Question

# State the AA-similarity criterion.

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Solution

## AA similarity : If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Paragraph proof : Let ΔABC and ΔDEF be two triangles such that ∠A = ∠D and ∠B = ∠E. ∠A + ∠B + ∠C = 180 0 (Sum of all angles in a Δ is 180) ∠D + ∠E + ∠F = 180 0 (Sum of all angles in a Δ is 180) ⇒ ∠A + ∠B + ∠C = ∠D + ∠E + ∠F ⇒ ∠D + ∠E + ∠C = ∠D + ∠E + ∠F (since ∠A = ∠D and ∠B = ∠E) ⇒ ∠C = ∠F Thus the two triangles are equiangular and hence they are similar by AA.

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