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Question (1)

QN0036721

Which statement correctly describes two similar figures?

(A) They always have the same size
(B) They have the same shape but may have different sizes
(C) They have different shapes but the same size
(D) They must be congruent

Correct Answer: B

Explanation:

Similar figures have the same shape, but their sizes may be different.

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Question (2)

QN0036722

If two polygons are similar, which pair of conditions must hold?

(A) Corresponding sides are equal only
(B) Corresponding angles are equal only
(C) Corresponding angles are equal and corresponding sides are proportional
(D) Their areas are equal

Correct Answer: C

Explanation:

Similar polygons have equal corresponding angles and proportional corresponding sides.

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Question (3)

QN0036723

All equilateral triangles are similar because

(A) their sides are always equal in length
(B) all their angles are equal and their corresponding sides are proportional
(C) their areas are equal
(D) they are always congruent

Correct Answer: B

Explanation:

Every equilateral triangle has three angles of 60°, and corresponding sides are proportional.

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Question (4)

QN0036724

If two triangles have corresponding angles equal, then their corresponding sides are

(A) equal
(B) perpendicular
(C) proportional
(D) always parallel

Correct Answer: C

Explanation:

By the AAA similarity criterion, equal corresponding angles imply proportional corresponding sides.

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Question (5)

QN0036725

If ΔABC ~ ΔDEF, then the correct correspondence is

(A) A ↔ E, B ↔ F, C ↔ D
(B) A ↔ D, B ↔ E, C ↔ F
(C) A ↔ F, B ↔ D, C ↔ E
(D) A ↔ D, B ↔ F, C ↔ E

Correct Answer: B

Explanation:

The order in ΔABC ~ ΔDEF gives A ↔ D, B ↔ E and C ↔ F.

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Question (6)

QN0036726

In ΔABC, D lies on AB and E lies on AC such that DE || BC. If AD = 4 cm, DB = 6 cm and AE = 6 cm, then EC is

(A) 6 cm
(B) 8 cm
(C) 9 cm
(D) 12 cm

Correct Answer: C

Explanation:

By BPT, AD/DB = AE/EC. Therefore 4/6 = 6/EC, giving EC = 9 cm.

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Question (7)

QN0036727

In ΔPQR, S lies on PQ and T lies on PR. If ST || QR, PS = 5 cm, SQ = 7 cm and PT = 10 cm, then TR is

(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) 15 cm

Correct Answer: C

Explanation:

By BPT, PS/SQ = PT/TR. Thus 5/7 = 10/TR, so TR = 14 cm.

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Question (8)

QN0036728

A line divides two sides of a triangle in the ratio 3 : 5. If the first part of one side is 9 cm and the corresponding first part of the other side is 12 cm, the second part of the other side is

(A) 15 cm
(B) 18 cm
(C) 20 cm
(D) 24 cm

Correct Answer: C

Explanation:

The ratio is 3:5. For the side having first part 12 cm, 12/x = 3/5, so x = 20 cm.

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Question (9)

QN0036729

In ΔABC, D and E are points on AB and AC respectively. If AD/DB = AE/EC, then

(A) DE ⟂ BC
(B) DE || BC
(C) DE = BC
(D) DE is a median

Correct Answer: B

Explanation:

By the converse of the Basic Proportionality Theorem, DE || BC.

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Question (10)

QN0036730

In ΔABC, DE || BC. If AD/AB = 2/5 and AC = 15 cm, then AE is

(A) 4 cm
(B) 5 cm
(C) 6 cm
(D) 8 cm

Correct Answer: C

Explanation:

Since AD/AB = AE/AC, AE/15 = 2/5. Hence AE = 6 cm.

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Question (1)

Which statement correctly describes two similar figures?

Explanation:

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Question (2)

If two polygons are similar, which pair of conditions must hold?

Explanation:

Link:

Question (3)

All equilateral triangles are similar because

Explanation:

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Question (4)

If two triangles have corresponding angles equal, then their corresponding sides are

Explanation:

Link:

Question (5)

If ΔABC ~ ΔDEF, then the correct correspondence is

Explanation:

Link:

Question (6)

In ΔABC, D lies on AB and E lies on AC such that DE || BC. If AD = 4 cm, DB = 6 cm and AE = 6 cm, then EC is

Explanation:

Link:

Question (7)

In ΔPQR, S lies on PQ and T lies on PR. If ST || QR, PS = 5 cm, SQ = 7 cm and PT = 10 cm, then TR is

Explanation:

Link:

Question (8)

A line divides two sides of a triangle in the ratio 3 : 5. If the first part of one side is 9 cm and the corresponding first part of the other side is 12 cm, the second part of the other side is

Explanation:

Link:

Question (9)

In ΔABC, D and E are points on AB and AC respectively. If AD/DB = AE/EC, then

Explanation:

Link:

Question (10)

In ΔABC, DE || BC. If AD/AB = 2/5 and AC = 15 cm, then AE is

Explanation:

Link:

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