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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.
By the Reflexive Property of Congruence, AP in △ ABP is congruent to AP in △ ACP. Because of the Angle-Angle-Side Congruence Theorem, both triangles are congruent. △ ABP ≅ △ ACP Since corresponding parts of congruent triangles are congruent, it follows that AB is congruent to AC. AB ≅ AC It has been proven that if two angles of a triangle are congruent, then the sides opposite them are congruent.