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Converse of Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite to these angles are congruent.

Proof

Draw , the bisector of the vertex angle .

Since is the angle bisector, .

By the Reflexive Property,

It is given that .

Therefore, by AAS congruent, .

Since corresponding parts of congruent triangles are congruent,