If two sides of a triangle are congruent, then the angles opposite to these sides are congruent.
Let S be the midpoint of .
Join R and S.
Since S is the midpoint of PQ, .
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 .