document.write( "Question 366939: Prove if the diagonals of a paarallelogram are congruent, then the parallelogram is a rectangle. \n" ); document.write( "

Algebra.Com's Answer #261624 by robertb(5830) $\"\"$ $\"About$

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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. \n" ); document.write( "

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