1. The diagonals of isosceles trapezoids share a side. By the identity theorem, this side is congruent to itself. 2. The diagonals bisect each angle in the trapezoid. 3. Since corresponding angles in a trapezoid are congruent, this means that the triangles share two sets of equal angles. 4. By ASA, the triangles are congruent. 5. Since CPCTC, this means that the diagonals are congruent as well.