- A△ABC ∼ △PQR
- B△ABC ∼ △RQP
- C△ABC ∼ △QRP
- D△ABC ∼ △PRQ
Step-by-Step Solution
Match the sides in order of size: , all equal to . So by SSS, A ↔ ↔ ↔ , i.e. △ ∼ △.
Answer: C) △ABC ∼ △QRP
Look at the side lengths marked on the two triangles. Which similarity statement is correct?
Class 10Triangles (Similarity)Geometry — Similarity
Key idea: Three similarity criteria
**AA (Angle-Angle)**: Two angles equal → similar. (Third angle is automatic by 180° angle sum.)
**SSS (Side-Side-Side proportionality)**: All three pairs of corresponding sides in same ratio → similar.
**SAS (Side-Angle-Side)**: Two pairs of sides proportional AND included angles equal → similar.
**Important**: SSA does NOT prove similarity (just like for congruence).
AA is by far the most-used in problems: spot two equal angles (often via parallel lines or shared angle) and declare similarity.
**SSS (Side-Side-Side proportionality)**: All three pairs of corresponding sides in same ratio → similar.
**SAS (Side-Angle-Side)**: Two pairs of sides proportional AND included angles equal → similar.
**Important**: SSA does NOT prove similarity (just like for congruence).
AA is by far the most-used in problems: spot two equal angles (often via parallel lines or shared angle) and declare similarity.
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