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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.


Draw S R ¯ , the bisector of the vertex angle P R Q .

Since S R ¯ is the angle bisector , P R S Q R S .

By the Reflexive Property ,

R S ¯ R S ¯

It is given that P Q .

Therefore, by AAS congruent, Δ P R S Δ Q R S .

Since corresponding parts of congruent triangles are congruent,

P R ¯ Q R ¯