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, and .
In the proof below, we need to show that .
The Isosceles Trapezoid Theorem
The base angles of an isosceles trapezoid are congruent.
Draw two perpendiculars to the base and (S).
since they are altitudes of the same trapezoid(S).
by the Hypotenuse Leg Theorem.
(SSS Triangle Congruence)
since corresponding parts of congruent triangles are congruent.