Complete the coordinate proof of the theorem. Given: A B C D is a rectangle. Prove: The diagonals of A B C D are congruent. Art: A rectangle is graphed on a coordinate plane. The horizontal x-axis and vertical y-axis are solid. The vertex labeled as A lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as B lies on begin ordered pair a comma 0 end ordered pair. The vertex labeled as D lies on begin ordered pair 0 comma b end ordered pair. The vertex C is unlabeled. Diagonals A C and B D are drawn by dotted lines.

The coordinates of rectangle ABCD are A(0, 0), B(a, 0), C( , ), and D(0, b). The length of AC⎯⎯⎯⎯⎯ is equal to . The length of BD⎯⎯⎯⎯⎯ is equal to . The diagonals of the rectangle have the same length. Therefore, AC⎯⎯⎯⎯⎯ is congruent to BD⎯⎯⎯⎯⎯.