Triangles — Multiple Choice Questions

Which of the following lengths can be the sides of a triangle?

1. 5 cm, 4 cm, 9 cm

2. 6 cm, 3 cm, 10 cm

3. 6 cm, 7 cm, 8 cm

4. 5 cm, 5 cm, 11 cm

Answer

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

⇒ For (1): 5 + 4 = 9, not greater than 9.

⇒ For (2): 6 + 3 = 9 < 10.

⇒ For (3): 6 + 7 = 13 > 8, and every other pair also has a sum greater than the third side.

⇒ For (4): 5 + 5 = 10 < 11.

Only the lengths in (3) satisfy the condition.

Hence, option 3 is the correct option.

Which of the following can be the angles of a triangle?

1. 30°, 40°, 50°

2. 40°, 50°, 60°

3. 50°, 60°, 70°

4. 55°, 65°, 75°

Answer

The sum of the angles of a triangle must be 180°.

⇒ In option (1): 30° + 40° + 50° = 120°.

⇒ In option (2): 40° + 50° + 60° = 150°.

⇒ In option (3): 50° + 60° + 70° = 180°.

⇒ In option (4): 55° + 65° + 75° = 195°.

Only the angles in option (3) add up to 180°.

Hence, option 3 is the correct option.

How many parts does a triangle have?

1. 2

2. 3

3. 4

4. 6

Answer

⇒ A triangle has 3 sides and 3 angles, so the total number of parts = 3 + 3 = 6.

Hence, option 4 is the correct option.

The angles of a triangle are in the ratio 3 : 4 : 5. The smallest angle of the triangle is

1. 30°

2. 45°

3. 50°

4. 60°

Answer

Given,

The angles of a triangle are in the ratio 3 : 4 : 5.

Let the angles of the triangle be 3x, 4x and 5x.

By the angle sum property of a triangle, the sum of all the angles of a triangle is 180°.

⇒ 3x + 4x + 5x = 180°

⇒ 12x = 180°

⇒ x = $\dfrac{180\degree}{12}$

⇒ x = 15°

So, the smallest angle = 3x = 3 × 15° = 45°.

Hence, option 2 is the correct option.

The sum of two angles of a triangle is 60°. The third angle is

1. 30°

2. 60°

3. 90°

4. 120°

Answer

Let the third angle be x.

It is given that the sum of the other two angles of the triangle is 60°.

By the angle sum property of a triangle, the sum of all the angles of a triangle is 180°.

⇒ 60° + x = 180°

⇒ x = 180° − 60°

⇒ x = 120°

So, the third angle is 120°.

Hence, option 4 is the correct option.

Each angle of an equilateral triangle measures

1. 30°

2. 45°

3. 50°

4. 60°

Answer

An equilateral triangle has all its three sides equal. Since the angles opposite to equal sides are equal, all its three angles are also equal.

Let each angle of the equilateral triangle be x.

By the angle sum property of a triangle, the sum of all the angles of a triangle is 180°.

⇒ x + x + x = 180°

⇒ 3x = 180°

⇒ x = $\dfrac{180\degree}{3}$

⇒ x = 60°

So, each angle of an equilateral triangle measures 60°.

Hence, option 4 is the correct option.

One of the base angles of an isosceles triangle is 50°. The vertical angle is

1. 50°

2. 65°

3. 80°

4. 25°

Answer

In an isosceles triangle, the two base angles are equal. Since one base angle is 50°, the other base angle is also 50°.

Let the vertical angle be x.

By the angle sum property of a triangle, the sum of all the angles of a triangle is 180°.

⇒ 50° + 50° + x = 180°

⇒ 100° + x = 180°

⇒ x = 180° − 100°

⇒ x = 80°

So, the vertical angle is 80°.

Hence, option 3 is the correct option.

Two angles of a triangle are 25° and 30° respectively. The third angle is

1. 35°

2. 45°

3. 65°

4. 125°

Answer

Let the third angle be x.

The other two angles of the triangle are 25° and 30°.

By the angle sum property of a triangle, the sum of all the angles of a triangle is 180°.

⇒ 25° + 30° + x = 180°

⇒ 55° + x = 180°

⇒ x = 180° − 55°

⇒ x = 125°

So, the third angle is 125°.

Hence, option 4 is the correct option.

A triangle having all sides of different lengths is called

1. an isosceles triangle

2. a scalene triangle

3. an equilateral triangle

4. a right triangle

Answer

⇒ A triangle whose sides are all of different lengths is a scalene triangle.

Hence, option 2 is the correct option.

In the adjoining figure, the point P lies

1. on △ABC

2. in the exterior of △ABC

3. in the interior of △ABC

4. none of these

Answer

⇒ The point P lies within the region enclosed by the triangle, so it is in the interior of △ABC.

Hence, option 3 is the correct option.