Prove that the bisector of the outer angle at the apex of an isosceles triangle opposite to the base is parallel to the base.

The outer angle of a triangle is equal to the sum of the inner angles of the triangle that are not adjacent to it. Since the angles at the base of an isosceles triangle are equal, they are equal to half the outer angle at the apex of the triangle. The bisector divides the outer angle in half, which means that half of the outer angle is equal to the angle at the base, and these are criss-crossing angles, which means that the bisector is parallel to the base.