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 .
Trapezoid with .
What to show: .
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.