# Proof that Isosceles Trapezoids Have Congruent Base Angles

##### Overview

A trapezoid is a quadrilateral with exactly one pair of parallel sides (definitions may differ in other sources). The parallel sides are the base and the non parallel sides are called the legs. An isosceles trapezoid is a trapezoid whose base are congruent.

In this post, we prove that  if a trapezoid is isosceles, its base angles are congruent. In trapezoid ABCD below, $latex \overline{BC} \parallel \overline{AD}$ and $latex \overline{AB} \cong \overline{CD}$.  Continue reading