The Diagonals of an Isosceles Trapezoid Are Congruent

An isosceles trapezoid is a trapezoid whose sides are congruent.  An example of an isosceles trapezoid is shown below. The trapezoid is isosceles with parallel to and congruent to .

In this post, we are going to show that the diagonals of an isosceles trapezoid are congruent. In the figure below, we will show that is congruent to .

Given:

Trapezoid with .

What to show:  .

Proof:

It is given that is an isosceles trapezoid with .

By the definition of isosceles trapezoid .

Now, since the base angles of an isosceles trapezoid  .

Also, , since congruence of segments is reflexive.

By the SAS Congruence postulate, .

since corresponding parts of congruent triangles are congruent.

This completes the proof.

Therefore, diagonals of an isosceles trapezoid are congruent.