Find the area of a parallelogram in which cm, cm, and cm.
Draw the parallelogram and its diagonals. Label point at the intersection of the diagonals.
The diagonals of a parallelogram bisect each other. Therefore,
The converse of Pythagoras' theorem states that if the square of the length of a side is equal to the sum of the squares of the other two sides, then the angle opposite to this side is a right angle. For ,
Since , then and .
Since is a right angle, . Therefore, we can use as the parallelogram's base and as the parallelogram's corresponding height to find the parallelogram's height.