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Question (1)

QN0030013

A triangle has side lengths 9 cm, 12 cm and 20 cm. Which statement is correct?

(A) The triangle can be constructed because 20 < 9 + 12
(B) The triangle cannot be constructed because 20 < 9 + 12 is false
(C) The triangle can be constructed because 9 + 12 = 20
(D) The triangle is equilateral

Correct Answer: A

Explanation:

Since 9 + 12 = 21 > 20, the triangle satisfies the triangle inequality. Hence, it can be constructed.

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Question (2)

QN0030014

While constructing a triangle with sides 5 cm, 6 cm and 7 cm, which side is the best choice for the base?

(A) 5 cm
(B) 6 cm
(C) 7 cm
(D) Any side; all give different triangles

Correct Answer: C

Explanation:

The longest side is generally chosen as the base to make the construction easier.

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Question (3)

QN0030015

Two circles have centres A and B. Their radii are 6 cm and 8 cm, while AB = 13 cm. What can you conclude?

(A) The circles touch externally.
(B) The circles intersect at two points.
(C) The circles do not intersect.
(D) One circle lies completely inside the other.

Correct Answer: B

Explanation:

Since 6 + 8 = 14 > 13, the circles intersect at two points, giving the possible third vertex of a triangle.

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Question (4)

QN0030016

A triangle has angles in the ratio 2 : 3 : 5. The largest angle is

(A) 72°
(B) 90°
(C) 108°
(D) 120°

Correct Answer: B

Explanation:

Total parts = 10. One part = 180° ÷ 10 = 18°. Largest angle = 5 × 18° = 90°.

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Question (5)

QN0030017

A student constructs a triangle with two angles measuring 65° and 80°. What will be the third angle?

(A) 25°
(B) 35°
(C) 45°
(D) 55°

Correct Answer: B

Explanation:

Third angle = 180° − (65° + 80°) = 35°.

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Question (6)

QN0030018

Which of the following sets of lengths can form an obtuse-angled isosceles triangle?

(A) 5 cm, 5 cm, 8 cm
(B) 4 cm, 4 cm, 10 cm
(C) 6 cm, 6 cm, 12 cm
(D) 3 cm, 4 cm, 5 cm

Correct Answer: A

Explanation:

Since 5 + 5 > 8, the triangle exists. It has two equal sides and is obtuse-angled.

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Question (7)

QN0030019

During construction, two arcs drawn from the endpoints of the base just touch each other at one point. This indicates that

(A) A unique triangle is formed.
(B) Infinitely many triangles are formed.
(C) No triangle is formed because the three points become collinear.
(D) An equilateral triangle is formed.

Correct Answer: C

Explanation:

When the arcs just touch, the sum of the two smaller sides equals the longest side. The three points become collinear, so no triangle is formed.

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Question (8)

QN0030020

The exterior angle of a triangle is 118°. One of the opposite interior angles is 47°. The other opposite interior angle is

(A) 61°
(B) 65°
(C) 71°
(D) 75°

Correct Answer: C

Explanation:

Exterior angle = sum of the two opposite interior angles. Therefore, the other angle = 118° − 47° = 71°.

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Question (9)

QN0030021

A triangle has sides 8 cm, 15 cm and 17 cm. Which statement is correct?

(A) It is an equilateral triangle.
(B) It is an isosceles triangle.
(C) It is a scalene triangle.
(D) It cannot be constructed.

Correct Answer: C

Explanation:

All three sides are different and satisfy the triangle inequality, so the triangle is scalene.

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Question (10)

QN0030022

A triangle has angles 40°, 60° and 80°. If an altitude is drawn from the vertex having angle 80°, where will its foot lie?

(A) Outside the triangle
(B) On the opposite side
(C) At the midpoint of the opposite side
(D) At one of the vertices

Correct Answer: B

Explanation:

Since all the angles are acute, every altitude lies inside the triangle and meets the opposite side.

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Question (1)

A triangle has side lengths 9 cm, 12 cm and 20 cm. Which statement is correct?

Explanation:

Link:

Question (2)

While constructing a triangle with sides 5 cm, 6 cm and 7 cm, which side is the best choice for the base?

Explanation:

Link:

Question (3)

Two circles have centres A and B. Their radii are 6 cm and 8 cm, while AB = 13 cm. What can you conclude?

Explanation:

Link:

Question (4)

A triangle has angles in the ratio 2 : 3 : 5. The largest angle is

Explanation:

Link:

Question (5)

A student constructs a triangle with two angles measuring 65° and 80°. What will be the third angle?

Explanation:

Link:

Question (6)

Which of the following sets of lengths can form an obtuse-angled isosceles triangle?

Explanation:

Link:

Question (7)

During construction, two arcs drawn from the endpoints of the base just touch each other at one point. This indicates that

Explanation:

Link:

Question (8)

The exterior angle of a triangle is 118°. One of the opposite interior angles is 47°. The other opposite interior angle is

Explanation:

Link:

Question (9)

A triangle has sides 8 cm, 15 cm and 17 cm. Which statement is correct?

Explanation:

Link:

Question (10)

A triangle has angles 40°, 60° and 80°. If an altitude is drawn from the vertex having angle 80°, where will its foot lie?

Explanation:

Link:

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