You know that the diagonals of a rhombus are perpendicular. Get a better sense of whether this is true for other parallelograms.
ABCD is currently a rhombus. Change [math]\alpha[/math] (m<DAB) to make squares and other rhombuses. Pay attention to [math]\beta[/math], the measure of the angle formed by the diagonals. Then, change the lengths of the sides to make rectangles and non-specific parallelograms. Is it still true that the diagonals have to be perpendicular? (For an obvious example, make a short (AD & BC small), long (AB & CD large) parallelogram.)