AA similarity

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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 $\angle B = \angle E$. $\angle A + \angle B + \angle C = 180$ (Sum of all angles in a triangle is $180$) $\angle D + \angle E + \angle F = 180$ (Sum of all angles in a triangle is $180$) $\angle A  + \angle B + \angle C=\angle D + \angle E + \angle F$ $\angle D + \angle E + \angle C = \angle D + \angle E + \angle F$ (since $\angle A = \angle D$ and $\angle B = \angle E$) $\angle C = \angle F$.

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