Converse of Isosceles Triangle Theorem

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

Proof

Draw SR ¯ , the bisector of the vertex angle PRQ .

Since SR ¯ is the angle bisector, PRSQRS .

By the Reflexive Property,

RS ¯ RS ¯

It is given that PQ .

Therefore, by AAS congruent, ΔPRSΔQRS .

Since corresponding parts of congruent triangles are congruent,

PR ¯ QR ¯