Let me go to school, please.”
9. The headmaster said to the teacher, “Let the boys play a match.”
10. I said to my brother, “Let us construct a new house.”

Optative Sentences

Optative Sentences को निम्नलिखित ढंग से बदला जाता है

1. said to को wished या prayed में बदला जाता है।
2. wished अथवा prayed के तुरन्त बाद that लगाया जाता है।
3. You के स्थान पर Reporting Verb के object का प्रयोग किया जाता है अथवा You को उसके अनुसार बदल दिया जाता है।
4. May को subject के बाद ले जाकर would में बदल दिया जाता है।
5. Pronouns आदि नियमानुसार बदले जाते हैं।
6. Sign of Exclamation विस्मयबोधक चिन्ह (!) के स्थान पर Full stop (.) लगाया जाता है।

Direct	Indirect
1. She said, “May God bless you with a son !” 2. “May you succeed in life !” said the old lady to her son. 3. “Would that I were rich !” said my friend. 4. He said, “May the king live long !” 5. He said, “O, for a glass of water !”	She prayed that God would bless him with a son. The old lady prayed for her son’s success in life. My friend wished that he had been rich. He prayed that the king would live long. He longed for a glass of water.

Change the form of Narration :

1. He said, “May God be kind to you !”
2. The mother said to her son, “May you prosper in life !”
3. He said, “Would that I were rich !”
4. She said, “O, for a loaf of bread !”
5. She said, “Would that I were the princess !”
6. He said, “May God reward this act of yours !”
7. The mother said, “May you pass in the test, my son !”
8. All said together, “May God grant peace to the departed soul !”
9. They said, “May there be peace and prosperity in this land !”
10. “Would that I were a bird !” said my friend.

Exclamatory Sentences

Exclamatory sentences को indirect में बदलने के लिए निम्नलिखित नियम याद रखिए1. Reporting Verb ‘said’ को Reported Speech के भाव अनुसार बदला जाता है।

• Hurrah वाले वाक्य में said को exclaimed with joy में बदला जाता है।
• Alas वाले वाक्यों में said को exclaimed with sorrow में बदला जाता है।
• What वाले वाक्यों में said को exclaimed with surprise में बदला जाता है।
• What a को a very में बदला जाता है।
• Bravo वाले वाक्यों में said to को applauded……… saying में बदला जाता है।

2. Comma तथा inverted commas को हटाकर that लगाया जाता है।
3. वाक्य में Hurrah, Alas आदि शब्द समाप्त कर दिए जाते हैं।
4. Verbs तथा Pronouns नियमानुसार बदले जाते हैं।
5. Exclamatory Sentences को Assertive Sentences में, अर्थात् एक साधारण वाक्य में बदल दिया जाता
6. Sign of Exclamation (!) को हटाकर Full Stop (.) लगा दिया जाता है।

Direct	Indirect
1. The boys said, “Hurrah ! We have won the match.”	The boys exclaimed with joy that they Rad won the match.
2. He said, “Alas ! I have failed.”	He exclaimed with sorrow that he had failed.
3. Prem said, “Alas ! How foolish I have been !”	Prem exclaimed with regret that he had been very foolish.
4. The General said to the jawans, “Splendid ! You have won the war.	The General applauded the jawans saying that they had won the war.
5. Ram said, “What a beautiful flower !”	Ram exclaimed with wonder that it was a very beautiful flower.
6. The captain said, “Bravo ! A good shot.”	The captain applauded him saying that it was a good shot.
7. I said, “Welcome, stranger, share what I have !”	I welcomed the stranger and invited him to share what I had.
8. He said, “Hurrah ! My brother has won a scholarship.”	He exclaimed with joy that his brother had won a scholarship.
9. She said, “Alas ! My husband is dead.”	She exclaimed with sorrow that her husband was dead.
10. Neha said, “What a beautiful sight it is !”	Neha exclaimed with wonder that it was a very beautiful sight.

Change the form of Narration :

1. The old man said, “Alas ! My only son is dead. ”
2. He said, “What a beautiful sight !”
3. Mohan said, “Hurrah ! We have won the match.”
4. The old man said, “How weak I have become !”
5. Sohan said, “What a dark night !”
6. The players said, “Hurrah ! We have scored four goals.”
7. Ram said, “Alas ! I have lost my all.”
8. The captain said, “Bravo ! You have done very well.”
9. He said, “Hurrah ! I will join my parents again after five years.”
10. My friend said, “Alas ! My cousin has lost his mother.”

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3

Question 1.
∆ ABC and ∆ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at D show that,

(i) ∆ ABD ≅ ∆ ACD
(ii) ∆ ABP ≅ ∆ ACP
(iii) AP bisects ∠ A as well as ∠ D.
(iv) AP is the perpendicular bisector of BC.
Answer:
∆ ABC and ∆ DBC are isosceles triangles on the same base BC.
∴ In ∆ ABC, AB = AC and in ∆ DBC, DB = DC.
In ∆ ABD and ∆ ACD,
AB = AC
DB = DC
and AD = AD (Common)
∴ ∆ ABD s ∆ ACD (SSS rule) [Result (i)]
∴ ∠ BAD = ∠ CAD (CPCT)
In ∆ ABP and ∆ ACP
AB = AC
∠ BAP = ∠ CAP (∵ ∠ BAD = ∠ CAD)
and AP = AP (Common)
∴ ∆ ABP ≅ ∆ ACP (SAS rule) [Result (ii)]
∴ BP = CP (CPCT)
In ∆ DBP and ∆ DCR
DB = DC
BP = CP
and DP = DP (Common)
∴ ∆ DBP ≅ ∆ DCP (SSS rule)
From ∆ ABP ≅ ∆ ACR ∠ BAP = ∠ CAP (CPCT)
∴ AP bisects ∠A.
From ∆ DBP ≅ ∆ DCR ∠BDP = ∠ CDP (CPCT)
∴ DP bisects ∠D.
Thus, AP bisects ∠A as well as ∠D. [Result (iii)]
∆ A ABP ≅ ∆ ACP
∴ BP = CP and ∠ APB = ∠ APC (CPCT)
But, ∠ APB + ∠ APC = 180° (Linear pair)
∴ ∠ APB = ∠ APC = \(\) = 90°
Thus, BP = CP and AP ⊥ BC.
∴ AP is the perpendicular bisector of BC. [Result (iv)]

Question 2.
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that:
(i) AD bisects BC
(ii) AD bisects ∠ A

Answer:
AD is an altitude of A ABC.
∴ ∠ ADB = ∠ ADC = 90°
In ∆ ADB and ∆ ADC,
hypotenuse AB = hypotenuse AC (Given)
∠ ADB = ∠ ADC (Right angles)
AD = AD (Common)
∴ ∆ ADB ≅ ∆ ADC (RHS rule)
∴ BD = CD and ∠ BAD = ∠ CAD (CPCT)
Now, BD = CD means D is the midpoint of BC.
Hence, AD bisects BC. [Result (i)]
Moreover, ∠ BAD = ∠ CAD and
∠ BAD + ∠ CAD = ∠ BAC.
Hence, AD bisects ∠A. [Result (ii)]

Question 3.
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see the given figure). Show that:
(i) ∆ ABM ≅ ∆ PQN
(ii) ∆ ABC ≅ ∆ PQR

Answer:
In ∆ ABC, AM is a median.
∴ BM = CM = \(\frac{1}{2}\) BC
In ∆ PQR, PN is a median.
∴ QN = RN = \(\frac{1}{2}\) QR
Now, BC = QR (Given)
∴ \(\frac{1}{2}\) BC = \(\frac{1}{2}\) QR
∴ BM = QN
In ∆ ABM and ∆ PQN,
AB = PQ (Given)
AM = PN (Given)
BM = QN (Proved)
∴ ∆ ABM ≅ ∆ PQN (SSS rule) [Result (i)]
∴ ∠ ABM = ∠ PQN (CPCT)
∴ ∠ ABC = ∠ PQR
Now, in ∆ ABC and ∆ PQR,
AB = PQ
∠ ABC = ∠ PQR
BC = QR .
∴ ∆ ABC ≅ ∆ PQR (SAS rule) [Result (ii)]

Question 4.
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Answer:
In ∆ FBC and ∆ ECB,
CF = BE (Given)
∠ CFB = ∠ BEC = 90° (Given)
BC = CB (Common)
∴ A FBC ≅ A ECB (RHS rule)
∴ ∠ FBC = ∠ ECB (CPCT)
∴ ∠ ABC = ∠ ACB
Now, in ∆ ABC, ∠ ABC = ∠ ACB
∴ AC = AB (Theorem 7.3)
Hence, ∆ ABC is an isosceles triangle.

Question 5.
ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠ B = ∠ C.
Answer:

In ∆ ABC, AP is an altitude.
∴ ∠ APB = ∠ APC = 90°
In ∆ APB and ∆ APC,
∠ APB = ∠ APC = 90°
AB = AC (Given)
AP = AP (Common)
∴ ∆ APB ≅ ∆ APC (RHS rule)
∴ ∠ ABP = ∠ AGP (CPCT)
∴ ∠ ABC = ∠ ACB
Thus, in ∆ ABC, ∠ B = ∠ C.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.2

Question 1.
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that:
(i) OB = OC
(ii) AO bisects ∠ A
Answer:

In ∆ ABC, AB = AC
∴ ∠ ABC = ∠ ACB (Theorem 7.2)
∴ \(\frac{1}{2}\) ∠ ABC = \(\frac{1}{2}\) ∠ ACB
∴ ∠ OBC = ∠ OCB (BO bisects ∠ ABC and CO bisects ∠ ACB)
Now, in ∆ OBC, ∠ OBC = ∠ OCB
∴ OB = OC (Theorem 7.3)
Similarly, ∠ ABC = ∠ ACB gives
∴ \(\frac{1}{2}\) ∠ ABC = \(\frac{1}{2}\) ∠ ACB
∴ ∠ ABO = ∠ ACO
Now, in ∆ ABO and ∆ ACO,
AB = AC (Given)
∠ ABO = ∠ ACO
and OB = OC
∴ ∆ ABO ≅ ∆ ACO (SAS rule)
∴ ∠ BAO = ∠ CAO (CPCT)
But, ∠ BAO + ∠ CAO = ∠ BAC (Adjacent angles)
∴ ∠ BAO = ∠ CAO = \(\frac{1}{2}\) ∠ BAC
Thus, AO bisects ∠ A.

Question 2.
In ∆ ABC, AD is the perpendicular bisector of BC (see the given figure). Show that ∆ ABC is an isosceles triangle in which AB = AC.

Answer:
In ∆ ABC, AD is the perpendicular bisector of BC.
∴ BD = CD and ∠ ADB = ∠ ADC = 90°
In ∆ ADB and ∆ ADC,
AD = AD (Common)
∠ ADB = ∠ ADC (Right angles)
and BD = CD
∴ ∆ ADB ≅ ∆ ADC (SAS rule)
∴ AB = AC (CPCT)
Now, in ∆ ABC, AB = AC.
Hence, ∆ ABC is an isosceles triangle in which AB = AC.

Question 3.
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

Answer:
In ∆ ABC, AC = AB
∴ ∠ ABC = ∠ ACB
∴ ∠ FBC = ∠ ECB
Now, in ∆ FBC and ∆ ECB,
∠ FBC = ∠ ECB
∠ BFC = ∠ CEB (Right angles)
BC = CB (Common)
∴ ∆ FBC ≅ ∆ ECB (AAS rule)
∴ CF = BE (CPCT)
Thus, the altitudes CF and BE on equal sides AB and AC respectively of ∆ ABC are equal.

Question 4.
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
(i) ∆ ABE ≅ ∆ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.

Answer:
In ∆ ABE and ∆ ACF,
∠ AEB = ∠ AFC (Right angles)
∠ A = ∠ A (Common)
BE = CF (Given)
∴ ∆ ABE ≅ ∆ ACF (AAS rule)
∴ AB = AC (CPCT)
Thus, ∆ ABC is an isosceles triangle.

Question 5.
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ ABD = ∠ ACD.

Answer:
∠ ABC and ∠ DBC are adjacent angles.
∴ ∠ ABC + ∠ DBC = ∠ ABD ………… (1)
∠ ACB and ∠ DCB are adjacent angles.
∴ ∠ ACB + ∠ DCB = ∠ ACD ………….. (2)
In ∆ ABC, AB = AC.
∴ ∠ ABC = ∠ ACB (Theorem 7.2)
In ∆ DBC, DB = DC.
∴ ∠ DBC = ∠ DCB (Theorem 7.2)
∴ ∠ ABC + ∠ DBC = ∠ ACB + ∠ DCB
∴ ∠ ABD = ∠ ACD [From (1) and (2))

Question 6.
∆ ABC is an isosceles triangle in which AB = AC. side BA is produced to D such that AD = AB (see the given figure). Show that ∠ BCD is a right angle.

Answer:
AB = AC and AD = AB
∴ AC = AD
In ∆ ABC, AB = AC
∴ ∠ ACB = ∠ ABC (Theorem 7.2) ……………… (1)
In A ADC, AC = AD
∴ ∠ ACD = ∠ ADC (Theorem 7.2) ……………… (2)
Adding (1) and (2),
∠ ACB + ∠ ACD = ∠ ABC + ∠ ADC
∴ ∠ BCD = ∠ DBC + ∠ BDC
(Adjacent angles and A lies on BD)
In ∆ BCD,
∠ DBC + ∠ BDC + ∠ BCD = 180°
∴ ∠ BCD + ∠ BCD = 180° (from (3)]
∴ 2 ∠ BCD = 180°
∴ ∠ BCD = 90°
Thus, ∠ BCD is a right angle.

Question 7.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠ B and ∠ C.
Answer:

In ∆ ABC, AB = AC
∴ Z C = Z B (Theorem 7.2)
In ∆ ABC,
∠ A + ∠ B + ∠ C = 180°
∴ 90° + ∠ B + ∠ B = 180° (Given and ∠ C = ∠ B)
∴ 2 ∠ B = 90°
∴ ∠ B = 45°
∴ ∠ C = 45°

Question 8.
Show that the angles of an equilateral triangle are 60° each.
Answer:

∆ ABC is an equilateral triangle.
∴ AB = BC = AC
In ∆ ABC, AB = BC
∴ ∠ C = ∠ A (Theorem 7.2)
In ∆ ABC, AB = AC
∴ ∠ C = ∠ B (Theorem 7.2)
Hence, ∠ A = ∠B = ∠ C.
Now, in ∆ ABC, ∠ A + ∠ B + Z C = 180°
∴ ∠ A = ∠ B = ∠ C = \(\frac{180^{\circ}}{3}\) = 60°
Thus, the angles of ah equilateral triangle are 60° each.

Punjab State Board PSEB 9th Class English Book Solutions English Grammar Voice Exercise Questions and Answers, Notes.

PSEB 9th Class English Grammar Voice

Change the voice in the following sentences :

1. Sita writes a letter.
2. He killed the lion.
3. They will help you.
4. He was eating an orange.
5. The nurse is looking after the patient.
6. I have completed my work.
7. I had learnt my lesson.
8. His enemies have defeated him.
Answer:
1. A letter is written by Sita.
2. The lion was killed by him.
3. You will be helped by them.
4. An orange was being eaten by him.
5. The patient is being looked after by the nurse.
6. My work has been completed (by me).
7. My lesson had been learnt (by me).
8. He has been defeated by his enemies.

Complete the passage with either the active or passive forms of the verbs given in the box :

block, press, blow, cause, live, sweep, cut, rescue.

Damage worth millions of rupees (a) ……………… by a storm which (b) ……………. across coastal areas of Orissa. The army (c) …………… into service. Many people (d) ……………… from the floods by the army. Winds ………….. (e) at the speed of about 150 kms. an hour in some places. Roads (f) …………… by fallen trees. Electricity lines (g) ……….. and people had to (h) …………. without electricity for several hours.
Answer:
(a) was caused
(b) swept
(c) was pressed
(d) were rescued
(e) were blowing
(f) were blocked
(g) were cut
(h) live.

Change the voice of the following passage :

Raju killed a snake with a stick. He threw it into a pond nearby. He played cricket for some time. Then he plucked some flowers to make garlands. He put the garland on Lord Krishna’s statue.
Answer:
A snake was killed with a stick by Raju. It was thrown by him into a pond nearby. Cricket was played by him for some time. Then some flowers were plucked by him to make garlands. The garland was put on Lord Krishna’s statue by him.

Look at some newspaper headlines given below. Then use the information in the headlines to complete the sentences that follow (select the proper form of the verb to be used) :

(a) Three Passengers Crushed
………………. to death when they fell from the rooftop of a bus.

(b) Fifty Huts Destroyed In Fire
A fire broke out in a resettlement colony in which ………….

(c) Leopard Beaten To Death
The police report that a …………… by villagers when it tried to attack them.

(d) Suspect Arrested
London police report that a suspect involved in the Bomb Blast Case …..

(e) Two Stabbed
It is learnt that …………………….. in two separate incidents yesterday.

(f) Indians To Pay More For Pak Citizenship.
Indians applying for Pakistani citizenship will ……………
Answer:
(a) Three passengers were crushed
(b) fifty huts were destroyed.
(c) leopard was beaten to death
(d) has been arrested.
(e) two men were stabbed
(f) have to pay more.

The passive voice can be used in several tenses. Complete the following table, filling up the blanks with suitable form of the verbs :

Tenses Subject	Verb ‘to be’	Past participle
1. (Future Indefinite)	Lunch	…………..  taken at 1 p.m here.
2. (Past Continuous)	The house	…………..  built.
3. (Present Perfect)	The lost purse	…………..  found.
4. (Past Simple)	The culprit	……….. produced in the court.
5. (Past Continuous)	The door	……….. repaired
6. (Past Perfect)	A suitable action	………… taken
7. (Past Indefinite)	My proposal	……… accepted
8. (Past Perfect)	Letters	………. posted

Answer:
1. will be
2. was being
3. has been
4. was
5. was being
6. had been
7. was
8. had been.

Complete the following sentences, using the correct form of the verb in the brackets :

1. This historical monument ………… (build) thousands of years ago.
2. The money …………… (steal) by Mr. Gupta’s servant yesterday.
3. The largest 9-way flyover ………….. (construct) last month in Delhi.
4. Seema’s marriage outfit …………. (design) by the famous designer Ritu Beri. (Present Perfect)
5. A letter ………….. (receive) by Mohan 10 days after it ………….. (post).
Answer:
1. was built
2. was stolen
3. was constructed
4. has been designed
5. was received, had been posted.

In the sentences given below, change the verb into passive form:

1. Robbers raided the bank.
2. The terrorists injured ten people.
3. They took away all the cash.
4. They also shot the security guards.
5. The police have arrested the thieves.
Answer:
1. The bank was raided by robbers.
2. Ten people were injured by the terrorists.
3. All the cash was taken away by them.
4. The security guards were also shot by them.
5. The thieves have been arrested by the police.

Using the outline given in the box, fill in the blanks in the passage below :

New school on the outskirts of Delhi. Is located in Tijara (90 km drive from Delhi). The brain child of legal expert, Vidya Sagar. Uniform syllabus. Yearly boarding and tuition expenses believed to be around 1.25 lacs.

There is a new school (a) …………………….. of Delhi. It (b) …………. in Tijara, 90 kms. from Delhi. It is the brainchild of legal expert Vidya Sagar. (c) ………….. introduced in this school. It (d) …………. that yearly boarding and tuition expenses would be around 1.25 lacs.
Answer:
(a) on the outskirts
(b) is located
(c) Uniform syllabus is
(d) is believed.

Read the following set of instructions and fill in the blanks :

How To Make Tea
(i) Take a kettle.
(ii) Put half a cup of water in it.
(iii) Put it on the gas stove.
(iv) Switch on the stove.
(v) When the water begins to boil, add a teaspoonful of tea-leaves
(vi) Add half a cup of milk and some sugar to it.
(vii) Switch off the stove when the mixture starts boiling.
(viii) Pour the mixture into a cup through a sieve (sifter).

A kettle was taken. Half a cup of water (a) …………. in it. It (b) ………… on the gas stove. The stove (c) ………… When the water began to boil, a teaspoonful of tea leaves (d) ………….. to it. Half a cup of milk and some sugar (e) ………….. to the mixture. The stove (f) ……… when the mixture started boiling. It was (g) ………… a cup through a sieve.
Answer:
(a) was put
(b) was put
(c) was switched on
(d) was added
(e) were added
(f) was switched off
(g) poured into.

Complete the passage with either the active or passive form of the verbs given in the box :

hit , admit, arrest, registed.

A Ludhiana BJP leader, Radhey Shyam (a) ………. by a truck near Patna bus depot last night. Radhey Shyam (b) ……… to a hospital in the city. The truck driver Hari Singh (c) ……… by the police. A case of causing death due to rash and negligent driving (d) ………… against him.
Answer:
(a) was hit
(b) was admitted
(c) was arrested
(d) was registered.

Change the Voice in the following passage :

A truck hit a bus yesterday. The carelessness of the driver caused the accident. The local people took the injured passengers to hospital. The police have arrested the driver.
Answer:
A bus was hit by a truck yesterday. The accident was caused by the carelessness of the driver. The injured passengers were taken to hospital by the local people. The driver has been arrested by the police.

Change the Voice in the following passage :

We saw a magic show yesterday. The magician showed a number of wonderful tricks. First, he took off his hat and put it on the table. He covered the hat with a piece of cloth. Then he moved a stick over the hat. He then took the cloth off. Out of the hat, he pulled out three chickens.
Answer:
A magic show was seen by us yesterday. A number of wonderful tricks were shown by the magician. First his hat was taken off by him and was put on the table. The hat was covered by him with a piece of cloth. Then a stick was moved by him over the hat. The cloth was then taken off by him. Out of the hat three chickens were pulled out by him.

Complete the passage with the Passive form of the verbs given in the box :

dig select prepare lower cover sprinkle

First, a plant (a) ………… Then a hole (b) ……….. where the plant was to be placed into the soil. The soil (c) ……….. by mixing manure in it. The plant (d) ………. into the hole carefully. The roots were (e) ……….. with the prepared soil. Some, water (f) ……… on the plant.
Answer:
(a) was selected
(b) was dug
(c) was prepared
(d) was lowered
(e) covered
(f) was sprinkled.

Complete the following passage, using the verbs in brackets in the Passive voice :

At least four crore worth of imported newsprint (a) ………. (destroy) in yesterday’s fire in one of the godowns outside Cochin port. The fire which broke out in the afternoon (b) ………. (bring) under control only this morning. Firefighting operations (c) ………. (hamper) by the delay and difficulty in removing the huge newsprint rolls from outside the godown. The godown (d) ………. (hire) for the Hindustan Newsprint by a private ‘dearing and forwarding’ agent. The port operations (e) ………. (affect) due to the incident.
Answer:
(a) was destroyed
(b) could be brought
(c) were hampered
(d) had been hired
(e) were affected.

Read the following set of instructions for the servicing of an air conditioner and complete the paragraph that follows, using passive form of the verbs used :

(i) Dismantle the air conditioner.
(ii) Take out the main machine from inside the box.
(iii) Blow off the entire dust from the body with the help of a vacuum cleaner.
(iv) Wash the body with a spray of water from a pipe.
(v) Let it dry in the sun for about an hour.
(vi) Fix it back into place.

The air conditioner is (a) ………. The main machine is (b) ………. out from inside the box. The entire dust from the body (c) ………. with the help of a vacuum cleaner. The body (d) ……………. with a spray of water from a pipe. It (e) ………. then (f) ………. in the sun for about an hour. It is now (g) ………. back into place.
Answer:
(a) dismantled
(b) taken
(c) is blown off
(d) is washed
(e) should
(f) be dried
(g) fixed.

Change the Voice in the following passage :

Sita is singing a song. She sings film songs as well as folk songs. All like her. She helps the poor with the money she earns. God will certainly bless her. The country needs such artists.
Answers
A song is being sung by Sita. Film songs as well as folk songs are sung by her. She is liked by all. The poor are helped by her with the money earned by her. She will certainly be blessed by God. Such artists are needed by the country.

Change the Voice in the following sentences :

1. The gardener is plucking flowers.
2. The boys are flying kites.
3. He is laughing at the beggar.
4. The peon was ringing the bell.
5. The watchman had already opened the gate.
Answers
1. Flowers are being plucked by the gardener.
2. Kites are being flown by the boys.
3. The beggar is being laughed at by him.
4. The bell was being rung by the peon.
5. The gate had already been opened by the watchman.

Rewrite the following sentences in the notice format, using the Passive Voice : (see example 1)

1. We do not allow cameras inside.
2. We do not allow children below 12 in this show.
3. We book seats here.
4. We require a shop assistant immediately.
5. We do not allow vehicles inside the campus.
Answers
1. Cameras are not allowed inside.
2. Children below 12 are not allowed in this show.
3. Seats are booked here.
4. A shop assistant is required immediately.
5. Vehicles are not allowed inside the campus.

Complete the passage with the Passive form of the verbs given in the brackets :

A three year old girl (a) ……….(rescue) by the police last Tuesday. She (b) ………… (kidnap) by a neighbour for ransom. The mother informed the police about the missing girl. The probe (c) ……… (supervise) by the DSP himself. More than 50 residents (d) ……… (interrogate). Ultimately, Danny, one of the residents of the colony, admitted the crime and disclosed where the girl (e) ………… (hide).
Answer:
(a) was rescued
(b) had been kidnapped
(c) was supervised
(d) were interrogated
(e) was hidden.

Read the newspaper headlines given below and complete the sentences that follow :

1. Rain Kills Over Two Dozen
Kathmandu : About ……….. in the remote villages of north-western
Kalikot district in the rains that hit the area.

2. Largest Discovery Of Dinosaur Eggs
Lerida : More than 100 eggs of dinosaur ………………….. in north-eastern Spain.

3. Pak Defeated By A Big Margin
The Pakistani cricket team ……………….. in the first one dayer by a big margin yesterday. The match ……………. at Lahore in the Gaddafi Stadium.

4. Obama Accorded Warm Welcome
President Barack Obama of USA ……… a warm welcome on his arrival in India this year. He ……. by the Prime Minister himself at the Delhi airport.

5. Underground Tunnel Unearthed
A half-dug underground tunnel ………. by the police personnel inside the jail compound yesterday. The digging ………… by two convicts undergoing life terms in the jail.

6. Cold Wave Claims 37 Lives
The cold wave prevailing in the Punjab for more than a week has worsened further. There ……. a fresh snowfall in the Himalayas. Meanwhile 37 lives ……… so far by the cold wave.

7. Rich Homage Paid To Mahatma Gandhi ; Statue Unveiled
Rich homage to the great Father of the Nation, Mahatma Gandhi,
on the occasion of his birth anniversary, yesterday. A bronze statue of the great visionary on the occasion.

8. D.J. Simpson Acquitted
In the judgement given today by an American court, the famous football legend D.J. Simpson ………. of murder charges against him.

9. Idols Immersed In River
The ten-day Dussehra festival comes to an end today when all the idols carried in a procession ……….. in the Ganga by the devotees.

10. Three Militants Killed, Seven Arrested
During the past 24 hours, three militants ………….. and seven have been arrested in the Kashmir Valley. A large number of weapons were also seized from those arrested.

11. Afghan Forces Capture Kabul Airport
After a five-day bloody battle, the Kabul Airport ……….. by the Afghan forces early today. Dozens of people were killed and more than 2500 were injured.

12. Govt. To Take Stern Steps
It has been announced by the government that ……….. to check the black-marketing and adulteration of essential goods.

13. Fire Destroys Goods Worth ₹ 25 Lac ; Cause Unknown
Goods ……… when two houses in Tilak Nagar caught fire yesterday. The cause of fire which rendered four families homeless, could not be known.

14. 193 Kg heroin seized :
In the biggest ever drug haul in the country, a consignment of 193 kg of heroin ………. by the Mumbai police from a luxury apartment, in Central Mumbai.

15. Tourists, Attacked By Shark
Last Monday several Australian tourists while surfing off Pasiraman beach.

16. Suspect Arrested
Shahpur police report that the suspect in the Nasir Khan murder case

17. Woman, Child Killed In Road Mishap — Six Injured
A woman and ……….. on the spot and six persons were injured, two of them seriously, when a tempo in which they were travelling, fell into a khud near Lalpani.

18. Bankmen Give Free Hawai Chappals For Lepers
Lepers, living in the Asha Deep Colony of the city, ……… on Thursday by the employees of State Bank of India. The Bankmen were celebrating the 42nd anniversary of their branch.

19. Shopkeeper Arrested, Fined :
Ashok Kumar, a shopkeeper of Bilaspur …………. by the police on Tuesday for selling adulterated atta. Later he was produced before the Chief Judicial Magistrate by whom he ………….. ₹ 5000.

20. Advani Relieved Of His Post :
The BJP President, L.K. Advani, ……… of his post today after he submitted his resignation in the meeting of the general body of the party.
Answer:
1. two dozen men are killed
2. have been discovered
3. was defeated; was played
4. was accorded; was received
5. was unearthed; had been done.
6. has been ; have been claimed.
7. was paid; was unveiled
8. was acquitted
9. are immersed
10. have been killed
11. was captured
12. stem steps will be taken
13. worth 25 lac were destroyed
14. has been seized
15. were attacked by shark
16. has been arrested
17. a child were killed
18. were given free Hawai chappals
19. was arrested ; was fined
20. was relieved.

Rewrite the following passages after changing the Voice :

Question 1.
The early men thought that every misfortune was caused by angry gods. They saw imaginary gods everywhere. They thought of God as a very irritable person who was always losing his temper. If due to some disaster, a large number of people were killed, they would think they had displeased God.
Answer
It was thought by the early men that angry gods cause every misfortune. Imaginary gods were seen everywhere by them. God was thought of by them as a very irritable person who was always losing his temper. If some disaster killed a large number of people, they would think God had been displeased by them.

Question 2.
Mr. Lai teaches us English. He was awarded Padma Shri by the President. He is one of the most dedicated teachers we have. Social work interests Mr. Lai very much. He loves his students as he loves his own children. We are lucky to be his pupils. May God bless him !
Answer
We are taught English by Mr. Lai. The President awarded him Padma Shri. He is one of the most dedicated teachers we have. Mr. Lai is very much interested in social work. His students are loved by him as his own children. We are lucky to be his pupils. May he be blessed by God !

Question 3.
A dove saw a bee fallen in a water tank. It dropped a large leaf into the water. The bee climbed on to the leaf and thanked the dove. A hunter took aim at the dove. The bee stung him. He missed his aim. Now the dove thanked the bee.
Answer
A bee fallen in a water tank was seen by a dove. A large leaf was dropped into the water by it. The bee climbed on to the leaf and the dove was thanked by the bee. The dove was taken aim at by a hunter. He was stung by the bee. His aim was missed by him. Now the bee was thanked by the dove.

Question 4.
Once a jester offended the king. The king at once condemned him to death. The jester pleaded for his life but the king refused to alter the sentence. One day, the king visited the prison. He asked the jester to choose his manner of death. The clever jester at once said that he would like to die of old age.
Answer
Once the king was offended by a jester. He was at once condemned to death by the king. The jester pleaded for his life but the king refused to alter the sentence. One day, the prison was visited by the king. The jester was asked to choose his manner of death by the king. It was at once said by the clever jester that he would like to die of old age.

Question 5.
I explained my case to the doctor. I was seated on a chair against the table by him. I held my hat in my right hand and explained my symptoms. He then gave his advice and helped me liberally.
Answer
My case was explained by me to the doctor. He seated me on a chair against the table. My hat was held in my right hand and my symptoms were explained. His advice was then given and I was helped liberally.

Question 6.
The emperor was adorned in his royal robes. He was attended by his courtiers. He was escorted to the seashore. There he was seated upon a high chair. The chair had been placed there for his reception.
Answer:
The emperor adorned himself in royal robes. His courtiers attended him. They escorted him to the seashore. There they seated him upon a high chair. They had placed the chair there for his reception.

Question 7.
If we look into practical life, we will find that fortune is usually on the side of the industrious. The winds and waves favour the best navigators. Lord Clive began his career in India as a clerk. When he ended his career, he had founded the British Empire in the East.
Answer
If practical life is looked into by us, it will be found by us that fortune is usually on the side of the industrious. The best navigators are favoured by the winds and waves. Lord Clive’s career was begun by him in India as a clerk. When his career was ended by him, the British Empire in the East had been founded by him.

Question 8.
A poor Arab saw a spring of sweet water. He had never before tasted such water. He filled his leather bottle from the spring. He wanted to present it to the Khalif. The courtiers desired to taste the precious water but the Khalif forbade them. The Khalif was touched by the Arab’s concern for him. He awarded the poor man.
Answer
A spring of sweet water was seen by a poor Arab. Such water had never been before tasted by him. His leather bottle was filled by him from the spring. He wanted it to be presented to the Khalif. It was desired by the courtiers to taste, the precious water, but they were forbidden by the Khalif. The Arab’s concern for the Khalif touched him. The poor man was awarded by him.

Question 9.
We all know that Columbus discovered America. He was provided with ships and men by the king of Spain. He met with many difficulties on the way. All his fellow men wanted to turn back. But he did not stop till he reached his goal.
Answer
It is known to all of us that America was discovered by Columbus. The king of Spain provided him with ships and men. He met with many difficulties on the way. All his fellow men wanted to turn back. But he did not stop till his goal was reached.

Question 10.
It is nice that you are taking your studies seriously. Please don’t do it at the cost of your health. Those who do brain work, need regular physical exercise. So don’t avoid games. They teach you something which books can never teach, i.e. discipline.
Answer
It is nice that your studies are being taken seriously by you. You are requested not to do it at the cost of your health. Regular physical exercise is needed by those who do brain work. So games should not be avoided. You are taught by them something which can never be taught by the books, i.e. discipline.

Complete the passage with the Passive form of the verbs given in the brackets :

A three year old girl (a) …………………………. (rescue) by the police last Tuesday. She (b) …………… (kidnap) by a neighbour for ransom. The mother informed the police about the missing girl. The probe (c) ………….. (supervise) by the DSP himself. More than 50 residents (d) …………… (interrogate). Ultimately, Danny, one of the residents of the colony, admitted the crime and disclosed where the girl (e) …………. (hide).
Answer:
(a) was rescued
(b) had been kidnapped
(c) was supervised
(d) were interrogated
(e) was hidden.

Read the newspaper headlines given below and complete the sentences that follow :

1. Rain Kills Over Two Dozen
Kathmandu : About ….. in the remote villages of north-western Kalikot district in the rains that hit the area.

2. Largest Discovery Of Dinosaur Eggs
Lerida : More than 100 eggs of dinosaur ………………… in north-eastern Spain.

3. Pak defeated by a big margin
The Pakistani cricket team …………………. in the first one dayer by a big margin yesterday. The match ……………… at Lahore in the Gaddafi Stadium.

4. Obama Accorded Warm Welcome President Barack Obama Of Usa …
a warm welcome on his arrival in india this year. He ………………….. by the prime minister himself at the delhi airport.

5. Underground Tunnel Unearthed
A half-dug underground tunnel …………. by the police personnel inside the jail compound yesterday. The digging ………………. by two convicts undergoing life terms in the jail.

6. Cold Wave Claims 37 Lives
The cold wave prevailing in Punjab for more than a week has worsened further. There ………….. a fresh snowfall in the Himalayas. Meanwhile 37 lives ………………….. so far by the cold wave.

7. Rich Homage Paid To Mahatma Gandhi; Statue Unveiled
Rich homage ………. … to the great father of the nation, mahatma gandhi, on the occasion of his birth anniversary, yesterday. a bronze statue of the great visionary …………………… on the occasion.

8. D.J. Simpson Acquitted
In the judgement given today by an american court, the famous football legend D.J simpson ……………………. of murder charges against him.

9. Idols Immersed In River
The ten-day dussehra festival comes to an end today when all the idols carried in a procession ……………………. in the ganga by the devotees.

10. Three Militants Killed, Seven Arrested
During the past 24 hours, three militants………………. and seven have been arrested in the kashmir valley. A large number of weapons were also seized from those arrested.

11. Afghan Forces Capture Kabul Airport
After a five-day bloody battle, the kabul airport ………… by the afghan forces early today. dozens of people were killed and more than 2500 were injured.

12. Govt. To Take Stern Steps:
It Has been announced by the government that ……………………….. to check the black-marketing and adulteration of essential goods.

13. Fire Destroys Goods Worth ₹ 25 Lac ; Cause Unknown
goods ……………… when two houses in tilak nagar caught fire yesterday.The cause of fire which rendered four families homeless, could not be known.

14. 193 Kg Heroin Seized :
in the biggest ever drug haul in the country, a consignment of 193 kg of heroin ……. by the mumbai police from a luxury apartment, in central mumbai.

15. Tourists, Attacked By Shark
last monday several australian tourists …………….. while surfing off pasiraman beach.

16. Suspect Arrested
shahpur police report that the suspect in the nasir khan murder case …………

17. Woman, Child Killed In Road Mishap — Six Injured
A woman and ………………… on the spot and six persons were injured, two of them seriously, when a tempo in which they were travelling, fell into a khud near Lalpani.

18. “Bankmen Give Free Hawai Chappals
For Lepers Lepers, living in the Asha Deep Colony of the city, ………………… on Thursday by the employees of State Bank of India. The Bankmen were celebrating the 42nd anniversary of their branch.

19. Shopkeeper Arrested, Fined :
ashok kumar, a shopkeeper of bilaspur …………………… by the police on tuesday for selling adulterated atta. later he was produced before the chief judicial magistrate by whom he ………………… ₹ 5000.

20. Advani Relieved Of His Post :
The BJP President, L.K. Advani, ………………….. of his post today after he submitted his resignation in the meeting of the general body of the party.
Answer:
1. two dozen men are killed
2. have been discovered
3. was defeated ; was played
4. was accorded ; was received
5. was unearthed ; had been done.
6. has been ; have been claimed.
7. was paid ; was unveiled
8. was acquitted
9. are immersed
10. have been killed
11. was captured
12. stern steps will be taken
13. worth ₹ 25 lac were destroyed
14. has been seized
15. were attacked by shark
16. has been arrested
17. a child were killed
18. were given free Hawai chappals
19. was arrested ; was fined
20. was relieved.

Rewrite the following passages after changing the Voice :

Question 1.
The early men thought that every misfortune was caused by angry gods. They saw imaginary gods everywhere. They thought of God as a very irritable person who was always losing his temper. If due to some disaster, a large number of people were killed, they would think they had displeased God.
Answer:
It was thought by the early men that angry gods cause every misfortune. Imaginary gods were seen everywhere by them. God was thought of by them as a very irritable person who was always losing his temper. If some disaster killed a large number of people, they would think God had been displeased by them.

Question 2.
Mr. Lal teaches us English. He was awarded Padma Shri by the President. He is one of the most dedicated teachers we have. Social work interests Mr. Lal very much. He loves his students as he loves his own children. We are lucky to be his pupils. May God bless him !
Answer:
We are taught English by Mr. Lal. The President awarded him Padma Shri. He is one of the most dedicated teachers we have. Mr. Lal is very much interested in social work. His students are loved by him as his own children. We are lucky to be his pupils. May he be blessed by God!

Question 3.
A dove saw a bee fallen in a water tank. It dropped a large leaf into the water. The bee climbed on to the leaf and thanked the dove. A hunter took aim at the dove. The bee stung him. He missed his aim. Now the dove thanked the bee.
Answer:
A bee fallen in a water tank was seen by a dove. A large leaf was dropped into the water by it. The bee climbed on to the leaf and the dove was thanked by the bee. The dove was taken aim at by a hunter. He was stung by the bee. His aim was missed by him. Now the bee was thanked by the dove.

Question 4.
Once a jester offended the king. The king at once condemned him to death. The jester pleaded for his life but the king refused to alter the sentence. One day, the king visited the prison. He asked the jester to choose his manner of death. The clever jester at once said that he would like to die of old age.
Answer:
Once the king was offended by a jester. He was at once condemned to death by the king. The jester pleaded for his life but the king refused to alter the sentence. One day, the prison was visited by the king. The jester was asked to choose his manner of death by the king. It was at once said by the clever jester that he would like to die of old age.

Question 5.
I explained my case to the doctor. I was seated on a chair against the table by him. I held my hat in my right hand and explained my symptoms. He then gave his advice and helped me liberally.
Answer:
My case was explained by me to the doctor. He seated me on a chair against the table. My hat was held in my right hand and my symptoms were explained. His advice was then given and I was helped liberally.

Question 6.
The emperor was adorned in his royal robes. He was attended by his courtiers. He was escorted to the seashore. There he was seated upon a high chair. The chair had been placed there for his reception.
Answer:
The emperor adorned himself in royal robes. His courtiers attended him. They escorted him to the seashore. There they seated him upon a high chair. They had placed the chair there for his reception.

Question 7.
If we look into practical life, we will find that fortune is usually on the side of the industrious. The winds and waves favour the best navigators. Lord Clive began his career in India as a clerk. When he ended his career, he had founded the British Empire in the East.
Answer:
If practical life is looked into by us, it will be found by us that fortune is usually on the side of the industrious. The best navigators are favoured by the winds and waves. Lord Clive’s career was begun by him in India as a clerk. When his career was ended by him, the British Empire in the East had been founded by him.

Question 8.
A poor Arab saw a spring of sweet water. He had never before tasted such water. He filled his leather bottle from the spring. He wanted to present it to the Khalif. The courtiers desired to taste the precious water but the Khalif forbade them. The Khalif was touched by the Arab’s concern for him. He awarded the poor man.
Answer:
A spring of sweet water was seen by a poor Arab. Such water had never been before tasted by him. His leather bottle was filled by him from the spring. He wanted it to be presented to the Khalif. It was desired by the courtiers to taste, the precious water, but they were forbidden by the Khalif. The Arab’s concern for the Khalif touched him. The poor man was awarded by him.

Question 9.
We all know that Columbus discovered America. He was provided with ships and men by the king of Spain. He met with many difficulties on the way. All his fellow men wanted to turn back. But he did not stop till he reached his goal.
Answer:
It is known to all of us that America was discovered by Columbus. The king of Spain provided him with ships and men. He met with many difficulties on the way. All his fellow men wanted to turn back. But he did not stop till his goal was reached.

Question 10.
It is nice that you are taking your studies seriously. Please don’t do it at the cost of your health. Those who do brain work, need regular physical exercise. So don’t avoid games. They teach you something which books can never teach, i.e. discipline.
Answer
It is nice that your studies are being taken seriously by you. You are requested not to do it at the cost of your health. Regular physical exercise is needed by those who do brain work. So games should not be avoided. You are taught by them something which can never be taught by the books, i.e. discipline.

Active Voice – जिस वाक्य में Subject का सीधा सम्बन्ध Verb के साथ होता है (अर्थात् कर्ता के अनुसार क्रिया का रूप निर्धारित होता है), उसे Active Voice का वाक्य कहा जाता है।

Passive Voice – जिस वाक्य में कर्म के अनुसार क्रिया का रूप निर्धारित होता है (और कर्ता का क्रिया पर कोई प्रभाव नहीं होता), उसे Passive Voice का वाक्य कहा जाता है।

निम्नलिखित वाक्यों को ध्यान से देखिए :

Active Voice                            ,	Passive Voice
1. Earn writes a letter, 2. Children like sweets.	1.   A letter is written by Ram. 2.    Sweets are liked by children

ऊपर के वाक्यों में हमने देखा कि
(1) Active Voice के वाक्य में जो Subject होता है, वह Passive Voice के वाक्य में Object बन जाता है।
(2) Active Voice के वाक्य में जो Object होता है, वह Passive Voice के वाक्य में Subject बन जाता है।
(3) Passive Voice के वाक्य में Object के साथ by अथवा कोई अन्य उपयुक्त Preposition लगाया जाता है।
(4) Subject से Object तथा Object से Subject का स्थान लेते समय Pronouns का रूप बदल जाता है;

Subject	Object	Subject	Object
I	me	He	him
We	us	She	her
You	You	They	them

किसी वाक्य का Voice बदलते समय Verb का रूप बदल जाता है। इसके लिए नीचे दी गई नियम तालिका याद रखिए :

Active Voice	Passive Voice
1. Present Indefinite Tense V1	is / am / are + V3
2. Past Indefinite Tense V2	was / were + V3
3. Future Indefinite Tense will / shall + V1	will / shall + be + V3
4. Present Continuous Tense is / am / are + V1 – ing	is/am / are + being + V3
5. Past Continuous Tense was / were + V-ing	was / were + being + V3
6. Present Perfect Tense has / have + V3	has / have + been + V3
7. Future Perfect Tense will/shall + have + V3	will/shall + have been + V3
8. Imperative Sentences V1 + Object	Object + should be + V3 (Or) Let + Object. + be + V3
9. can/could/may/might/must/ ought to / should+ V1	can/couldlmay/might/must/ ought to / should + be + V3

Examples of Present Indefinite . Tense
(is/am/are + V₃)

Active	Passive
1. She helps the poor. 2. We expect good news. 3. I know him. 4. Radha does not sing a song. 5. Who teaches you English ? 6. What do you want ?	1. The poor are helped by her. 2. Good news is expected by us. 3. He is known to me. 4. A song is not sung by Radha. 5. By whom are you taught English ? 6. What is wanted by you ?

Change the voice of the following sentences :

1. I take tea.
2. He drinks milk.
3. The boys make a noise.
4. They wash their clothes.
5. I do not like this book.
6. What do you do ?
7. Does he respect his elders ?
8. People praise her for her beauty.
9. A story is written by us.
10. The poor are helped by them.
11. She sings a song.
12. I do not like him.
13. Ram does not like him.
14. Do they learn their lessons ?
15. Where does he place his books ?

Examples of Past Indefinite Tense
(was/were + V₃)

Active	Passive
1. She kept us waiting.	1. We were kept waiting by her.
2. I employed two hundred men.	2. Two hundred men were employed by me.
3. The hunter did not aim at the bird.	3. The bird was not aimed at by the hunter.
4. Did he give you anything?	4. Were you given anything by him?
5. Who lent you this book?	5. By whom were you lent this book?
6. Which picture did you see last night?	6. Which picture was seen by you last night?

Change the voice of the following sentences :

1. Ram told a lie.
2. We played football.
3. We bought new pens.
4. The baby did not drink milk.
5. She did not open the window.
6. She did. her papers well.
7. Who told you this story?
8. Did you see him today?
9. A match was played by us.
10. America was discovered by Columbus.
11. Usha won a race.
12. The thief stole a number of things.
13. We did not laugh at the beggar.
14. He helped Ram in the hour of need.
15. Who gave you this book ?

Examples of Future Indefinite Tense
(will/shall + be + V₃)

Active	Passive
1. I shall buy this pen. 2. I will not take the test. 3. He will do his duty. 4. Will he not mend his ways ? 5. Which book will you read tomorrow ? 6. Who will answer this question ?	1. This pen will be bought by me. 2. The test shall not be taken by me. 3. His duty will be done by him. 4. Will his ways not be mended by him? 5. Which book will be read by you tomorrow? 6. By whom will this question be answered?

Change the voice of the following sentences :

1. She will teach English.
2. He will never tell a lie.
3. The teacher will not punish the boys.
4. When will you take exercise ?
5. We shall draw water from the well.
6. Who will prepare tea ?
7. This letter will be posted by me.
8. My pen will not be stolen by him.
9. They will not help the needy.
10. We shall consult the doctor.
11. How will you pass the examination ?
12. She will not obey you.
13. John will not run a race.
14. When will he return your money ?
15. Will you help me in need ?

Examples of Present Continuous Tense
(is/am/are + being + V₃)

Active	Passive
1. The gardener is plucking flowers. 2. He is driving a motor car. 3. Boys are flying kites. 4. Is she reading a book ? 5. Why are you wasting your time ? 6. Who is laughing at the beggar ?	1. Flowers are being plucked by the gardener. 2. A motor car is being driven by him. 3. Kites are being flown by boys. 4. Is a book being read by her ? 5. Why is your time being wasted by you ? 6. By whom is the beggar being laughed at?

Change the voice of the following sentences :

1. I am playing a match.
2. She is speaking the truth.
3. You are helping me.
4. The boys are not flying kites.
5. The teacher is not punishing the boys.
6. Are you insulting him ?
7. Sohan is wasting his time.
8. She is singing a song.
9. They are not wasting their time.
10. Is Mohan flying a kite ?
11. Is she not cooking the food ?
12. Why are you making a noise ?
13. Who is calling you ?
14. When is he finishing his work ?
15. What are you looking for ?

Examples of Past Continuous Tense
(was/were + being + V₃)

Active	Passive       ‘
1. The hunter was aiming at the lion. 2. She was milking the cow. 3. The peon was ringing the bell. 4. The farmer was not ploughing the field. 5. Were they learning their lesson ? 6. What was Sohan doing ?	1. The lion was being aimed at by the hunter. 2. The cow was being milked by her. 3. The bell was being rung by the peon. 4. The field was not being ploughed by the farmer. 5. Was their lesson being learnt by them ? 6. What was being done by Sohan ?

Change the voice of the following sentences :
1. Ram was not selling his old car.
2. They were insulting me.
3. She was not helping anybody.
4. He was building a new house.
5. He was opening the box.
6. Leela was washing the dishes.
7. The watchman was informing the police.
8. I was taking my class.
9. They were digging the ground.
10. The shopkeeper was closing his shop.
11. The people were not raising slogans.
12. Were they misleading you ?
13. Who was looking into the matter ?
14. What were they searching for ?
15. Why were the people stoning the bus ?

Examples of Present Perfect Tense
(has/have + been + V₃)

Active	Passive
1.    I have done my duty. 2.    She has sold her cow. 3.    They have not broken the windowpane. 4.    Have you ever seen a lion ? 5.    Why has Sohan not finished his work ? 6.    Who has stolen my pencil ?	1.      My duty has been done by me. 2.      Her cow has been sold by her. 3.      The windowpane has not been broken by them. 4.      Has a lion ever been seen by you ? 5.      Why has his work not been finished by Sohan ? 6.      By whom has my pencil been stolen ?

Change the voice of the following sentences :

1. He has forgotten me.
2. The judge has set the prisoner free.
3. He has finished his job.
4. He has obliged me.
5. The bell has been rung by the peon.
6. The letter has been posted by my father.
7. What has he done for you ?
8. Who has helped you ?
9. The principal has given away the prizes.
10. We have played the game.
11. He has given me a book.
12. They have not committed the theft.
13. Have you attended the class ?
14. Has the peon not locked the office ?
15. Why have you insulted your teacher ?

Examples of Past Perfect Tense
(had + been + V₃)

Active	Passive
1. The watchman had already opened the gate. 2. We had never visited Amritsar before. 3. Had you never seen this place before? 4. Who had invited you to the feast? 5. Had he finished his work by 4 p.m.?	1. The gate had already been opened by the watchman. 2. Amritsar had never been visited by us before. 3 . Had this place never been seen by you before ? 4. By whom had you been invited to the feast ? 5. Had his work been finished by him by 4 p.m.?

Change the voice of the following sentences :

1. He had killed a snake before.
2. She had already finished her work.
3. Someone had already stolen the box.
4. You had already received the letter.
5. They had not yet built the house.
6. We had already killed the lion.
7. The lock had been opened by the peon.
8. He had bought a new car.
9. She had passed the examination.
10. You had not made the proper use of your time.
11. Had he abused you ?
12. They had not’disturbed us.
13. Who had mentioned your name ?
14. When had you rung him up ?
15. What had he lost ?

Examples of Future Perfect Tense
(will / shall + have been + V₃₎

Active	Passive
1. I shall have planted a tree. 2. He will have read this book. 3. He will not have sold his house. 4. She will have taken the test. 5. Will he have written a letter ?	1. A tree will have been planted by me. 2. This book will have been read by him. 3. His house will not have been sold by him. 4. The test will have been taken by her. 5. Will a letter have been written by him ?

Change the voice of the following sentences :

1. The teacher will have taught the lesson.
2. He will have signed the papers.
3. She will have learnt her lesson.
4. He will not have done his homework.
5. He will have changed the clothes before my arrival.
6. They will have whitewashed the home before evening.
7. I shall have paid my fees.
8. You will have seen the lion before.
9. The police will have arrested the culprits before.
10. A letter will have been posted by him.
11. He will not have opened the window.
12. Will you have brought him a gift ?
13. Where will you have spent your holidays ?
14. Who will have helped him ?
15. He will have taught you English.

Examples of Imperative Sentences
(Object + should be + V₃) Or (Let + Object + be + V₃)

Active	Passive
1. Shut the door. 2. Obey your parents. 3. Carry it home. 4. Never tell a lie. 5. Let him play the match. 6. Please bring me a glass of water.	1. The door should be shut. 2. Let your parents be obeyed. 3. Let it be carried home. 4. A lie should never be told. 5. Let the match be played by him. 6. You are requested to bring me a glass of water.

Change the voice of the following sentences :

1. Change these clothes.
2. Summon the peon.
3. Kindly call in the doctor.
4. Please help him.
5. Do not waste your time.
6. Always speak the truth.
7. Do not hate the poor.
8. Do not write anything against him.
9. Help the poor.
10. Duty must be done.
11. Send for the doctor at once.
12. Kindly help me.
13. Always get up early in the morning.
14. Write a letter to your father.
15. You are ordered to sit down.

Examples of the Use of can, could, may, etc.
(can, could, may, might, should, would, dare, etc. + be + V₃)

Active	Passive
1. You should write the address neatly. 2. One cannot please everybody. 3. We should always speak the truth. 4. You must listen to his words. 5. One should do one’s duty. 6. Somebody must help this poor woman.	1. The address should be written neatly. 2. Everybody cannot be pleased. 3. The truth should always be spoken by us. 4. His words must be listened to. 5. Duty should be done. 6 This poor woman must be helped.

Change the voice of the following sentences :

1. I can open this box.
2. He could tell the truth.
3. We could have learnt our lesson.
4. You must finish this work.
5. She might miss the bus.
6. They might call me.
7. May I see this picture ?
8. You must tell me everything.
9. May God bless you with a son !
10. Why should I do it ?
11. They might have won the match.
12. They might have told the truth.
13. You should have done it by now.
14. Our parents and teachers ought to be respected by us.
15. They could pass the admission test.

The Use of Prepositional Verbs

कुछ Verbs के साथ विशेष Prepositions या Adverb Particles का प्रयोग किया जाता है। Active तथा Passive दोनों तरह के वाक्यों में ये Prepositions या Adverb Particles सम्बन्धित Verbs के साथ ही लगाए जाने चाहिएं। इन्हें Verbs से अलग नहीं किया जा सकता है। जैसे

Active

Passive

1. The people listened to him with respect. 2. I objected to his proposal. 3. The rich often laugh at the poor. 4. We must take care of our health. 5. They switched off the lights. 6. A car ran over an old man. 7. The police charged her with murder. 8. The Principal turned down my request. 9. The thieves cut down the telephone wires. 10. I cannot think of such a thing.

1. He was listened to with respect by the people. 2. His proposal” was objected to by me. 3. The poor are often laughed at by the rich. 4. Health must be taken care of. 5. The lights were switched off. 6. An old man was run over by a car. 7. She was charged with murder by the police. 8. My request was turned down by the Principal. 9. The telephone wires were cut down by the thieves. 10. Such a thing cannot be thought of by me.

Change the voice of the following sentences :

1. We are waiting for you.
2. What is contained in this pot ?
3. She is knocking at the door.
4. He enquired into the matter.
5. I do not agree to your plan.
6. What are you searching for ?
7. I don’t care for him.
8. You should not laugh at the old woman.
9. You looked after him.
10. They made fun of the poor man.
11. She laughs at you.
12. She will look into this matter.
13. He agreed to your proposal.
14. He picked up a letter.
15. The boys looked at the picture on the wall.

The Use of Prepositions other than ‘by’

कुछ वाक्यों के Passive voice में ‘by’ के स्थान पर किसी अन्य Preposition का प्रयोग होता है; जैसे

Active	Passive
1. His behaviour disgusts me. 2. The jug contains milk. 3. The news surprised us. 4. Gardening interests my mother. 5. You cannot please her. 6. I know him. 7. His jokes amused us. 8. His conduct amazed us.	1. I am disgusted with his behaviour. 2. Milk is contained in the jug. 3. We were surprised at the news. 4. My mother is interested in gardening. 5. She cannot be pleased with you. 6. He is known to me. 7. We were amused at his jokes. 8. We were amazed at his conduct.

Change the voice of the following sentences :

1. You cannot please all.
2. The news of his failure has shocked me.
3. Your success pleases me.
4. Everybody knows him.
5. Many pictures are contained in this book.
6. I was satisfied with her work.
7. This beaker contains water.
8. Your behaviour annoyed me.
9. He was delighted at your brilliant success.
10. My success astonished all.
11. Your behaviour displeased me.
12. The boss is satisfied with his work.
13. What is contained in this purse ?
14. His fathers death shocked all.
15. Do you know the Principal ?

Examples of Interrogative Sentences (Mixed Type) :

नोट : What, why, when, how, which, where, who आदि से शुरू होने वाले निम्नलिखित प्रश्नात्मक वाक्यों का ध्यानपूर्वक अध्ययन कीजिए

Active	Passive
1. What do you want ? 2. Who teaches you English ? 3. Who do you love ? 4. Where will you spend your holidays ? 5. Whence have you bought this pen ? 6. When will you see him ? 7. Why did he abuse you ?	1. What is wanted by you ? 2. By whom are you taught English ? 3. Who is loved by you ? 4. Where will your holidays be spent by you ? 5. Whence has this pen been bought by you ? 6. When will he be seen by you ? 7. Why were you abused by him ?

Change the voice of the following sentences :

1. Who stole your pen ?
2. Who will you elect President ?
3. Why has the teacher marked me absent ?
4. Who had visited Delhi ?
5. Who told a lie ?
6. When did you pluck these flowers ?
7. Who did you see ?
8. Why am I cursed by you ?
9. Whose book had been taken by him ?
10. How was the river crossed by them ?
11. By whom will the hockey match be played ?
12. Had the poem been learnt by them before ?
13. By whom had the windowpane been broken before you arrived ?
14. By whom has the picture been painted ?
15. Why has so much been spent by you?

Examples of Sentences with the Double Object

कुछ वाक्यों में दो Objects होते हैं; जैसे
I gave him a book.
पहले Object को Indirect Object और दूसरे को Direct Object कहा जाता है।

Passive Voice बनाते समय प्राय: Indirect Object को ही Subject के रूप में प्रयोग किया जाता है; जैसे
He was given a book by me.

किन्तु यदि Direct Object को Subject के रूप में प्रयोग किया जाना हो तो Indirect Object से पूर्व to अथवा for का प्रयोग करना पड़ता है; जैसे
A book was given to him by me.

कुछ अन्य उदाहरण :

Active	Passive
1. I gave him a book.	1. A book was given to him by me. (Or) He was given a book by me.
2. He teaches us English.	2. English is taught to us by him. (Or) We are taught English by him.
3. You have written him a letter.	3. A letter has been written to him by you. (Or) He has been written a letter by you.
4. She handed Ram a letter.	4. A letter was handed to Ram by her. (Or) Ram was handed a letter by her.
5. They gave her a test.	5. She was given a test by them. (Or) A test was given to her by them.
6. He sent me an invitation.	6. I was sent an invitation by him. (Or) An invitation was sent to me by him.
7. Ram offered me a job.	7. I was offered a job by Ram. (Or) A job was offered to me by Ram.
8. Who gave you this book ?	8. By whom were you given this book ? (Or) By whom was this book given to you ?

Change the voice of the following sentences

1. She gave me five rupees.
2. I told him a story.
3. You sent him a letter.
4. Ram gave me good news.
5. We showed him a picture.
6. He lent me some money.
7. The teacher was teaching me English.
8. They were given some money by my father.
9. They were showing her their new books.

10. She was sent a letter by me.
11. She wrote him a letter.
12. Ram lent me some books.
13. I paid him his salary.
14. I shall forgive him his fault.
15. He gives them food and clothes.

Examples of Sentences with an Implied Subject

Passive Voice के कुछ वाक्यों में by + agent नहीं दिया गया होता है किन्तु ऐसे वाक्यों में कर्ता का अनुमान लगाने में कोई कठिनाई नहीं होती है। अत: Passive Voice से Amtive Voice बनाने में उसी कर्ता का प्रयोग किया जाना चाहिए; जैसे

Passive	Active
1. You are wanted outside. 2. The thief has been arrested. 3. The telephone wires were cut. 4. The matter will be discussed matter tomorrow. 5. He was elected Member of Parliament. 6. The crops can be reaped. 7. The result has been declared. 8. English is spoken all over the world.	1. Someone wants you outside. 2. The police have arrested the thief. 3. The thieves cut the telephone wires. 4. The committee will discuss the tomorrow. 5. People elected him Member of Parliament. 6. The farmers can reap the crops. 7. The Principal has declared the result. 8. People speak English all over the world.

Change the voice of the following sentences :

1. Sums are being solved.
2. All the horses were sold.
3. Flowers were being plucked.
4. He is wanted at home.
5. Children are being looked after.
6. People use telephone all over the world.
7. None can defeat him.
8. We grow rice in the rainy season.
9. The committee has made new plans.
10. Neeru was being forced to resign.
11. The culprit was hanged.
12. He has been asked to resign.
13. My brother has never been beaten at tennis.
14. A meeting is being held here.
15. Many persons were thrown out of jobs.

Examples of the Passive of Infinitives

Active	Passive
1. She begged the Principal to forgive her.	1. She begged the Principal to be forgiven.
2. I hope to overcome my difficulties.	2. I hope my difficulties to be overcome.
3. I have to do this work.	3. This work has to be done.
4. I expect you to finish the you.	4. I expect the work to be finished by work.
5. It is time to give the order.	5. It is time for the order to be given.
6. It is time to feed the baby.	6. It is time for the baby to be fed.
7. It is time to ring the bell.	7. It is time for the bell to be rung.
8. It is time to tell stories.	8. It is time for. the stories to be told.

Change the voice of the following sentences :

1. It is time to see the picture.
2. It is time to take the meals.
3. It is time to open the door.
4. It is time to save money.
5. It is time to wash the clothes.
6. It is time to discuss the matter.
7. It is time to open the school.
8. It is time to start the journey.
9. It is time to leave the class.
10. It is time for a song to be sung.
11. It is time to do the job.
12. It is time to run a race.
13. It is time to call in the doctor.
14. It is time to say prayers.
15. It is time to open the shop.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1

Question 1.
In quadrilateral ACBD. AC = AD and AB bisects ∠ A (see the given figure). Show that ∆ ABC ≅ ∆ ABD. What can you say about BC and BD?

Answer:
In ∆ ABC and ∆ ABD,
AC = AD (Given)
∠ BAC = ∠ BAD (AB bisects ∠ A)
AB = AB (Common)
∴ ∆ ABC ≅ ∆ ABD (SAS rule)
∴ BC = BD (CPCT)
Thus, BC and BD are equal.

Question 2.
ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see the given figure). Prove that (i) ∆ ABD ≅ ∆ BAC, (ii) BD = AC and (iii) ∠ ABD = ∠ BAC

Answer:
In ∆ ABD and ∆ BAC,
AD = BC (Given)
∠ DAB = ∠ CBA (Given)
AB = BA (Common)
∴ ∆ ABD ≅ ∆ BAC (SAS rule)
∴ BD = AC (CPCT)
∴ ∠ ABD = ∠ BAC (CPCT)

Question 3.
AD and BC are equal perpendiculars to a line segment AB (see the given figure). Show that CD bisects AB.

Answer:
AD and BC are equal perpendiculars to line segment AB.
∴ AD = BC and ∠ OAD = ∠ OBC = 90°.
Now, in ∆ ADO and ∆ BCO,
AD = BC
∠ OAD = ∠ OBC
∠ AOD = ∠ BOC (Vertically opposite angles)
∴ ∆ ADO ≅ ∆ BCO (AAS rule)
∴ OA = OB (CPCT)
CD intersects AB at O and OA = OB.
Hence, CD bisects AB.

Question 4.
l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that:
∆ ABC ≅ ∆ CDA.

Answer:
l || m and AC is their transversal.
∴ ∠ BCA = ∠ DAC (Alternate angles)
p l| q and AC is their transversal.
∴ ∠ BAC = ∠ DCA (Alternate angles)
Now, in ∆ ABC and ∆ CDA,
∠ BCA = ∠ DAC
∠ BAC = ∠ DCA
AC = CA (Common)
∴ ∆ ABC ≅ ∆ CDA (ASA rule)

Question 5.
Ray l is the bisector of an angle ∠ A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A (see the given figure). Show that:
(i) ∆ APB ≅ ∆ AQB
(ii) BP = BQ or B is equidistant from the arms of ∠ A.

Answer:
l is the bisector of ∠ PAQ and B is any point on l.
∴ ∠ PAB = ∠ QAB
BP and BQ are perpendiculars from B to AP and AQ.
∴ ∠ BPA = ∠ BQA = 90°.
Now, in ∆ APB and ∆ AQB,
∠ PAB = ∠ QAB
∠ BPA = ∠ BQA
AB = AB (Common)
∴ ∆ APB ≅ ∆ AQB (AAS rule)
∴ BP = BQ (CPCT)
BP and BQ are perpendiculars from B to arms AP and AQ of ∠ A.
∴ BP is the distance of B from AP and BQ is the distance of B from AQ.
Thus, B is equidistant from the arms of ∠ A.

Question 6.
In the given figure, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE

Answer:
∠ BAD = ∠ EAC
∴ ∠ BAD + ∠ DAC = ∠ EAC + ∠ DAC
∴ ∠ BAC = ∠ DAE (Adjacent angles)
Now, in ∆ BAC and ∆ DAE,
AC = AE (Given)
AB = AD (Given)
∠ BAC = ∠ DAE
∴ ∆ BAC ≅ ∆ DAE (SAS rule)
∴ BC = DE (CPCT)

Question 7.
AB is a line segment and P is its midpoint. D and E are points on the same side of AB such that ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see the given figure). Show that:
(i) ∆ DAP ≅ ∆ EBP
(ii) AD = BE

Answer:
∠ BAD = ∠ ABE
∴ ∠ PAD = ∠PBE (∵ P lies on AB.)
∠ EPA = ∠ DPB
∴ ∠ EPA + ∠ EPD = ∠ DPB + ∠ EPD
∴ ∠ APD = ∠ BPE (Adjacent angles)
P is the midpoint of AB.
∴ AP = BP
Now, in ∆ DAP and ∆ EBP
∠ PAD = ∠ PBE
∠ APD = ∠ BPE
AP = BP
∴ ∆ DAP ≅ ∆ EBP (ASA rule)
∴ AD = BE (CPCT)

Question 8.
In right triangle ABC, right angled at C, M is the midpoint of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
(i) ∆ AMC ≅ ∆ BMD
(ii) ∠ DBC is a right angle
(iii) ∆ DBC ≅ ∆ ACB
(iv) CM = \(\frac{1}{2}\) AB

Answer:
In ∆ AMC and ∆ BMD,
AM = BM (∵ M is the midpoint of AB.)
CM = DM (Given)
∠ AMC = ∠ BMD (Vertically opposite angles)
∴ By SAS rule, ∆ AMC ≅ ∆ BMD [Result (i)]
∴ ∠ MCA = ∠ MDB (CPCT)
∠ MCA and ∠ MDB are alternate angles formed by transversal CD of lines AC and BD and they are equal.
∴ AC || BD
Now, ∠ DBC and ∠ ACB are interior angles on the same side of transversal BC of AC || BD.
∴ ∠ DBC + ∠ ACB = 180°
∴ ∠ DBC + 90° = 180° (Given : ∠ C = 90°)
∴ ∠ DBC = 90°
Thus, ∠ DBC is a right angle. [Result (ii)]
Now, ∆ AMC ≅ ∆ BMD
∴ AC = BD
In ∆ DBC and ∆ ACB,
BD = CA
∠ DBC = ∠ ACB (Right angles)
BC = CB (Common)
∴ ∆ DBC ≅ ∆ ACB [Result (iii)]
∴ DC = AB (CPCT)
DM = CM and M lies on line’ segment CD.
∴ DC = 2 CM
∴ AB = 2CM
∴ \(\frac{1}{2}\)AB = CM
∴ CM = \(\frac{1}{2}\)AB