Prove that an isosceles triangles angles are congruent.
From the angle contained by the equal sides draw the bisector
of the opposite side. The two triangles that this divides the triangle
into two congruent trianges by SSS. Hence the base angles of the
isosceles triangle (the ones other that the one we drew the side
bisector from) are congruent as they are corresponding angles in
two congruent triangles.