- A70
- B77
- C63
- D140
Step-by-Step Solution
∠C = 180° − 50° − 60° = 70°. Since the triangles are similar, ∠F corresponds to ∠C, so ∠F = 70°.
Answer: A) 70
ΔABC ~ ΔDEF. If ∠A = 50° and ∠B = 60°, what is the measure of ∠F?
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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