5.2a Diagonals of Rectangles

You know that the diagonals of a rectangle are congruent. Get a better sense of whether this is true for other parallelograms.

ABCD is currently a rectangle. Change the lengths of the sides to make squares other rectangles. Pay attention to the lengths of the diagonals (AC and BD), listed at the bottom right. Then, change [math]\alpha[/math] (m<DAB) along with the lengths of the sides to make rhombuses and non-specific parallelograms. Is it still true that the diagonals have to be congruent? (For an obvious example, make a very skewed parallelogram by setting [math]\alpha[/math] to be very small or very large.)