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Converse of Isosceles Triangle Theorem

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

Proof

Draw$\overline{SR}$, the bisector of the vertex angle$\angle PRQ$.

Since$\overline{SR}$is theangle bisector,$\angle PRS\cong \angle QRS$.

By theReflexive Property,

$\overline{RS}\cong \overline{RS}$

It is given that$\angle P\cong \angle Q$.

Therefore, by AAS congruent,$\Delta PRS\cong \Delta QRS$.

Since corresponding parts of congruent triangles are congruent,

$\overline{PR}\cong \overline{QR}$