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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,