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∠B≅∠C ⇒ AB≅AC
This theorem is the converse theorem to the Isosceles Triangle Theorem. It is also known as the Converse Base Angles Theorem.
Consider a triangle ABC with two congruent angles.
Let P be the point of intersection of BC and the angle bisector of ∠A. Since AP is the angle bisector of ∠A, then ∠BAP≅∠CAP.