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Question (11)

QN0030203

In an isosceles triangle, the vertex angle is four times one base angle. What is the measure of the vertex angle?

(A) 120°
(B) 135°
(C) 144°
(D) 150°

Correct Answer: A

Explanation:

Let each base angle be x°. Then vertex angle = 4x°. So, x + x + 4x = 180°. Hence x = 30° and the vertex angle = 120°.

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Question (12)

QN0030204

Two triangles have sides 7 cm, 9 cm and 12 cm each. Which additional information is required to prove their congruence?

(A) No additional information is required.
(B) One corresponding angle only
(C) The perimeter
(D) The area

Correct Answer: A

Explanation:

Three equal corresponding sides satisfy the SSS congruence criterion.

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Question (13)

QN0030205

Which statement is true regarding an equilateral triangle?

(A) It has three equal sides but unequal angles.
(B) It has three equal angles but unequal sides.
(C) Every median is also an angle bisector.
(D) It has exactly one line of symmetry.

Correct Answer: C

Explanation:

In an equilateral triangle, every median is also an altitude, angle bisector and perpendicular bisector.

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Question (14)

QN0030206

The base angles of an isosceles triangle are each 15° less than the vertex angle. What is the measure of the vertex angle?

(A) 60°
(B) 70°
(C) 75°
(D) 90°

Correct Answer: B

Explanation:

Let the vertex angle be x°. Then each base angle = (x − 15)°. So, x + (x − 15) + (x − 15) = 180°. Hence x = 70°.

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Question (15)

QN0030207

Which pair of triangles can be proved congruent using the ASA criterion?

(A) Two corresponding sides and the included angle are equal.
(B) Three corresponding sides are equal.
(C) Two corresponding angles and the included side are equal.
(D) Hypotenuse and one corresponding side are equal.

Correct Answer: C

Explanation:

ASA requires two equal angles and the included side.

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Question (16)

QN0030208

In an isosceles triangle, each base angle is half the vertex angle. The vertex angle is:

(A) 60°
(B) 72°
(C) 90°
(D) 120°

Correct Answer: C

Explanation:

Let each base angle be x°. Then vertex angle = 2x°. So, x + x + 2x = 180°. Hence x = 45° and the vertex angle = 90°.

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Question (17)

QN0030209

A triangle has sides 5 cm, 5 cm and 8 cm. It is:

(A) Scalene
(B) Equilateral
(C) Isosceles
(D) Right-angled

Correct Answer: C

Explanation:

Two sides are equal, so the triangle is isosceles.

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Question (18)

QN0030210

Which congruence criterion cannot be applied to general triangles?

(A) SAS
(B) RHS
(C) ASA
(D) SSS

Correct Answer: B

Explanation:

RHS applies only to right-angled triangles.

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Question (19)

QN0030211

If two corresponding sides and the included angle of two triangles are equal, then the triangles are:

(A) Similar
(B) Congruent
(C) Equilateral
(D) Isosceles

Correct Answer: B

Explanation:

This is the SAS congruence criterion.

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Question (20)

QN0030212

A student says that every equilateral triangle is congruent to every other equilateral triangle. Which statement is correct?

(A) The statement is always true.
(B) The statement is false because equilateral triangles can have different side lengths.
(C) The statement is true only for right triangles.
(D) The statement is true only when the areas are equal.

Correct Answer: B

Explanation:

All equilateral triangles are similar, but they are congruent only if their corresponding side lengths are equal.

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Question (11)

In an isosceles triangle, the vertex angle is four times one base angle. What is the measure of the vertex angle?

Explanation:

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Question (12)

Two triangles have sides 7 cm, 9 cm and 12 cm each. Which additional information is required to prove their congruence?

Explanation:

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Question (13)

Which statement is true regarding an equilateral triangle?

Explanation:

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Question (14)

The base angles of an isosceles triangle are each 15° less than the vertex angle. What is the measure of the vertex angle?

Explanation:

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Question (15)

Which pair of triangles can be proved congruent using the ASA criterion?

Explanation:

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Question (16)

In an isosceles triangle, each base angle is half the vertex angle. The vertex angle is:

Explanation:

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Question (17)

A triangle has sides 5 cm, 5 cm and 8 cm. It is:

Explanation:

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Question (18)

Which congruence criterion cannot be applied to general triangles?

Explanation:

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Question (19)

If two corresponding sides and the included angle of two triangles are equal, then the triangles are:

Explanation:

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Question (20)

A student says that every equilateral triangle is congruent to every other equilateral triangle. Which statement is correct?

Explanation:

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