Question

State the AA-similarity criterion.

Answer 1

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.