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Question (41)

QN0036761

Two right triangles have hypotenuses 10 cm and 15 cm, and one corresponding side is 6 cm and 9 cm. They are

(A) similar by RHS
(B) similar only by AA
(C) not similar
(D) congruent

Correct Answer: A

Explanation:

10/15 = 6/9 = 2/3, and both triangles are right-angled. Hence they are similar by RHS.

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Question (42)

QN0036762

If ΔABC ~ ΔDEF, ∠A = 50° and ∠B = 70°, then ∠F is

(A) 40°
(B) 50°
(C) 60°
(D) 70°

Correct Answer: C

Explanation:

∠C = 180° − 50° − 70° = 60°. Since C corresponds to F, ∠F = 60°.

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Question (43)

QN0036763

Two triangles have corresponding sides 7 cm, 9 cm, 11 cm and 14 cm, 18 cm, 22 cm. If the angle opposite the side 11 cm in the first triangle is 50°, the corresponding angle in the second triangle is

(A) 25°
(B) 40°
(C) 50°
(D) 100°

Correct Answer: C

Explanation:

The corresponding sides are proportional in the ratio 1:2. Hence the triangles are similar by SSS and corresponding angles are equal.

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Question (44)

QN0036764

In ΔABC, D lies on BC such that ∠ADC = ∠BAC. Which relation is obtained from the similarity of the relevant triangles?

(A) CA² = CB × CD
(B) CA² = AB × BD
(C) AB² = BC × CD
(D) BC² = CA × CD

Correct Answer: A

Explanation:

From the similarity relation, CA² = CB × CD.

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Question (45)

QN0036765

If two triangles are similar and their corresponding sides are in the ratio 1 : 3, then the ratio of their areas is

(A) 1 : 3
(B) 1 : 6
(C) 1 : 9
(D) 3 : 1

Correct Answer: C

Explanation:

Area ratio is the square of the side ratio. Therefore 1²:3² = 1:9.

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Question (46)

QN0036766

A map is drawn using a scale factor of 1 : 50,000. If a road measures 3 cm on the map, its actual length is

(A) 0.15 km
(B) 1.5 km
(C) 15 km
(D) 150 km

Correct Answer: B

Explanation:

Actual length = 3 × 50,000 cm = 150,000 cm = 1.5 km.

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Question (47)

QN0036767

If ΔABC ~ ΔDEF and AB = 15 cm, DE = 10 cm, then the area of ΔABC is 90 cm². The area of ΔDEF is

(A) 40 cm²
(B) 45 cm²
(C) 60 cm²
(D) 75 cm²

Correct Answer: A

Explanation:

Side ratio ABC:DEF = 15:10 = 3:2. Area ratio = 9:4. Therefore area of ΔDEF = 90 × 4/9 = 40 cm².

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Question (48)

QN0036768

If two triangles have two pairs of corresponding angles equal, which additional information is necessary to prove their similarity?

(A) No additional information is necessary
(B) Their areas must be equal
(C) Their corresponding sides must be equal
(D) Their perimeters must be equal

Correct Answer: A

Explanation:

Two pairs of equal corresponding angles are sufficient by the AA similarity criterion.

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Question (49)

QN0036769

A student claims that two quadrilaterals are similar because all their corresponding angles are equal. Which additional condition is required to validate the claim?

(A) Their diagonals must be perpendicular
(B) Their corresponding sides must be proportional
(C) Their areas must be equal
(D) Their perimeters must be equal

Correct Answer: B

Explanation:

For polygons, equal corresponding angles alone are not sufficient. Corresponding sides must also be proportional.

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Question (50)

QN0036770

Two similar triangles have areas 81 cm² and 144 cm². If a corresponding side of the smaller triangle is 9 cm, the corresponding side of the larger triangle is

(A) 12 cm
(B) 14 cm
(C) 16 cm
(D) 18 cm

Correct Answer: A

Explanation:

Side ratio = √(81/144) = 9/12. Therefore the corresponding side of the larger triangle is 12 cm.

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Question (41)

Two right triangles have hypotenuses 10 cm and 15 cm, and one corresponding side is 6 cm and 9 cm. They are

Explanation:

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Question (42)

If ΔABC ~ ΔDEF, ∠A = 50° and ∠B = 70°, then ∠F is

Explanation:

Link:

Question (43)

Two triangles have corresponding sides 7 cm, 9 cm, 11 cm and 14 cm, 18 cm, 22 cm. If the angle opposite the side 11 cm in the first triangle is 50°, the corresponding angle in the second triangle is

Explanation:

Link:

Question (44)

In ΔABC, D lies on BC such that ∠ADC = ∠BAC. Which relation is obtained from the similarity of the relevant triangles?

Explanation:

Link:

Question (45)

If two triangles are similar and their corresponding sides are in the ratio 1 : 3, then the ratio of their areas is

Explanation:

Link:

Question (46)

A map is drawn using a scale factor of 1 : 50,000. If a road measures 3 cm on the map, its actual length is

Explanation:

Link:

Question (47)

If ΔABC ~ ΔDEF and AB = 15 cm, DE = 10 cm, then the area of ΔABC is 90 cm². The area of ΔDEF is

Explanation:

Link:

Question (48)

If two triangles have two pairs of corresponding angles equal, which additional information is necessary to prove their similarity?

Explanation:

Link:

Question (49)

A student claims that two quadrilaterals are similar because all their corresponding angles are equal. Which additional condition is required to validate the claim?

Explanation:

Link:

Question (50)

Two similar triangles have areas 81 cm² and 144 cm². If a corresponding side of the smaller triangle is 9 cm, the corresponding side of the larger triangle is

Explanation:

Link:

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