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Question (11)

QN0030023

A triangle has sides 7 cm, 9 cm and 14 cm. If each side is increased by 2 cm, what can be concluded about the new triangle?

(A) It cannot be constructed.
(B) It can be constructed because the triangle inequality is still satisfied.
(C) It becomes an equilateral triangle.
(D) It becomes a right-angled triangle.

Correct Answer: B

Explanation:

The new sides are 9 cm, 11 cm and 16 cm. Since 9 + 11 > 16, the triangle inequality is satisfied.

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Question (12)

QN0030024

A student is given two angles of 95° and 90° along with the included side. What should the student conclude before starting the construction?

(A) The triangle can always be constructed.
(B) The triangle cannot be constructed because the sum of the two angles exceeds 180°.
(C) The triangle is right-angled.
(D) The third angle is 5°.

Correct Answer: B

Explanation:

Since 95° + 90° = 185°, which is greater than 180°, no triangle is possible.

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Question (13)

QN0030025

Which of the following sets of side lengths can form exactly one isosceles triangle?

(A) 6 cm, 6 cm, 11 cm
(B) 5 cm, 5 cm, 10 cm
(C) 7 cm, 8 cm, 8 cm
(D) 4 cm, 5 cm, 10 cm

Correct Answer: C

Explanation:

The sides 7 cm, 8 cm and 8 cm satisfy the triangle inequality and have two equal sides, so they form an isosceles triangle.

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Question (14)

QN0030026

The exterior angle at one vertex of a triangle is 135°. If one of the remote interior angles is 58°, the third interior angle is

(A) 67°
(B) 77°
(C) 45°
(D) 58°

Correct Answer: B

Explanation:

Exterior angle = sum of the two remote interior angles. Hence the other remote angle = 135° − 58° = 77°.

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Question (15)

QN0030027

In a triangle, two angles are equal. If the third angle is 44°, each of the equal angles measures

(A) 66°
(B) 68°
(C) 70°
(D) 72°

Correct Answer: B

Explanation:

Remaining angle sum = 180° − 44° = 136°. Each equal angle = 136° ÷ 2 = 68°.

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Question (16)

QN0030028

A triangle has side lengths 5 cm, 12 cm and 13 cm. Which type of triangle is it based on its sides?

(A) Equilateral
(B) Isosceles
(C) Scalene
(D) Cannot be determined

Correct Answer: C

Explanation:

All three sides are unequal, so the triangle is scalene.

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Question (17)

QN0030029

A student draws an altitude from the right-angled vertex of a right triangle to the side opposite it. This altitude is drawn to the

(A) shortest side
(B) longest side (hypotenuse)
(C) equal side
(D) base only

Correct Answer: B

Explanation:

In a right triangle, the side opposite the right angle is the hypotenuse. The altitude from the right-angled vertex is drawn to the hypotenuse.

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Question (18)

QN0030030

Two sides of a triangle are 9 cm and 15 cm. Which of the following cannot be the third side?

(A) 8 cm
(B) 10 cm
(C) 20 cm
(D) 25 cm

Correct Answer: D

Explanation:

The third side must be greater than 6 cm and less than 24 cm. Therefore, 25 cm is not possible.

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Question (19)

QN0030031

While constructing a triangle using two sides and the included angle, after drawing the base and the given angle, what is the next step?

(A) Draw the third side directly.
(B) Measure the second given side on the arm of the angle using a compass.
(C) Draw another angle at the second endpoint.
(D) Draw two intersecting circles.

Correct Answer: B

Explanation:

After constructing the given angle, mark the required length of the second side on its arm using a compass and then join the remaining vertex.

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Question (20)

QN0030032

Which of the following statements is always true for every triangle?

(A) All three sides are equal.
(B) One angle is always 90°.
(C) The sum of the three interior angles is 180°.
(D) Two sides must be equal.

Correct Answer: C

Explanation:

By the angle sum property, the sum of the three interior angles of every triangle is always 180°.

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Question (11)

A triangle has sides 7 cm, 9 cm and 14 cm. If each side is increased by 2 cm, what can be concluded about the new triangle?

Explanation:

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Question (12)

A student is given two angles of 95° and 90° along with the included side. What should the student conclude before starting the construction?

Explanation:

Link:

Question (13)

Which of the following sets of side lengths can form exactly one isosceles triangle?

Explanation:

Link:

Question (14)

The exterior angle at one vertex of a triangle is 135°. If one of the remote interior angles is 58°, the third interior angle is

Explanation:

Link:

Question (15)

In a triangle, two angles are equal. If the third angle is 44°, each of the equal angles measures

Explanation:

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Question (16)

A triangle has side lengths 5 cm, 12 cm and 13 cm. Which type of triangle is it based on its sides?

Explanation:

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Question (17)

A student draws an altitude from the right-angled vertex of a right triangle to the side opposite it. This altitude is drawn to the

Explanation:

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Question (18)

Two sides of a triangle are 9 cm and 15 cm. Which of the following cannot be the third side?

Explanation:

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Question (19)

While constructing a triangle using two sides and the included angle, after drawing the base and the given angle, what is the next step?

Explanation:

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Question (20)

Which of the following statements is always true for every triangle?

Explanation:

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