SOLUTION: Prove if the diagonals of a paarallelogram are congruent, then the parallelogram is a rectangle.

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Question 366939: Prove if the diagonals of a paarallelogram are congruent, then the parallelogram is a rectangle.
Answer by robertb(5830) About Me  (Show Source):
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The relationship between the sides of a parallelogram L,L,W,W and its diagonals A and B:2L%5E2+%2B+2W%5E2+=+A%5E2+%2B+B%5E2. If the diagonals are congruent, then A = B, hence 2L%5E2+%2B+2W%5E2+=+2A%5E2. Dividing both sides by 2 we get L%5E2+%2B+W%5E2+=+A%5E2, which is a statement of the Pythagorean Theorem. By the converse of the Pythagorean Theorem the sides L, W, and A form a right triangle, hence the parallelogram is a rectangle.