AA Similarity Criteria

Transcript

AA Criteria If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Given :- Two triangles ∆ABC and ∆DEF such that ∠B = ∠E & ∠C = ∠F To Prove :- ∆ABC ~ ∆DEF Proof:- From (1) and (2) ∠A + ∠B + ∠C = ∠D + ∠E + ∠F ∠A + ∠E + ∠F = ∠D + ∠E + ∠F ∠ A = ∠ D Thus, In Δ ABC & Δ DEF ∠ A = ∠ D ∠ B = ∠ E ∠ C = ∠ F ∴ Δ ABC ~ Δ DEF Hence, proved