Class 6

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 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 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes Ex 9.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 9 Understanding Elementary Shapes Ex 9.3

1. Identify the shape having perpendicular lines:

Solution:
(ii), (iii), (v).

2. Identify the examples having perpendicular lines:

Question (i)
(i) Lines of railway track.
(ii) Adjacent edges of a table.
(iii) Line segment forming letter ‘L’.
Solution:
(ii) Adjacent edges of a table.
(iii) Line segment forming letter ‘L’.

3. Let \(\overrightarrow{\mathbf{AB}}\) be perpendicular to \(\overrightarrow{\mathbf{PQ}}\) and they intersect at O. What is the measure of \(\angle \mathbf{AOP}\)?
Solution:

\(\angle \mathbf{AOP}\) = 90°, because AB ⊥ PQ.

4. Line m is perpendicular to line l in the given figure. Each point on the line l is marked at equal intervals. Study the diagram and state true or false.

Question (i)
Line m is ⊥ bisector of line segment AI.
Solution:
True

Question (ii)
CE = EG
Solution:
True

Question (iii)
DF = 2DE.
Solution:
True.

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes Ex 9.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 9 Understanding Elementary Shapes Ex 9.2

1. Classify the angles as acute, obtuse, right, straight or reflex angles:

Solution:
(i) Acute angle
(ii) Obtuse angle
(iii) Reflex angle
(iv) Straight angle
(v) Acute angle
(vi) Right angle
(vii) Obtuse angle
(viii) Right angle
(ix) Reflex angle
(x) Acute angle.

2. Classify the angles:

Question (i)
80°
Solution:
80° is between 0° and 90°.
∴ It is an acute angle.

Question (ii)
172°
Solution:
172° is between 90° and 180°
∴ It is an obtuse angle.

Question (iii)
90°
Solution:
90° is a right angle.

Question (iv)
0°
Solution:
0° is a zero angle.

Question (v)
179°
Solution:
179° is between 90° and 180°.
∴ It is an obtuse angle.

Question (vi)
215°
Solution:
215° is between 180° and 360°.
∴ It is an reflex angle.

Question (vii)
360°
Solution:
360° is a complete angle.

Question (viii)
350°
Solution:
350° is between 180° and 360°.
∴ It is a reflex angle.

Question (ix)
15°
Solution:
15° is between 0° and 90°.
∴ It is an acute angle.

Question (x)
180°
Solution:
180° is a straight angle.

3. Measure the following angles with protractor and write their measurement:

Solution:
(i) 60°
(ii) 125°
(iii) 110°
(iv) 80°
(v) 120°
(vi) 105°
(vii) 80°
(viii) 135°
(ix) 88°
(x) 90°.

4. How many degrees are there in

Question (i)
Two right angles
Solution:
1 right angle = 90°
∴ Two right angles = 2 × 90°
= 180°

Question (ii)
\(\frac {2}{3}\) right angles
Solution:
1 right angle = 90°
∴ \(\frac {2}{3}\) right angles = \(\frac {2}{3}\) × 90°
= 2 × 30°
= 60°

Question (iii)
Four right angles?
Solution:
1 right angle = 90°
∴ Four right angles = 4 × 90°
= 360°

5. What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from:

Question (i)
3 to 9
Solution:
3 to 9 : Half or \(\frac {1}{2}\)

Question (ii)
5 to 8
Solution:
5 to 8 : Quarter or \(\frac {1}{4}\)

Question (iii)
10 to 4
Solution:
10 to 4 : Half or \(\frac {1}{2}\)

Question (iv)
2 to 11
Solution:
2 to 11 : 3 Quarters or \(\frac {3}{4}\)

Question (v)
6 to 3
Solution:
6 to 3 : 3 Quarters or \(\frac {3}{4}\)

Question (vi)
2 to 7.
Solution:
2 to 7 : \(\frac {5}{12}\)

6. Find the number of right angles turned through by the hour hand of a dock when it goes from

Question (i)
5 to 8
Solution:
5 to 8 : 1 right angle

Question (ii)
1 to 7
Solution:
1 to 7 : 2 right angles

Question (iii)
4 to 10
Solution:
4 to 10 : 2 right angles

Question (iv)
9 to 12
Solution:
9 to 12 : 1 right angles

Question (v)
11 to 2
Solution:
11 to 2 : 1 right angles

Question (vi)
9 to 6
Solution:
9 to 6 : 3 right angles

Question (vii)
2 to 11
Solution:
2 to 11 : 3 right angles

Question (viii)
10 to 1
Solution:
10 to 1 : 1 right angles

Question (ix)
12 to 6
Solution:
12 to 6 : 2 right angles

Question (x)
5 to 2.
Solution:
5 to 2 : 3 right angles.

7. Where will be the hand of a clock stop if it starts at:

Question (i)
12 and make \(\frac {1}{4}\) revolution clock-wise.
Solution:
For 1 revolution, the hour hand takes 12 hours.
For \(\frac {1}{4}\) revolution, the hour hand takes \(\frac {1}{4}\) × 12 hours = 3 hours.
If hour hand starts at 12 and make \(\frac {1}{4}\) revolution clockwise it will stop at 3.

Question (ii)
2 and make \(\frac {1}{2}\) revolution clock-wise.
Solution:
For 1 revolution, the hour hand takes 12 hours.
For \(\frac {1}{2}\) revolution, the hour hand takes \(\frac {1}{2}\) × 12 hours = 6 hours.
If hour hand starts at 2 and make \(\frac {1}{2}\) revolution clockwise it will stop at 8.

Question (iii)
5 and make \(\frac {1}{4}\) revolution clock-wise.
Solution:
For 1 revolution, the hour hand takes 12 hours.
For \(\frac {1}{4}\) revolution, the hour hand takes \(\frac {1}{4}\) × 12 hours = 3 hours
If hour hand starts at 5 and make \(\frac {1}{4}\) revolution clockwise it will stop at 8.

Question (iv)
5 and make \(\frac {3}{4}\) revolution clock-wise.
Solution:
For 1 revolution, the hour hand takes 12 hours .
For \(\frac {3}{4}\) revolution, the hour hand takes \(\frac {3}{4}\) × 12 hours = 9 hours.
If hour hand starts at 5 and make \(\frac {3}{4}\) revolution clockwise it will stop at 2.

8. What part of revolution have you turned through if you stand facing:

Question (i)
East and turn clockwise to North
Solution:
I turned through \(\frac {3}{4}\) part of a revolution.

Question (ii)
South and turn clockwise to North
Solution:
I turned through \(\frac {1}{2}\) part of a revolution.

Question (iii)
South and turn clockwise to East
Solution:
I turned through \(\frac {3}{4}\) part of a revolution.

Question (iv)
West and turn clockwise to East
Solution:
I turned through \(\frac {1}{2}\) part of at revolution.

9. Find the angle measure between the hands of the clock in each figure:

Solution:
(i) Angle measure between the hands of the clock at 3.00 a.m.
= \(\frac {3}{12}\) × 360° = 90°
(ii) Angle measure between the hands of the clock at 6.00 a.m.
= \(\frac {6}{12}\) × 360° = 180°
(iii) Angle measure between the hands of the clock at 2.00 a.m.
= \(\frac {2}{12}\) × 360° = 60°

10. Draw the following angles by protractor:

Question (i)
(i) 40°
(ii) 75°
(iii) 105°
(iv) 90°
(v) 130°
Solution:

11. State true or false:

Question (i)
The sum of two right angles is always a straight angle.
Solution:
True

Question (ii)
The sum of two acute angles is always a reflex angle.
Solution:
False

Question (iiii)
The obtuse angle has measurement between 90° to 180°.
Solution:
True

Question (iv)
A complete revolution has four right angles.
Solution:
True

12. Fill in the blanks:

Question (i)
The angle which is greater than 0° and less than 90° is called ………….. .
Solution:
acute angle

Question (ii)
The angle whose measurement equal to two right angle is …………….. .
Solution:
straight angle

Question (iii)
The angle between 90° and 180° is ……………. .
Solution:
obtuse angle.

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 9 Understanding Elementary Shapes Ex 9.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 9 Understanding Elementary Shapes Ex 9.1

1. Measure the line segments using a ruler and a divider:

Solution:
(i) PQ = 4.4 cm
(ii) CD = 3.6 cm
(iii) XY = 2.5 cm
(iv) AB = 5.8 cm
(v) LM = 5 cm.

2. Compare the line segments in the figure and fill in the blanks:

Question (i)
AB _ AB
Solution:
AB = AB

Question (ii)
CD _ AC
Solution:
CD < AC Question (iii) AC _ AD Solution: AC > AD

Question (iv)
BC _ AC
Solution:
BC < AC Question (v) BD _ CD. Solution: BD > CD.

3. Draw any line segment AB. Take any point C between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?
Solution:
If A, B, C are any three points on a line such that AC + CB = AB, then we are sure that C lies between A and B.

On measuring the lengths of AB, BC and AC, we get
AB = 6 cm, AC = 4 cm, CB = 2 cm
Now, AC + CB = 4 cm + 2 cm = 6 cm
Hence, AB = AC + CB.

4. Draw a line segment AB = 5 cm and AC = 9 cm in such a way that points A, B, C are collinear. What is the length of BC?
Solution:

AB = 5 cm and AC = 9 cm
Since, A, B and C are collinear
∴ AB + BC = AC
⇒ 5 cm + BC = 9 cm
⇒ BC = 9 cm – 5 cm
= 4 cm.
Hence, Length of BC = 4 cm

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 8 Basic Geometrical Concepts MCQ Questions with Answers.

PSEB 6th Class Maths Chapter 8 Basic Geometrical Concepts MCQ Questions

Multiple Choice Questions

Question 1.
How many lines can pass through a point?
(a) 1
(b) 2
(c) 4
(d) Infinite.
Answer:
(d) Infinite.

Question 2.
The number of points lie on a line are
(a) 2
(b) 4
(c) 1
(d) Infinite.
Answer:
(d) Infinite.

Question 3.
The number of lines passes through two points are ……………… .
(a) 1
(b) 2
(c) 3
(d) Infinite.
Answer:
(a) 1

Question 4.
In how many parts, a closed curve divides the plane?
(a) 1
(b) 2
(c) 3
(d) 4.
Answer:
(c) 3

Question 5.
A quadrilateral has……………. diagonals.
(a) 1
(b) 2
(c) 3
(d) 4.
Answer:
(b) 2

Question 6.
Which of the following is not a polygon?
(a) Triangle
(b) Pentagon
(c) Circle
(d) Quadrilateral.
Answer:
(c) Circle

Question 7.
A triangle has…………… parts.
(a) 3
(b) 6
(c) 9
(d) 2.
Answer:
(b) 6

Question 8.
Which of file following is not a quadrilateral?

Answer:

Question 9.
A line segment joining the opposite vertices of a quadrilateral is called its …………. .
(a) Diagonal
(b) Side
(c) Angle
(d) Region.
Answer:
(a) Diagonal

Question 10.
The radius of a circle is 4 cm then the diameter is …………….. .
(a) 8 cm
(b) 2 cm
(c) 6 cm
(d) 12 cm.
Answer:
(a) 8 cm

Question 11.
The diameter of a circle is 12 cm then the radius is …………….. .
(a) 24 cm
(b) 6 cm
(c) 18 cm
(d) 4 cm.
Answer:
(b) 6 cm

Question 12.
The longest chord of a circle is…………….
(a) Arc
(b) Perimeter
(c) Diameter
(d) Radius.
Answer:
(c) Diameter

Question 13.
Which of the following figure is not a polygon?

Answer:

Question 14.
Which of the following figure is a polygon?

Answer:

Question 15.
Which of the following is a closed curve?

Answer:

Question 16.
Which of the following is an open curve?

Answer:

Question 17.
Two different line when intersect each other at some point, they are called:
(a) Intersecting lines
(b) Parallel lines
(c) Concurrent lines
(d) None of these.
Answer:
(a) Intersecting lines

Fill in the blanks:

Question (i)
In the environment, a railway track is an example of ……………. .
Answer:
parallel lines

Question (ii)
In the environment, a nail fixed in the wall is an example of ……………….. .
Answer:
a point

Question (iii)
The intersection of the three walls of a room, is an example of …………… .
Answer:
concurrent lines

Question (iv)
……………….. is the longest chord of a circle.
Answer:
Diameter

Question (v)
A triangle has ……………… part.
Answer:
six

Write True/False:

Question (i)
Three lines can pass through a point. (True/False)
Answer:
False

Question (ii)
The number of lines passing through two points is one. (True/False)
Answer:
True

Question (iii)
Every circle has a centre. (True/False)
Answer:
True

Question (iv)
The diameter is twice the radius. (True/False)
Answer:
True

Question (v)
Every chord of a circle is also a diameter. (True/False)
Answer:
False

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 8 Basic Geometrical Concepts Ex 8.6 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 8 Basic Geometrical Concepts Ex 8.6

1. In the given figure, write the name of:

Question (i)
Centre
Solution:
Centre: O

Question (ii)
Radii
Solution:
Radii: OX, OY, OP

Question (iii)
Diameter
Solution:
Diameter: XY

Question (iv)
Chord.
Solution:
Chord: QR.

2. In the given figure, write the name

Question (i)
minor arc
Solution:
Minor arc : PAQ

Question (ii)
major arc
Solution:
Major arc : PBQ

Question (iii)
minor sector
Solution:
Minor sector: OPAQ

Question (iv)
major sector.
Solution:
Major sector : OPBQ.

3. In the given figure, write the name

Question (i)
Minor segment
Solution:
Minor segment: ACBA

Question (ii)
Major segment.
Solution:
Major segment: ADBA

4. In the given figure, name the points:

Question (i)
In its interior
Solution:
Points in its interior : O, A, D, F

Question (ii)
On its boundary (circumference)
Solution:
Points on its boundary (circumference) C

Question (iii)
In its exterior.
Solution:
Points in its exterior : B, E

5. Find the diameter of the circle whose radius is:

Question (i)
5 cm
Solution:
Given Radius of the circle = 5 cm
∴ Diameter of the Circle = 2 × radius = 2 × 5 cm = 10 cm

Question (ii)
4 cm
Solution:
Given radius of the circle = 4 cm
∴ Diameter of the circle = 2 × radius = 2 × 4m = 8m

Question (iii)
10 cm.
Solution:
Given radius of the circle = 10 cm
∴ Diameter of circle = 2 × Radius = 2 × 10 cm = 20 cm

6. If the diameter of the circle is 12 cm. Find the radius:
Solution:
Given diameter of a circle = 12 cm
∴ Radius of circle = Diameter + 2
= 12 cm + 2
= 6 cm

7. Fill in the blanks:

Question (i)
The distance around a circle is called ……………… .
Solution:
Circumference

Question (ii)
The diameter of a circle is ……………… times its radius.
Solution:
two

Question (iii)
The longest chord of circle is …………….. .
Solution:
diameter

Question (iv)
All the radii of a circle are of ……………… length.
Solution:
equal

Question (v)
The diameter of a circle passes through ……………. .
Solution:
centre

Question (vi)
A circle divides all the points in a plane into ……………… parts.
Solution:
three.

8. State true or false:

Question (i)
The diameter of a circle is equal to its radius.
Solution:
False

Question (ii)
The diameter is a chord of circle.
Solution:
True

Question (iii)
A radius is a chord of the circle.
Solution:
False

Question (iv)
Every circle has a centre.
Solution:
True

Question (v)
The region enclosed by a chord and arc is called a segment
Solution:
True

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 8 Basic Geometrical Concepts Ex 8.5 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 8 Basic Geometrical Concepts Ex 8.5

1. Out of the following, Identify the quadrilateral:

Solution:

2. Name the given quadrilaterals:

Solution:
(i) ABCD
(ii) PQRS
(iii) XYZW.

3. Write the name of all vertices, angles, sides, diagonals of the following quadrilaterals:

Solution:
(i) Vertices = O, N, M, L;
Angles = \(\angle \mathrm{O}, \angle \mathrm{N}, \angle \mathrm{M}, \angle \mathrm{L}\)
Sides = ON, NM, ML, LO;
Diagonals = OM, NL

(ii) Vertices = H, G, F, E;
Angles = \(\angle \mathrm{H}, \angle \mathrm{G}, \angle \mathrm{F}, \angle \mathrm{E}\)
Sides = HG, GF, FE, EH;
Diagonals = EG, FH.

4. For the given quadrilateral ABCD, name:

Question (i)
(i) Side opposite to AB
(ii) Angles adjacent to B
(iii) Diagonal joining B and D
(iv) Angle opposite to A
(v) Sides adjacent to CD.

Solution:
(i) CD
(ii) \(\angle \mathrm{A} \text { and } \angle \mathrm{C}\)
(iii) BD
(iv) \(\angle \mathrm{C}\)
(v) AD and BC.

5. In the given quadrilateral JUMP, name the points.

Question (i)
In its interior
Solution:
Points in the interior of quad. JUMP are :
L, N, C

Question (ii)
In its exterior
Solution:
Points in its exterior of quad. JUMP are :
B, O, X

Question (iii)
On its boundary.
Solution:
Points on the boundary of quad. JUMP are :
P, M, U, Y, J, A.

6. Fill in the blanks:

Question (i)
A quadrilateral has …………….. vertices.
Solution:
4

Question (ii)
A quadrilateral has …………… sides.
Solution:
4

Question (iii)
A quadrilateral has …………… angles.
Solution:
4

Question (iv)
A quadrilateral has ………….. diagonals.
Solution:
2

Question (v)
A diagonal divides the quadrilateral into……………… triangles.
Solution:
2

Question (vi)
A line segment joining the opposite vertices of a quadrilateral is called its ………. .
Solution:
Diagonal

Question (vii)
The interior and the boundary of a quadrilateral together constitute the ……………. region.
Solution:
Quadrilateral.

7. State True or False:

Question (i)
A diagonal divides quadrilateral into four triangles.
Solution:
False

Question (ii)
The angle that have a common vertex are called adjacent angles.
Solution:
True

Question (iii)
The sides that have a common vertex are called adjacent sides.
Solution:
True

Question (iv)
A quadrilateral has four diagonals.
Solution:
False

Question (v)
The quadrilateral region consists of the exterior and the boundary of the quadrilateral.
Solution:
False

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 8 Basic Geometrical Concepts Ex 8.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 8 Basic Geometrical Concepts Ex 8.4

1. Write all the names of the following triangles in all orders:

Solution:
(i) ∆ABC, ∆ACB, ∆BAC, ∆BCA, ∆CAB, ∆CBA.
(ii) ∆XYZ, ∆XZY, ∆YZX, ∆YXZ, ∆ZXY, ∆ZYX
(iii) ∆LMN, ∆LNM, ∆MNL, ∆MLN, ∆NML, ∆NLM.

2. Write the name of vertices, sides and angles of the following triangles:

Solution:

	(i)	(ii)	(iii)
Vertices	P, R, Q	D, E, F	T, P, S
Sides	PR, QR, PQ	DE, EF, DF	TP, PS, TS
Angles	\(\angle \mathrm{P}, \angle \mathrm{R}, \angle \mathrm{Q}\)	\(\angle \mathrm{D}, \angle \mathrm{E}, \angle \mathrm{F}\)	\(\angle \mathrm{T}, \angle \mathrm{P}, \angle \mathrm{S}\)

3. In the given figure, name the points that lie:

Question (i)
On the boundary of ∆GEM
Solution:
Points on the boundary of AGEM are: G, A, E, C, M

Question (ii)
In the interior of ∆GEM
Solution:
Points in the interior of AGEM are : P, X, D

Question (iii)
In the exterior of ∆GEM.
Solution:
Points in the exterior of AGEM are : Y, B.

4. In the given figure, write the name of:

Question (i)
All different triangles
Solution:
All different triangles are :
∆AOD, ∆DOC, ∆BOC, ∆AOB, ∆ABD, ∆BCD, ∆ACD, ∆ABC

Question (ii)
Triangles having O as the vertex
Solution:
Triangles having O as the vertex are :
∆AOB, ∆BOC, ∆COD, ∆AOD

Question (iii)
Triangles having A as the vertex.
Solution:
Triangles having A as the vertex are:
∆AOB, ∆AOD, ∆ABD, ∆ABC, ∆ACD.

5. Fill in the blanks of the following:

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

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

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

Question (iv)
A triangle divide the plane into ……………. parts.
Solution:
3

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

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 8 Basic Geometrical Concepts Ex 8.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 8 Basic Geometrical Concepts Ex 8.3

1. Name the given angles in all ways:

Solution:
(i) \(\angle \mathrm{DEF}, \angle \mathrm{FED}, \angle \mathrm{E}, \angle a\)
(ii) \(\angle \mathrm{XOY}, \angle \mathrm{YOX}, \angle \mathrm{O}, \angle 1\)
(iii) \(\angle N O M, \angle M O N, \angle O, \angle x\)

2. Name the vertex and the arms of given angles:

Solution:

	(i)	(ii)	(iii)
Vertex	B	Q	o
Arm	\(\overrightarrow{\mathrm{BC}}, \overrightarrow{\mathrm{BA}}\)	\(\overrightarrow{\mathrm{QP}}, \overrightarrow{\mathrm{QR}}\)	\(\overrightarrow{\mathrm{OS}}, \overrightarrow{\mathrm{OP}}\)

3. Name all the angles of the given figure:

Solution:
(i) \(\angle \mathrm{X}, \angle \mathrm{Y}, \angle \mathrm{Z}\)
(ii) \(\angle \mathrm{P}, \angle \mathrm{Q}, \angle \mathrm{R}, \angle \mathrm{S}\)
(iii) \(\angle \mathrm{AOB}, \angle \mathrm{BOC}, \angle \mathrm{AOC}\)

4. In the given figure, name the points that lie:

Question (i)
In the interior of \(\angle \mathrm{DOE}\)
Solution:
Points in the interior of \(\angle \mathrm{DOE}\) are :
A, X, M

Question (ii)
In the exterior of \(\angle \mathrm{DOE}\)
Solution:
Points in the exterior of \(\angle \mathrm{DOE}\) are :
H, L

Question (iii)
On the \(\angle \mathrm{DOE}\)
Solution:
Points on the \(\angle \mathrm{DOE}\) are :
D, B, O, E.

5. In the given figure, write another name for the following angles :

Question (i)
\(\angle \mathrm{1}\)
Solution:
\(\angle S \text { or } \angle PSR \text { or } \angle RSP\)

Question (ii)
\(\angle \mathrm{2}\)
Solution:
\(\angle \mathrm{RPQ} \text { or } \angle \mathrm{QPR}\)

Question (iii)
\(\angle \mathrm{3}\)
Solution:
\(\angle \mathrm{SRP} \text { or } \angle \mathrm{PRS}\)

Question (iv)
\(\angle \mathrm{a}\)
Solution:
\(\angle \mathrm{Q} \text { or } \angle \mathrm{RQP} \text { or } \angle \mathrm{PQR}\)

Question (v)
\(\angle \mathrm{b}\)
Solution:
\(\angle \mathrm{PRQ} \text { or } \angle \mathrm{QRP}\)