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Class 10 Maths Chapter 6: Triangles MCQs with answers

10 multiple-choice questions on Triangles, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
A photograph 10 cm × 15 cm is enlarged to a print 20 cm × 30 cm. The photograph and the enlarged print are
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Answer: (b) similar but not congruent

Both are rectangles, so all angles are 90°, and 20/10 = 30/15 = 2: same shape, different size. Similar, not congruent.

Question 2
Which of the following statements is always true?
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Answer: (b) Any two congruent triangles are similar.

Congruent triangles have equal angles and sides in the ratio 1 : 1, so they are similar; similar triangles need not be the same size.

Question 3
Which pair of figures is NOT necessarily similar?
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Answer: (a) two rhombuses, each of side 5 cm

Regular hexagons have every angle 120° and proportional sides; all circles are similar; a right isosceles triangle always has angles 90°, 45°, 45°. Two rhombuses of side 5 cm have equal sides but their angles can differ, so they need not be similar.

Question 4
Rectangle KLMN is 3 cm × 4 cm and rectangle WXYZ is 6 cm × 9 cm. Which statement is correct?
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Answer: (d) They are not similar, because their sides are not in the same ratio.

All angles are 90°, but 6/3 = 2 while 9/4 = 2.25. Equal angles alone do not make two quadrilaterals similar.

Question 5
On a map of a town, 1 cm stands for 500 m. The map and the town are similar figures, with representative fraction
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Answer: (d) 150000

500 m = 50 000 cm, so 1 cm on the map stands for 50 000 cm on the ground: the scale factor is 1/50 000.

Question 6
ΔABC ~ ΔDEF and ΔDEF ~ ΔPQR. Which of these must be true?
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Answer: (b) ΔABC ~ ΔPQR

Similarity is transitive: the angles and side ratios carry through ΔDEF, with the vertices in the same order.

Question 7
In ΔABC, ∠A = 52° and ∠B = 71°. In ΔXYZ, ∠X = 52° and ∠Y = 57°. Then
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Answer: (d) ΔABC ~ ΔXZY

∠C = 180° − 52° − 71° = 57° and ∠Z = 180° − 52° − 57° = 71°. So A ↔ X, B ↔ Z, C ↔ Y, and ΔABC ~ ΔXZY by AA.

Question 8
Two angles of a triangle are 48° and 67°. A triangle similar to it has angles
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Answer: (d) 65°, 48°, 67°

The third angle is 180° − 48° − 67° = 65°. A similar triangle is equiangular with it: 48°, 67°, 65° in any order.

Question 9
ΔABC and ΔDEF are equiangular, with A, B, C matching D, E, F. AB = 4 cm, BC = 6 cm and DE = 10 cm. Then EF is
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Answer: (c) 15 cm

In equiangular triangles corresponding sides are in one ratio: EF/BC = DE/AB = 10/4, so EF = 6 × 2.5 = 15 cm. (12 cm adds 6 instead of multiplying.)

Question 10
In ΔXYZ, a line parallel to YZ meets XY at M and XZ at N. Which of these is true?
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Answer: (b) XMMY = XNNZ

By the Basic Proportionality Theorem the parallel line divides XY and XZ in the same ratio, XM : MY = XN : NZ.

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