Bhagya

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes Ex 9.6 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 9 Understanding Elementary Shapes Ex 9.6

1. Give two examples of each of the following shapes from your surroundings:

Question (i)
Cube
Solution:
Cube. Examples:
(i) Dice,
(ii) Sugar cubes.

Question (ii)
Cuboid
Solution:
Cuboid. Examples:
(i) Matchbox,
(ii) Geometry box.

Question (iii)
Cone
Solution:
Cone: Examples:
(i) Ice cream cone,
(ii) Joker cap.

Question (iv)
Cylinder
Solution:
Cylinder. Examples:
(i) Drum,
(ii) Circular pipe.

Question (v)
Shpere.
Solution:
Shpere. Examples:
(i) Globe,
(ii) Ball.

2. Classify the following as plane figures and solid figures:

Question (i)
(i) Rectangle
(ii) Sphere
(iii) Cylinder
(iv) Circle
(v) Cube
(vi) Cuboid
(vii) Triangle
(viiii) Cone
(ix) Square
(x) Prism.
Solution:
Plane figures:
(i) Rectangle
(iv) Circle
(vii) Triangle
(ix) Square.

Solid figures:
(ii) Sphere
(iii) Cylinder
(v) Cube
(vi) Cuboid
(viii) Cone
(x) Prism.

3. Write the name of shapes in the base of the following solids:

Question (i)
Cube
Solution:
Square

Question (ii)
Cylinder
Solution:
Circle

Question (iii)
Tetrahedron
Solution:
Equilateral triangle

Question (iv)
Cuboid
Solution:
Rectangle

Question (v)
Square Pyramid.
Solution:
Square.

4. Fill in the table:

Shape	Number of Flat Faces	Number of Curved Faces	Number of Vertices	Number of Edges
(i) Cuboid
(ii) Cube
(iii) Cylinder
(iv) Cone
(v) Sphere
(vi) Triangular Prism
(vii) Square Pyramid
(viii) Tetrahedron

Solution:

Shape	Number of	Number of	Number of	Number of
	Flat Faces	Curved Facet!	Vertices	Edges
(i) Cuboid	6	Nil	8	12
(ii) Cube	6	Nil	8	12
(iii) Cylinder	2	1	Nil	2
(iv) Cone	1	1	1	1
(v) Sphere	Nil	1	Nil	Nil
(vi) Triangular Prism	5	Nil	6	9
(vii) Square Pyramid	5	Nil	5	8
(viii) Tetrahedron	4	Nil	4	6

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 15 Visualising Solid Shapes Ex 15.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Ex 15.3

1. Count the number of cubes in each of the following figures :


Solution:
(i) 6
(ii) 21
(iii) 32
(iv) 13

2. If three cubes of dimensions 2 cm × 2 cm × 2 cm are placed side by side, what would be the dimensions of resulting cuboid ?

Solution:
Length 6 cm, breadth 2 cm and height 2 cm.

3. If we throw light an the following solids from the top name the shape of shadow obtained in each case and also give a rough sketch of the shadow.
(i) DVD player

Solution:

(ii) Sandwich

Solution:

(iii) Straw

Solution:

4. What cross-sections do you get when you given a.
(i) Vertical cut
(ii) Horizontal cut.
to the following solids ?
(a) A die
(b) A square pyramid
(c) A round melon
(d) A circular pipe
(e) A brick
(f) An ice cream cone.
Solution:
(a) Square, Square,
(b) Triangle, Square,
(c) Circle, circle
(d) Circle, Rectangle
(e) Rectangle, Rectangle
(f) Triangle, Circle.

5. If we throw light on following solids, from left name the shape of shadow in each and also give a rough sketch of the shadow.
(i)

Solution:

(ii)

Solution:

6. Here are the shadows of some 3-D objects, when seen under the lamp of an overhead projector. Identify the solids that match each shadow (There may be multiple answers for these)

Solution:
(i) Dice, chalk box etc
(ii) Book, Mobile, DVD Player etc
(iii) Cricket ball, Disc etc.
(iv) Birthday cap, Icecream cone etc.

7. Sketch the front, side and top view of the following figures :
(i)

Solution:

(ii)

Solution:

(iii)

Solution:

(iv)

Solution:

8. Multiple choice questions :

Question (i).
The number of cubes in the given structure is ?

(a) 12
(b) 10
(c) 9
(d) 8
Answer:
(a) 12

Question (ii).
The number of unit cubes to be added in above students to make a cuboid of dimensions 4 unit × 2 unit × 3 unit is ?
(a) 11
(b) 12
(c) 13
(d) 14
Answer:
(b) 12

Question (iii).
What cross-section is made by vertical cut in a cuboid
(a) Square
(b) Rectangle
(c) Circle
(d) Triangle
Answer:
(b) Rectangle

Question (iv).
What cross section is made by horizontal cut in a cone
(a) Triangle
(b) Circle
(c) Square
(d) Rectangle
Answer:
(b) Circle

Question (v).
Which solid cost a shadow of triangle under the effect of light
(a) Sphere
(b) Cylinder
(c) Cone
(d) Cube
Answer:
(c) Cone

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 15 Visualising Solid Shapes Ex 15.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Ex 15.2

1. Use isometric dot paper and make an isometric sketch of the following figures :
Question (i).

Solution:

Question (ii).

Solution:

Question (iii).

Solution:

Question (iv).

Solution:

2. Draw (i) an oblique sketch (ii) Isometric sketch for :
(a) A cube with a edge of 4 cm long
(b) A cuboid of length 6 cm, breadth 4 cm and height 3 cm
Solution:
(a) (i) Oblique sketch of cube with a edge 4 cm long.

(ii) Iso metric sketch for a cube with a edge of 4 cm long.

(b) (i) an oblique sketch for a cuboid of length 6 cm, breadth 4 cm and height 3 cm.

(ii) Isometric sketch for a cuboid of length 6 cm, breadth 4 cm and height 3 cm.

3. Two cubes each with edge 3 cm are placed side by side to form a cuboid, sketch oblique and isometric sketch of this cuboid.
Solution:

4. Draw an Isometric sketch of triangular pyramid with base as equilateral triangle of 6 cm and height 4 cm.
Solution:

5. Draw an Isometric sketch of square pyramid.
Solution:

6. Make an oblique sketch for each of the given Isometric shapes.

Question (i).

Solution:

Question (ii).

Solution:

7. Using an isometric dot paper draw the solid shape formed by the given net.

Solution:

8. Multiple choice questions:

Question (i).
An oblique sheet is made up of:
(a) Rectangles
(b) Squares
(c) Right angled triangles
(d) Equilateral triangles.
Answer:
(b) Squares

Question (ii).
An isometric sheet is made up of dots forming :
(a) Squares
(b) Rectangles
(c) Equilateral triangles
(d) Right angled triangle
Answer:
(c) Equilateral triangles

Question (iii).
An oblique sketch has :
(a) Proportional lengths
(b) Parallel lengths
(c) Non-Proportional lengths
(d) Perpendicular lengths.
Answer:
(c) Non-Proportional lengths

Question (iv).
An Isometric sketch has :
(a) Non proportional lengths
(b) Parallel lengths
(c) Perpendicular lengths
(d) Proportional lengths.
Answer:
(d) Proportional lengths.

Question (v).
Isometric sketches shows objects of:
(a) Two dimensions
(b) Shadows
(c) Three dimensions
(d) One dimension.
Answer:
(c) Three dimensions

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 10 Practical Geometry Ex 10.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 10 Practical Geometry Ex 10.1

1. What is the use of instrument ruler?
Solution:
We use instrument ruler to draw line segment and to measure their lengths.

2. What is the use of protractor?
Solution:
We use a protractor to draw and measure angle.

3. What is the use of compasses?
Solution:
We use compasses to mark equal lengths, draw arcs and circles.

4. Construct the following angles using set squares.

Question (i)
(i) 30°
(ii) 45°
(iii) 60°
(iv) 75°
(v) 90°.
Solution:
(i) Steps of Construction:

1. Draw a ray OA.

2. To construct an angle of 30° we use 30° set square. Place the set square in such a way that one of its edges containing the 30° angle coincides with the ray OA as shown in the figure.

3. Draw a ray OB starting from the vertex O along the 30° edge of the set square as shown in figure.
4. Remove the set square.
Thus, the required \(\angle \mathrm{AOB}\) = 30°.

(ii) Steps of Construction:

1. Draw a ray OA.

2. To construct an angle of 45° we use 45° set square.
Place a 45° set square along ray OA as shown in the figure.

3. Draw a ray OB starting from the vertex O along 45° the, edge of set square.
4. Remove the 45° set square. Thus, the required \(\angle \mathrm{AOB}\) = 45°

(iii) Steps of Construction.

1. Draw a ray OA.

2. To construct an angle of 60°. We use 30° set square.

Place a 30° set square with 60° edge along ray OA as shown in the figure.
3. Draw a ray OB starting from the vertex O along 60° edge of the set square.
4. Remove the 30° set square. Thus the required \(\angle \mathrm{AOB}\) = 60°.

(iv) Steps of Construction

1. Draw a ray of OA.

2. To draw angle of 75° we use both set squares in combination as 45° + 30° = 75°.
Place 45° set square with 45° edge along OA

3. Place 30° set square adjacent to 45° set square as show. Draw a ray starting from the vertex O along the edge of 30° set square.
4. Remove both the set squares. Thus required \(\angle \mathrm{AOB}\) = 75°.

(v) Steps of Construction

1. Draw a ray OA.

2. To construct angle of 90° place any set square with 90° corner at O along OA.

3. Draw a ray OB starting from the vertex O along 90° edge of the set square.
4. Remove the set square. Thus, the required \(\angle \mathrm{AOB}\) = 90°.

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes MCQ Questions with Answers.

PSEB 6th Class Maths Chapter 9 Understanding Elementary Shapes MCQ Questions

Multiple Choice Questions

Question 1.
In the figure, which of the following is true?
(a) PR = PQ
(b) PR > QR
(c) PS > PR
(d) PR < PQ.
Answer:
(b) PR > QR

Question 2.
Which angle is represented in the given figure?
(a) Reflex
(b) Acute
(c) Obtuse
(d) Right angle.
Answer:
(a) Reflex

Question 3.
Which angle is represented in the given figure?
(a) Acute
(b) Right angle
(c) Obtuse
(d) Reflex
Answer:
(b) Right angle

Question 4.
Which of the following is the example of perpendicular lines?
(a) Railway lines
(b) Line segment forming letter ‘X’
(c) Adjacent edges of a table
(d) Line segment forming line ‘M’.
Answer:
(c) Adjacent edges of a table

Question 5.
Which of the following forms triangles?
(a) 60°, 72°, 48°
(b) 73°, 54°, 59°
(c) 60°, 51°, 70°
(d) 100°, 42°, 39°.
Answer:
(a) 60°, 72°, 48°

Question 6.
Which of the following are sides of a triangle?
(a) 1, 2, 3
(b) 2, 2,1
(c) 3, 4, 2
(d) 5, 6, 12.
Answer:
(c) 3, 4, 2

Question 7.
A parallelogram having adjacent sides equal is called a …………… .
(a) Trapezium
(b) Rhombus
(c) Rectangle
(d) Square.
Answer:

Question 8.
Which of the following is not true for rectangle?
(a) Diagonals are equal
(b) Diagonals bisect each other
(c) Each angle is 90°
(d) All sides are equal.
Answer:
(d) All sides are equal

Question 9.
Which of the following is not true?
(a) Every rhombus is a parallelogram
(b) Each square is rhombus.
(c) Each rectangle is a square.
(d) Each square is parallelogram.
Answer:
(c) Each rectangle is a square

Question 10.
A cuboid has ………….. edges.
(a) 10
(b) 6
(c) 12
(d) 8.
Answer:
(c) 12

Question 11.
The following angle is an:

(a) acute angle
(b) obtuse angle
(c) right angle
(d) straight angle.
Answer:
(a) acute angle

Question (ii)
What is the angle name for half a revolution?
(a) acute angle
(b) obtuse angle
(c) straight angle
(d) right angle.
Answer:
(c) straight angle

Question (iii)
What is the angle name for one-fourth revolution?
(a) right angle
(b) straight angle
(c) complete angle
(d) acute angle.
Answer:
(a) right angle

Question (iv)
An angle whose measure is less than that of a right angle is …………….. .
(a) complete angle
(b) acute angle
(c) obtuse angle
(d) straight angle.
Answer:
(b) acute angle

Question (v)
An angle whose measure is greater than that of a right angle:
(a) acute angle
(b) complete angle
(c) obtuse angle
(d) straight angle.
Answer:
(c) obtuse angle

Fill in the blanks:

Question (i)
An angle whose measure is equal to 90°, is called ……………….. .
Answer:
right angle

Question (ii)
An angle whose measure is the sum of the measure of two right angle is ………………. .
Answer:
straight angle

Question (iii)
Your instrument box looks like a ………………. .
Answer:
cuboid

Question (iv)
A road-roller looks like a ……………… .
Answer:
cylinder

Question (v)
A cuboid has ……………. faces.
Answer:
six

Write True/False:

Question (i)
Every rhombus is a parallelogram. (True/False)
Answer:
True

Question (ii)
Every square is a rhombus. (True/False)
Answer:
True

Question (iii)
All sides of a rectangle are equal. (True/False)
Answer:
False

Question (iv)
Each rectangle is a square. (True/False)
Answer:
False

Question (v)
Each angle of a rectangle is of 90°. (True/False)
Answer:
True.

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes Ex 9.5 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 9 Understanding Elementary Shapes Ex 9.5

1. Which of the following are polygons and there is no polygon. Give the reason:

Solution:
(i) It is not a closed figure. Therefore it is not a polygon.
(ii) It is made up of lines segment. Therefore it is polygon.
(iii) It is not a polygon, because it is not made of line segments.
(iv) It is not closed by line segment. Therefore, it is not a polygon.
(v) It is not polygon because line segments are intersecting each other.
(vi) It is made up of line segments, therefore it is a polygon.

2. Classify the following as concave or convex polygons:

Solution:
(i) Concave Polygon
(ii) Convex Polygon
(iii) Concave Polygon
(iv) Concave Polygon
(v) Convex Polygon
(vi) Convex Polygon.

3. Tick in the boxes, if the property holds true for a particular quadrilateral otherwise eroes out ‘x’:

Quadrilateral Properties	Rectangle	Parallelogram	Rhombus	Trapezium	Square
All sides are equal
Only opposite sides are equal
Diagonals are equal
Diagonals bisect each other
Diagonals are perpendicular to each other
Each angle is 90°

Solution:

Quadrilateral Properties	Rectangle	Parallelogram	Rhombus	Trapezium	Square
All sides are equal	×	×	√	×	√
Only opposite sides are equal	√	√	×	×	×
Diagonals are equal	√	×	×	×	√
Diagonals bisect each other	√	√	√	×	√
Diagonals are perpendicular to each other	×	×	√	×	√
Each angle is 90°	√	×	X	×	√

4. Fill in the blanks:

Question (i)
…………… is a quadrilateral with only one pair of opposite sides parallel.
Solution:
Trapezium

Question (ii)
…………….. is a quadrilateral with all sides equal and diagonals of equal length.
Solution:
Square

Question (iii)
A polygon with atleast one angle is reflex is called ……………….. .
Solution:
Concave polygon

Question (iv)
………….. is a regular quadrilateral.
Solution:
Square

Question (v)
…………… is a quadrilateral with opposite sides equal and diagonals of unequal length.
Solution:
Parallelogram.

5. State True or False:

Question (i)
A rectangle is always a rhombus.
Solution:
False

Question (ii)
The diagonals of a rectangle are perpendicular to each other.
Solution:
False

Question (iii)
A square is a parallelogram.
Solution:
True

Question (iv)
A trapezium is a parallelogram.
Solution:
False

Question (v)
Opposite sides of a parallelogram are parallel.
Solution:
True.

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 15 Visualising Solid Shapes Ex 15.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Ex 15.1

1. Match the two dimensional figure with the names.

Answer:
(i) (e)
(ii) (d)
(iii) (a)
(iv) (b)
(v) (c)

2. Match the three dimension shapes with the names.

Answer:
(i) (d)
(ii) (e)
(iii) (a)
(iv) (c)
(v) (b)

3. Identify the nets which can be used to make cubes (cut out copies of the nets and try it).


Answer:
(i), (iv)

4. Draw the net for a square pyramid with base as square of sides 5 cm and slant edges 7 cm.
Answer:

5. Draw a net for the following cylinder.

Answer:

6. Draw the net of the solid given in figure.

Answer:

7. Dice are cubes with dots on each face opposite faces of a die always have a total of seven dots on them following are two nets to make dice (cuber) the number inserted in each square indicate the number of dots in that box insert suitable number in the blank squares.


Solution:

8. Which solid will be obtained by folding the following net ?

Solution:

9. Complete the following table.


Solution:
(i) Faces : 6.
(ii) Edges : 2. vertices : NIL,
(iii) Faces : 7. Edges : 15.
(iv) faces : 5, vertices : 5.

10. Multiple Choice questions :

Question (i).
Out of following which is 3-D figure ?
(a) Square
(b) Triangle
(c) Sphere
(d) Circle
Answer:
(c) Sphere

Question (ii).
Total number of faces a cylinder has :
(a) 0
(b) 2
(c) 1
(d) 3
Answer:
(d) 3

Question (iii).
How many edges are there in a square pyramid ?
(a) 5
(b) 8
(c) 1
(d) 4
Answer:
(b) 8

Question (iv).
Sum of number on the opposite faces of a die is :
(a) 8
(b) 7
(c) 9
(d) 6
Answer:
(b) 7

Question (v).
Which is not a solid figure ?
(a) Cuboid
(b) Sphere
(c) Quadrilateral
(d) Pyramid
Answer:
(c) Quadrilateral

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes Ex 9.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 9 Understanding Elementary Shapes Ex 9.4

1. Classify each of the following triangles as scalene, isosceles or equilateral:

Solution:
(i) Here, two sides of triangle are equal in length.
∴ It is an isosceles triangle.
(ii) Here, all the three sides of the triangle are equal in length.
∴ It is an equilateral triangle.
(iii) Here, no two sides are equal in length.
∴ It is scalene triangle.
(iv) Here, two sides of triangle are equal in length.
∴ It is an isosceles triangle.
(v) Here, no two sides are equal in length.
∴ It is scalene triangle.
(vi) Here, all the three sides of the triangle are equal in length.
∴ It is equilateral triangle.

2. Classify each of the following triangles as acute, obtuse or right triangle:

Solution:
(i) Here, one angle is 120°, which is obtuse angle.
∴ It is an obtuse-angled triangle.
(ii) Here, one angle is 90°, which is right angle.
∴ It is an right-angled triangle.
(iii) Here, each angle is acute angle.
∴ It is an acute-angled triangle.
(iv) Here, one angle is 90°, which is right angle.
∴ It is an right-angled triangle.
(v) Here, one angle is 120°, which is obtuse angle.
∴ It is an obtuse-angled triangle.
(vi) Here, each angle is 60°, which is actute angle.
∴ It is an actute angled triangle.

3. Which of the following triangles are possible with the given angles?

Question (i)
60°, 60°, 60°
Solution:
In a triangle sum of the three angles of a triangle is equal to 180°.
Here, sum of the three angles of triangle is:
60° + 60° + 60° = 180°
∴ This triangle is possible.

Question (ii)
110°, 50°, 30°
Solution:
Here, sum of the three angles of triangle is:
110° + 50° + 30°= 190° ≠ 180°
∴ This triangle is not possible.

Question (iii)
65°, 55°, 60°
Solution:
Here, sum of the three angles of triangle is:
65°+ 55°+ 60°= 180°
∴ This triangle is possible.

Question (iv)
90°, 40°, 50°
Solution:
Here, sum of the three angles of triangle is:
90°+ 40°+ 50°= 180°
∴ This triangle is possible.

Question (v)
48°, 62°, 50°
Solution:
Here, sum of the three angles of triangle is:
48°+ 62°+ 50°= 160° ≠ 180°
∴ This triangle is not possible.

Question (vi)
90°, 95°, 30°.
Solution:
Here, sum of the three angles of triangle is:
90°+ 95°+ 30° =215° ≠ 180°
∴ This triangle is not possible.

4. Classify each of the following triangles as scalene, isosceles or equilateral triangle:

Question (i)
4 cm, 5 cm, 6 cm
Solution:
The sides of triangle are 4 cm, 5 cm, 6 cm
No, two sides of this triangle are equal.
∴ This is a scalene triangle.

Question (ii)
5 cm, 7 cm, 5 cm
Solution:
The sides of triangle are 5 cm, 7 cm, 5 cm
Here, two sides are equal each of 5 cm in length.
∴ This is an isosceles triangle.

Question (iii)
4.2 m, S3 m, 6.1 m
Solution:
The sides of triangle are 4.2 m, 5.3 m, 6.1 m
Here, all sides are of different length.
∴ This is a scalene triangle.

Question (iv)
3.5 cm, 3.5 cm, 33 cm
Solution:
The sides of triangle are 3.5 cm, 3.5 cm, 3.5 cm
All the sides of triangle are of equal length.
∴ This is an equilateal triangle.

Question (v)
8 cm, 4.2 cm, 4.2 cm
Solution:
The sides of triangle are 8 cm, 4.2 cm, 4.2 cm
Here, two sides of the triangle are of equal length.
∴ This is an isosceles triangle.

Question (vi)
2 cm, 3 cm, 4 cm.
Solution:
The sides of triangle are 2 cm, 3 cm, 4 cm
All the sides of the triangle are of different lengths
∴ This is a scalene triangle.

5. Name the following triangles in both ways: (Based on sides and angles)

Solution:
(i) Based on sides: In this triangle, no two sides of the triangle are equal.
∴ This is a scalene triangle.
Based on angles: All the three angles of the triangle are acute.
∴ This is an acute-angled triangle.

(ii) Based on sides: In this triangle, two sides are of equal length each is 4 cm.
∴ This is an isosceles triangle.
Based on angles: In this triangle, one angle is of 90° which is a right angle.
∴ This is a right-angled triangle.

(iii) Based on sides: In this triangle, two sides are of equal length.
∴ This is an isosceles triangle.
Based on angles: In this triangle one angle is of 110°, which is obtuse angle.
∴ This is an obtuse-angled triangle.

(iv) Based on sides: In this triangle, all the sides are of equal length i.e. each = 4 cm.
∴ This is an equilateral triangle.
Based on angles: In this triangle, all the angles are acute angles.
∴ This is an acute-angled triangle.

(v) Based on sides: In this triangle, all the three sides are of different lengths.
∴ This is a scalene triangle.
Based on angles: In this triangle, one angle is 105°, which is obtuse angle.
∴ This is an obtuse-angled triangle.

6. Fill in the blanks:

Question (i)
A triangle has …………. sides.
Solution:
3

Question (ii)
A triangle has …………. vertices.
Solution:
3

Question (iii)
A triangle has …………. angles.
Solution:
3

Question (iv)
A triangle has …………. parts.
Solution:
6

Question (v)
A triangle whose all sides are different is known as ………………. .
Solution:
Scalene triangle

Question (vi)
A triangle whose all angles are acute is known as ……………….. .
Solution:
Acute angled triangle

Question (vii)
A triangle whose two sides are equal is known as ……………….. .
Solution:
Isosceles triangle

Question (viii)
A triangle whose one angle is obtuse is known as ……………….. .
Solution:
obtuse-angled triangle

Question (ix)
A triangle whose all sides are equal is known as ……………….. .
Solution:
Equilateral triangle

Question (x)
A triangle whose one angle is right angle is known as ……………….. .
Solution:
Right-angled triangle

7. State True or False:

Question (i)
Each equilateral triangle is an isosceles triangle.
Solution:
True

Question (ii)
Each acute-angled triangle is a scalene triangle.
Solution:
False

Question (iii)
Each isosceles triangle is an equilateral triangle.
Solution:
False

Question (iv)
There are two obtuse angles in an obtuse triangle.
Solution:
False

Question (v)
In right triangle, there is only one right angle.
Solution:
True

Question (vi)
Right triangle can never be isosceles.
Solution:
False.

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 7 Coordinate Geometry Ex 7.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2

Q.uestion 1.
Find the co-ordinates of the point which divides the join (- 1, 7) and (4, – 3) in the ratio 2 : 3.
Solution:
Let required point be P (x, y) which divides the join of given points A (- 1, 7)
and B (4, – 3) in the ratio of 2 : 3.
(-1, 7) (x, y) (4, – 3)

∴ x = \(\frac{2 \times 4+3 \times-1}{2+3}=\frac{8-3}{5}=\frac{5}{5}=1\)

and y = \(\frac{2 \times-3+3 \times 7}{2+3}=\frac{-6+21}{5}=\frac{15}{5}=3\)
Hence, required point be (1, 3).

Question 2.
Find the co-ordinates of the points of trisection of the line segment joining (4, – 1) and (2, – 3).
Solution:
Let P (x₁, y₁) and Q (x₂, y₂) be the required points which trisect the line segment joining A (4, – 1)and B (- 2, – 3) i.e., P(x₁, y₁) divides AB in ratio 1: 2 and Q divides AB in ratio 2 : 1.

∴ x₁ = \(\frac{1 \times-2+2 \times 4}{1+2}=\frac{-2+8}{3}=\frac{6}{3}=2\)

and y₁ = \(\frac{1 \times-3+2 \times-1}{1+2}=\frac{-3-2}{3}=-\frac{5}{3}\)
∴ P(x₁, y₁) be (2, \(-\frac{5}{3}\))

Now, x₂ = \(\frac{2 \times-2+1 \times 4}{2+1}\)
= \(\frac{-4+4}{3}\) = 0

y₂ = \(\frac{2 \times-3+1 \times-1}{2+1}=\frac{-6-1}{3}=-\frac{7}{3}\)

∴ Q(x₂, y₂) be (0, \(-\frac{7}{3}\))
Hence, required points be (2, \(-\frac{5}{3}\)) and (0, \(-\frac{7}{3}\)).

Question 3.
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in fig. Niharika runs \(\frac{1}{4}\) th the distance AD on the 2nd line and posts a green flag.

Preet runs \(\frac{1}{5}\) th the distance AD on the eighth line and posts a red flag. What is the distance betweenboth the flags? If Rashmi has to post a blue flag exactly half way between the line (segment) joining the two flags, where should she post her flag?

Solution:
In the given figure, we take A as origin. Taking x-axis along AB and y-axis along AD.
Position of green flag = distance covered by Niharika
= Niharika runs \(\frac{1}{4}\)th distance AD on the 2nd line
= \(\frac{1}{4}\) × 100 = 25 m
∴ Co-ordinates of the green flag are (2, 25)
Now, position of red flag = distance covered by Preet = Preet runs \(\frac{1}{5}\)th the distance AD on the 8th line
= \(\frac{1}{5}\) × 100 = 20 m.
Co-ordinates of red flag are (8, 20)
∴ distance between Green and Red flags = \(\sqrt{(8-2)^{2}+(20-25)^{2}}\)
= \(\sqrt{36+25}=\sqrt{61}\) m.
Position of blue flag = mid point of green flag and red flag
= \(\left(\frac{2+8}{2}, \frac{25+20}{2}\right)\)
= (5, 22.5).
Hence, blue flag is in the 5th line and at a distance of 22.5 m along AD.

Question 4.
Find the ratio in which (he segment joining the points (- 3, 10) and (6, – 8) is divided by (- 1, 6).
Solution:
Let point P (- 1, 6) divides the line segment joining the points A (- 3, 10) and B (6, – 8) the ratio K : 1.

∴ -1 = \(\frac{6 \times \mathrm{K}-3 \times 1}{\mathrm{~K}+1}\)
or – K – 1 = 6K – 3
or – K – 6K = – 3 + 1
or – 7K = – 2
K : 1 = \(\frac{2}{7}\) : 1 = 2 : 7
Hence, required ratio is 2 : 7.

Question 5.
Find the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis. Also find the co
ordinates of the point of division.
Solution:
Let required point on x-axis is P (x, 0) which divides the line segment joining the points A (1, – 5) and B (- 4, 5) in the
ratio K : 1.

Consider, y co-ordinates of P ¡s:
0 = \(\frac{5 \times \mathrm{K}+(-5) \times 1}{\mathrm{~K}+1}\)

or 0 = \(\frac{5 \mathrm{~K}-5}{\mathrm{~K}+1}\)
or 5K – 5 = 0
or 5K = 5
or K = \(\frac{5}{5}\) = 1
∴ Required ratio is K : 1 = 1 : 1.
Now, x co-ordinate of P is:
x = \(\frac{-4 \times K+1 \times 1}{K+1}\)
Putting the value of K = 1, we get:
x = \(\frac{-4 \times 1+1 \times 1}{1+1}=\frac{-4+1}{2}\)
x = \(-\frac{3}{2}\)
Hence, required point be (\(-\frac{3}{2}\), 0).

Question 6.
If (1, 2); (4, y); (x, 6) and (3, 5)are the vertices of a parallelogram taken in order, find x and y.
Solution:
Let points of parallelogram ABCD are A (1, 2) (4, y) ; C (x, 6) and D (3, 5)
But diagonals of a || gm bisect each other.
Case I. When E is the mid point of A (1, 2) and C (x, 6)
∴ Co-ordinates of E are:
E = \(\left(\frac{x+1}{2}, \frac{6+2}{2}\right)\)
E = (\(\frac{x+1}{2}\), 4) …………..(1)

Case II. When E is the mid point B (4, y) and D (3, 5)
∴ Co-ordinates of E are:

E = \(\left(\frac{3+4}{2}, \frac{5+y}{2}\right)\)

E = \(\left(\frac{7}{2}, \frac{5+y}{2}\right)\) …………….(2)
But values of E in (1) and (2) are same, so comparing the coordinates, we get
\(\frac{x+1}{2}=\frac{7}{2}\)
or x + 1 = 7
or x = 6.

and 4 = \(\frac{5+y}{2}\)
or 8 = 5 + y
or y = 3
Hence, values of x and y are 6 and 3.

Question 7.
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).
Solution:
Let, coordinates of A be (x, y). But, centre is the’ niij ioint of the vertices of the diameter.

∴ O is the mid point of A(x, y) and B(1, 4)
∴ \(\left(\frac{x+1}{2}, \frac{y+4}{2}\right)\) = (2, -3)
On comparing, we get
\(\frac{x+1}{2}\)
or x + 1 = 4
or x = 3

and \(\frac{y+4}{2}\) = – 3
or y + 4 = – 6
or y = – 10
Hence, required point A be (3, – 10).

Question 8.
If A and B are (- 2, – 2) and (2, – 4) respectively, find the coordinates of P such that AP = AB and P lies ¡n the line segment AB.
Solution:
Let required point P be (x, y)
Also AP = \(\frac{3}{7}\) AB …(Given)
But, PB = AB – AP
= AB – \(\frac{3}{7}\) AB = \(\frac{7-3}{7}\) AB
PB = \(\frac{4}{7}\) AB
∴ \(\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{\frac{3}{7} \mathrm{AB}}{\frac{4}{7} \mathrm{AB}}=\frac{3}{4}\).

∴ P divides given points A and B in ratio 3 : 4.
Now,
x = \(\frac{3 \times 2+4 \times-2}{3+4}\)

or x = \(\frac{6-8}{7}=-\frac{2}{7}\)

and y = \(\frac{3 \times-4+4 \times-2}{3+4}\)
= \(\frac{-12-8}{7}=-\frac{20}{7}\)

Hence, coordinates of P be (\(-\frac{2}{7}\), \(-\frac{20}{7}\)).

Question 9.
Find the coordinates of the points which divides the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.
Solution:
Let required points are C, D and E which divide the line segment joming the points A (- 2, 2) and B (2, 8) into four equal parts. Then D is mid point of A and B ; C is the mid point of A and D ; E is the mid point of D and B such that
AC = CD = DE = EB

Now, mid point of A and B (i.e., Coordinates of D)
= \(\left(\frac{-2+2}{2}, \frac{2+8}{2}\right)\) = (0, 5)

Mid point of A and D (i.e., Coordinates of C)
= \(\left(\frac{-2+0}{2}, \frac{2+5}{2}\right)=\left(-1, \frac{7}{2}\right)\)

Mid point of D and B (i.e., Coordinates of E)
= \(\left(\frac{2+0}{2}, \frac{8+5}{2}\right)=\left(1, \frac{13}{2}\right)\)

Hence, requned points be (0, 5), (-1, \(\frac{7}{2}\)), (1, \(\frac{13}{2}\)).

Question 10.
Find the area of a rhombus if the vertices are (3, 0); (4, 5); (- 1, 4) and(- 2, – 1) taken in order.
[Hint: Areas of a rhombus = \(\frac{1}{2}\) (Product of its diagonals)]
Solution:
Let coordinates of rhombus ABCD are A (3, 0); B(4, 5); C(-1, 4) and D(- 2, – 1).
Diagonal, AC = \(\sqrt{(-1-3)^{2}+(4-0)^{2}}\)
= \(\sqrt{16+16}=\sqrt{32}=\sqrt{16 \times 2}\) = 4√2

and diagonal BD
BD = \(\sqrt{(-2-4)^{2}+(-1-5)^{2}}\)
= \(\sqrt{36+36}=\sqrt{72}=\sqrt{36 \times 2}\) = 6√2.

∴ Area of rhombus ABCD = \(\frac{1}{2}\) × AC × BD
ABCD = [\(\frac{1}{2}\) × 4√2 × 6√2] sq. units
(\(\frac{1}{2}\) × 24 × 2) sq. units
= 24 sq. units
Hence, area of rhombus is 24 sq. units.

Punjab State Board PSEB 8th Class English Book Solutions English Grammar Determiners Exercise Questions and Answers, Notes.

PSEB 8th Class English Grammar Determiners

Determiners वे शब्द है जो संज्ञा (noun) से पूर्व उसके अर्थ को किसी न किसी रूप से स्माष्ट करने या निरिचत करने के लिए प्रयुक्त होते हैं। यहां पर हम Determiners की एक सूची दे रहे हैं-
(i) Demonstratives. this, that, these, those.
(ii) Possessives. my, your, his, her, its, our, their
(iii) Cardinal numbers. one, two, three, etc.
(iv) Ordinal numbers. first, second, third, etc.
(v) Articles. a, an, the.
(vi) Miscellaneous. Some, any, both, certain, enough, few, every, least, less, little, more, most, much, next, other, own, plenty, several, such, many, another, each, no, a few, a large number of, a small number of, a great deal of, a good deal of, a large quantity of, a small quantity of, all, etc.

(i) Demonstratives (Paderat ya). This, that, these, those the procesu alert a Ridha करते हैं। अत: वे निर्देशक कहलाते हैं और इनसे Determiners की एक श्रेणी बनती है; जैसे:

• This book was purchased by me.
• That book was purchased by me.
• These girls are singing.
• Those girls are dancing.

Note. This और that एकवचन हैं जबकि these और those बहुवचन हैं।

(ii) Possessives (सम्बन्धवचक सब्द). My, her, your, his its, our, their सम्बन्धवचक सर्वनाम है ओर इनका प्रयोग एकवचन और बहुवचन दोनों प्रकार की संज्ञाओं के साथ किया जाता है; जैसे,
1. (a) I like my book. (Singular)
(b) I kept my books in order. (Plural)

2. (a) He told his story in tears. (Singular)
(b) People tell his stories in tears (Plural)

3. (a) Let me see your note-book. (Singular)
(b) Teacher will check your note-books. (Plural)

Note. सम्बन्धवाचक शब्द अगणनीय संज्ञाओं से पूर्व भी प्रयुक्त किए जा सकते हैं; जैसे-

• I took my bath. (uncountable)
• His courage failed him. (uncountable)
• We cannot doubt their patriotism. (uncountable)

(iii) and (iv) Cardinal and Ordinal Numbers.
Cardinal and Ordinal संख्याएं भी Determiners का एक भाग हैं।

• Two miles are left to be covered.
• I am reading the third chapter now.
• I need fifty rupees for this.

(v) The Articles. a, an तथा the को अंग्रेजी व्याकरण में articles के नाम से पुकारा जाता है। ये वास्तव में Adjective determiners हैं।

Filling the Blanks with Articles

1. Ram is ………. honest man. (an)
2. ………. book you gave me is lost. (The)
3. ………. cow is a useful animal. (The)
4. ………. Himalayas have many ranges. (The)
5. Gardening is ………. useful hobby. (a)
6. I have been waiting for you for ……. hour. (an)
7. I saw ……. Sri Harmandar Sahib. (the)
8. Who is ……… head of your family ? (the)
9. He is ……… boy who stole my pen. (the)
10. Our Principal is ……… intelligent man. (an)
11. ………. stitch in time saves nine. (A)
12. Do not make ………. noise (a)
13. My brother is ………. M.A., you are ………. B.A. (an, a)
14. New Delhi is ……… capital of India. (the)
15. This is ……… interesting story. (an)
16. He has ……… lot of money. (a)
17. He has ………. monthly income of Rs. 7000. (a)
18. ………. stars are a beautiful sight. (The)
19. Give me ……… apple or ………. orange. (an, an)
20. You should always show sympathy to ……… poor. (the)
21. Get me ………. nice cup of tea. (a)
22. This is ………. excellent watch. (an)
23. ………. rose smells sweet. (The)
24. Where is ………. book which I gave you? (the)
25. He is ……….. able student but not ………. ablest. (an, the)
26. Why are you in ………. hurry? (a)
27. I hate ………. dishonest servant. (a)
28. He is ……. idiot. (an)
29. ……… rich are not always happy. (The)
30. …….. moon has risen. (The)
31. There was ………. army of monkeys near …….. temple. (an, the)
32. This is quite …….. new idea. (a)
33. He is ………. hardworking boy. (a)
34. I need ………. pen and ………. inkpot. (a, an)
35. I read ……… Hindustan Times everyday. (the)
36. I have not seen ……… Taj as yet. (the)
37. ………. bad workman quarrels with his tools. (A)
38. ………. apple ………. day keeps ………. doctor away. (An, a, the)
39. …….. Ganga is ……… sacred river. (The, a)

More Exercises (Solved)

1. Fill up the blanks with the Articles (a, an, the):

1. He can read ………. Vedas.
2. She is ……… intelligent girl.
3. …….. sun shines brightly.
4. Life is not ………. bed of roses.
5. ……… higher you climb ……… colder it gets.
6. In ………. park I saw ………. one-eyed beggar.
7. Mumbai is ………. Manchester of India.
8. ………. Sikhs are a brave nation.
9. ………. owl cannot see during day time.
10. ………. Ganges is ………. sacred river.
11. We started late in ………. afternoon.
12. ………. rose smells sweet.
13. He reads ………. Bible everyday.
14. Kalidas was …….. Shakespeare of India.
15. Einstein was ………. Newton.
16. I read ………. Tribune daily.
17. I am in ……… hurry.
18. Help ……… poor.
19. Both ………. robbers were arrested.
20. Keep to ….. left.
21. ……… housemaid pulls up ……….. blind.
22. What ………. lovely girl !
23. What ……… ripe apple !
24. Not ……… word was said.
25. Help ……… poor, ……… needy and ………. miserable.
Hints:
1. the
2. an
3. The
4. a
5. The, the
6. the, a
7. the
8. The
9. An
10. The, a
11. the
12. The
13. the
14. the
15. the
16. the
17. a
18. the
19. the
20. the
21. The, the
22. a
23. a
24. a
25. the, the, the.

II. Correct the following sentences:

1. Only few. men are honest.
2. The man is mortal.
3. He acted like man.
4. Beas flows in Punjab.
5. You are in wrong but he is in right.
6. He is by far ablest boy.
7. Nobody likes a person with bad temper
8. The iron is useful metal.
9. Not word was said.
10. He has too high a opinion of you.
11. Learn this poem by the heart.
12. Never tell lie.
Hints:
1. Only a few men are honest.
2. Man is mortal.
3. He acted like a man.
4. The Beas flows in the Punjab.
5. You are in the wrong but he is in the right.
6. He is by far the ablest boy.
7. Nobody likes a person with a bad temper.
8. Iron is a useful metal.
9. Not a word was said.
10. He has too high an opinion of you.
11. Learn this poem by heart.
12. Never tell a lie.

III. Fill in the blanks with suitable determiners:

1. I went to ………. window which commanded a large green garden.
2. I have heard so ……… about your school.
3. Look out of the window for ………. minute.
4. It is really something of ………. joke.
5. There you have …….. essential part of our system.
6. I asked her by way of ………. opening.
7. But I had ………. idea of all this.
8. Come down into ………. garden.
9. Having ………. arm tied up is troublesome.
10. It educates both ………. blind and the helpers.
Hints:
1. the
2. much
3. a
4. a
5. an
6. an
7. an
8. the
9. an
10. the.

IV. Insert the determiners this, that, these, those in the blanks:

1. ………. shirt is costly but ……… shirt is cheap.
2. Would you like to take … book or ………. one ?
3. ……… sum cannot be solved by ………. silly boys.
4. ……… flowers are beautiful but ………. flowers are ordinary ones.
5. He likes this pair of trousers but he does not like ……… one.
Hints :
1. This, that
2. this, that
3. This, those
4. These, those
5. that.

V. Insert ‘a few’ or ‘the few’ whichever is suitable:

1. ………. books she had were all lost.
2. It is question of spending ………. rupees.
3. ………. suggestions she gave were all carried out.
4. …….. hints on essay-writing are quite to the point.
5. ………. boys attended the class.
Hints:
1. The few
2. a few
3. The few
4. A few
5. A few.

VI. Insert ‘little’, a little, or ‘the little’ whichever is suitable

1. ………. knowledge is a dangerous thing.
2. There is ………. hope of his recovery.
3. He has ………. money with him.
4. ……… Strength he had in him proved useless.
5. He takes ……… interest in me.
Hints:
1. A little
2. little
3. a little
4. The little
5. little.

VII. Fill in the blanks with determiners ‘each, every, either or neither:

1. ………. pen costs ten rupees.
2. He comes here on ………. Sunday.
3. ………. of you may take this book.
4. ………. man wants to rise in the world.
5. ………. seat in the hall was occupied.
Hints:
1. Each
2. every
3. Either
4. Every
5. Every.