Class 10 Triangles (Similarity) — practice questions with answers
Geometry — Similarity · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Two triangles are similar if their corresponding angles are equal and sides are in ____.
ASame difference
BSame ratio (proportion)
CSame sum
DSame product
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Answer: B) Same ratio (proportion)
Definition of similar triangles: angles equal AND sides proportional.
2. ΔABC ~ ΔDEF. If ∠A = 50° and ∠B = 60°, what is the measure of ∠F?
A70
B77
C63
D140
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Answer: A) 70
∠C = 180° − 50° − 60° = 70°. Since the triangles are similar, ∠F corresponds to ∠C, so ∠F = 70°.
3. Two similar triangles are congruent when their scale factor (ratio of corresponding sides) is ____.
A1
B0
C2
DAny value
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Answer: A) 1
When the scale factor is 1, corresponding sides are equal, so the similar triangles are also congruent.
4. In trapezium ABCD, AB ∥ DC. A point E on AD and a point F on BC are joined so that EF ∥ AB. If AE = 3.5 cm, ED = 5 cm and BF = 4.2 cm, find FC.
A2.94 cm
B10.2 cm
C5 cm
D6 cm
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Answer: D) 6 cm
Join AC, meeting EF at G. In ΔADC, EG ∥ DC gives EDAE=GCAG; in ΔCAB, GF ∥ AB gives GCAG=FCBF. So 53.5=FC4.2 and FC = 3.54.2×5 = 6 cm. 10.2 cm comes from using the whole side AD = 8.5 cm in place of ED — BPT applied to the wrong pair of segments; 2.94 cm comes from inverting the ratio; 5 cm is copying ED.
5. In ΔABC, D lies on AB and E lies on AC with DE ∥ BC and AD : DB = 3 : 4. If the area of trapezium DBCE is 120 cm², find the area of ΔADE.
A51.4 cm²
B22 cm²
C90 cm²
D27 cm²
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Answer: D) 27 cm²
AD : AB = 3 : 7, and ΔADE ~ ΔABC, so ar(ADE) : ar(ABC) = 9 : 49. The trapezium is the remaining 49 − 9 = 40 parts, so ar(ADE) : ar(DBCE) = 9 : 40 and ar(ADE) = 120×409 = 27 cm². 51.4 cm² uses the SIDE ratio 73 on an area; 22 cm² applies the area ratio 499 to the trapezium instead of to the whole triangle; 90 cm² uses AD : DB = 3 : 4 directly.