AA similarity

Theorem: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.

Proof

Let ABC and DEF be two triangles such that $\angle A = \angle D$ and $\angle B = \angle E$ . The sum interior angles of a triangle is equal to 180. Therefore, $\angle A + \angle B + \angle C = 180$ , and $\angle D + \angle E + \angle F = 180$ . We can write the equation: $\angle A + \angle B + \angle C = 180 = \angle D + \angle E + \angle F \Longrightarrow \angle D + \angle E + \angle C = \angle D + \angle E + \angle F$ , acknowledging the fact that $\angle A = \angle D$ and $\angle B = \angle E$ . To conclude, by subtracting $\angle D + \angle E$ by both equations, we get $\angle C = \angle F$ . Since the three angles are congruent, the two triangles are similar.

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AA similarity

Proof

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