What do you prove to show the sides of an isosceles trapezoid are congruent?

To show that the non-parallel sides of an isosceles trapezoid are congruent, one must recognize some properties specific to isosceles trapezoids. An isosceles trapezoid has one pair of parallel sides, known as the bases, and the lengths of the other two sides, referred to as the legs, are equal in length.

When tasked with proving the congruence of the non-parallel sides, one can use methods such as the definition of an isosceles trapezoid itself, which states that the legs must be congruent. This characteristic can also be demonstrated through congruency criteria, like the use of triangle congruence theorems if angles or certain lengths can be established or compared, leading to the conclusion that the non-parallel sides are indeed equal.

The focus here is primarily on the properties of the non-parallel sides and how they relate to the definitions and characteristics of isosceles trapezoids, making it pertinent to demonstrate their congruence when establishing the identity and properties of this specific geometric figure.