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.

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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¯¯¯¯¯.