Question 366939
The relationship between the sides of a parallelogram L,L,W,W and its diagonals A and B:{{{2L^2 + 2W^2 = A^2 + B^2}}}.  If the diagonals are congruent, then A = B, hence {{{2L^2 + 2W^2 = 2A^2}}}.  Dividing both sides by 2 we get {{{L^2 + W^2 = A^2}}}, 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.