The DAV Class 5 Maths Solutions and **DAV Class 5 Maths Chapter 16 Brain Teasers** Solutions of Triangles offer comprehensive answers to textbook questions.

## DAV Class 5 Maths Ch 16 Brain Teasers Solutions

Question 1.

Tick (✓) the correct answer.

(a) Which of the following cannot be the angles of a triangle?

(i) 70°, 50°, 60°

(ii) 90°, 45°, 45°

(iii) 100°, 40°, 30°

(iv) 100°, 50°, 30°

Solution:

(iii) 100°, 40°, 30°

∵ 100° + 40° + 30° = 170°

(b) The third angle of a right-angled triangle whose one angle is 50° is-

(i) 40°

(ii) 130°

(iii) 55°

(iv) 45°

Solution:

(i) 40°

∴ 90° + 50° + x° = 180°

⇒ x° = 180 – 140°

⇒ x° = 40°

(c) There are ________ triangles in the given figure.

(i) 4

(ii) 6

(iii) 8

(iv) 5

Solution:

(iii) 8

(d) Which of the following can be the third side of a triangle whose two sides are 7 cm and 9 cm respectively?

(i) 16 cm

(ii) 18 cm

(iii) 14 cm

(iv) 17 cm

Solution:

(iii) 14 cm

As sum of the two sides must be greater than the third side.

(e) In the given figure ∆ABC is an equilateral triangle. What type of triangle is ∆ACD?

(i) Scalene triangle

(ii) Right-angled triangle

(iii) Equilateral triangle

(iv) Isosceles triangle

Solution:

(iii) Equilateral triangle

Question 2.

A closed figure is made of three line segments what is the figure called?

Solution:

Triangle

Question 3.

Name the vertices, sides, and angles of a triangle.

Solution:

Vertices = X, Y, Z

Sides = XY, YZ, XZ

Angles = ∠X or ∠YXZ, ∠Y or ∠XYZ, ∠Z or ∠XZY

Question 4.

How many triangles are there in each?

(a)

Solution:

5 triangles

(b)

Solution:

6 triangles

Question 5.

Find the missing angle. State the kind of triangle.

(a)

Solution:

Let the missing angle be x°

52° + 38° + x° = 180° (sum of angles of Δ is 180°)

⇒ 90° + x° = 180°

⇒ x = 90°

(b)

Solution:

Let the missing angle be x°

75° + 65° + x° = 180° (Sum of angles of Δ is 180°)

⇒ 140° + x° = 180°

⇒ x° = 180° – 140°

⇒ x° = 40°

Question 6.

State the kind of triangle.

(a)

Solution:

Isosceles triangle

(b)

Solution:

Equilateral triangle

Question 7.

Can you construct a triangle with angles 70°, 35°, 85°? Why.

Solution:

To construct a triangle we must have the sum of three angles 180°.

70° + 35° + 85° = 190°

But in this case, the sum is greater than 180° so is not possible to construct a triangle.

Question 8.

Can you construct a triangle with line segments of lengths 11 cm, 7 cm, and 8 cm? Give reasons.

Solution:

To construct a triangle, the sum of two sides of a triangle must be greater than the third side.

So 11 cm + 7 cm = 18 cm (sum of two sides)

One of the sides is 8 cm

18 cm > 8 cm possible.

Sum of two sides = 7 cm + 8 cm = 15 cm

Third side = 11 cm

15 cm > 11 cm possible.

Sum of other two sides = 11 cm + 8 cm = 19 cm

Third side = 7 cm

19 cm > 7 cm possible

So we can construct a triangle.

Question 9.

State True or False.

(a) A triangle can have two right angles. ________

Solution:

False

(b) An obtuse-angled triangle has one obtuse angle and two acute angles. ________

Solution:

True

(c) The sum of the lengths of any two sides of a triangle is equal to the third side. ________

Solution:

False

(d) The sides of an equilateral triangle are of equal length. ________

Solution:

True

Additional Questions

Question 1.

Name the closed figure made of three line segments. How many vertices, sides, and angles it has?

Solution:

Triangle: A triangle has three vertices, three sides, and three angles.

Question 2.

Write two properties of a triangle.

Solution:

Two properties are given below:

- The sum of measures of three angles of a triangle is always 180°.
- The sum of the two sides of a triangle is always greater than the third side.

Question 3.

How many ways a triangle is classified?

Solution:

Triangles are classified in two ways.

- According to sides
- According to angles

Question 4.

Classify the following ∆ as acute, obtuse, and right triangle.

(a)

Solution:

Acute angled triangle

(b)

Solution:

Right triangle

(c)

Solution:

Obtuse triangle

(d)

Solution:

Acute angled triangle

Question 5.

Find which of the following can be measured by three angles of a triangle.

(a) 45°, 90°, 45°

Solution:

45° + 90° + 45° = 180°

Yes, it can be a measure of the angle ∆.

(b) 65°, 30°, 10°

Solution:

65° + 30° + 10° = 105°

No, it cannot be measured by angle ∆.

(c) 60°, 40°, 80°

Solution:

60° + 40° + 80° = 180°

Yes, it can be a measure of the angle ∆.

(d) 75°, 35°, 45°

Solution:

75° + 35° + 45° = 155°

No, it cannot be measured by angle ∆.

Question 6.

Classify the following triangle as equilateral, acute, scalene, and isosceles triangle.

(a)

Solution:

Equilateral triangle

(b)

Solution:

Scalene triangle

(c)

Solution:

Isosceles triangle

(d)

Solution:

Isosceles triangle

(e)

Solution:

Scalene triangle

Question 7.

Find whether it is possible to draw a triangle with a line segment of length

(a) 12 cm, 7 cm, 8 cm

Solution:

12 cm, 7 cm, 8 cm

Sum of 2 sides = 12 cm + 7 cm = 19 cm

Third side = 8 cm

So 19 > 8 possible

Sum of 2 sides = 7 cm + 8 cm = 15 cm

Third side = 12 cm

15 cm > 12 cm possible

or

Sum of 2 side = 12 cm + 8 cm = 20 cm

Third side = 7 cm

20 cm > 7 cm possible

So triangle is possible.

(b) 2 cm, 3 cm, 9 cm

Solution:

2 cm, 3 cm, 9 cm

Sum of two side = 2 cm + 3 cm = 5 cm

Third side = 9 cm

5 cm < 9 cm So, the triangle is not possible.

(c) 20 cm, 17 cm, 18 cm

Solution:

20 cm, 17 cm, 18 cm

Sum of 2 sides = 20 cm + 17 cm = 37 cm

Third side = 18 cm

So 37 > 18 possible

Sum of 2 sides = 17 cm + 18 cm = 35 cm

Third side = 20 cm

35 cm > 20 cm possible

or

Sum of 2 side = 20 cm + 18 cm = 38 cm

Third side = 17 cm

38 cm > 17 cm possible

So triangle is possible.

(d) 2.3 cm, 3.2 cm, 6.6 cm

Solution:

2.3 cm, 3.2 cm, 6.6 cm

Sum of two side = 2.3 cm + 3.2 cm = 5.5 cm

Third side = 6.6 cm

5.5 cm < 6.6 cm

So, the triangle is not possible.

Question 8.

Identify the scalene, isosceles, and equilateral triangles.

(a)

Solution:

Equilateral triangle.

(b)

Solution:

Isosceles triangle

(c)

Solution:

Isosceles triangle

(d)

Solution:

Scalene triangle

Question 9.

Find the third angle of this triangle. What type of triangle is this?

Solution:

Let the third angle be x°

80° + 70° + x° = 180° (sum of angles of Δ is 180°)

⇒ 150° + x° = 180°

⇒ x = 70°

∴ 80°, 70°, 70°

The triangle is an acutely angled triangle.

Question 10.

If the measure of one angle of a right triangle is 60°. Find the third angle.

Solution:

As it is a right-angled triangle one of the angles is 90°.

Other angle = 60°

Let the third angle be x°

x° + 90° + 60° = 180°

⇒ x° + 150° = 180°

⇒ x° = 180° – 150°

⇒ x° = 30°

So, the other two angles are 90° and 30°.

Question 11.

The sum of two angles of a triangle is 100°. Find the third angle.

Solution:

Sum of two angles = 100°

Let the third angle = x°

x° + sum of two angles = 180° (sum of 3 angles of triangle is 180°)

⇒ x + 100° = 180°

⇒ x° = 180° – 100°

⇒ x° = 80°

The third angle is 80°.

Question 12.

Identify the acute, obtuse, and right-angled triangle.

(a)

Solution:

Acute angled triangle

(b)

Solution:

Obtuse angled triangle

(c)

Solution:

Right-angled triangle