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.