Question 388932: prove that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! If the diagonals of a parallelogram are perpendicular, then there would be four right triangles that are congruent (by the LL theorem)and side by side each other. ( This is due to the fact that the diagonals of a parallelogram bisect each other.) The hypotenuses of these congruent right triangles are the sides of this parallelogram, and since they (the hypotenuses) are congruent, the parallelogram is a rhombus.
