Question: how to prove that the diagonals of a rectangle are congruent?
Answer: The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB. Since ABCD is a rectangle, it is also a parallelogram. Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.