- A27
- B60
- C30
- D33
Step-by-Step Solution
Scale factor PQ/AB = 8/4 = 2. Perimeter of ABC = 4 + 5 + 6 = 15 cm. So perimeter of PQR = cm.
Answer: C) 30
ΔABC ~ ΔPQR. If AB = 4 cm, BC = 5 cm, CA = 6 cm and PQ = 8 cm, find the perimeter of ΔPQR in cm.
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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