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Isosceles Triangle Theorem

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

 

Proof:

Let S be the midpoint of .

Join R and S.

Since S is the midpoint of  PQ, .

By Reflexive Property,

It is given that

Therefore, by SSS,

Since corresponding parts of congruent triangles are congruent,

The converse of the Isosceles Triangle Theorem is also true.

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

If , then .