To show that the parallelogram ABCD is a rectangle, we only need to prove one of its interior angle is 90º.
We can prove this by establishing the congruency of appropriate triangles.
By congruency of triangles ABC and DCB, we will get that pair of angles ABC and DCB to be equal.
Then, we will use a result:
sum of measures of angles on the same side of transversal is 180º
So, we will then get the measure of both these angles as 90 degrees which will give the desired result that ABCD is a rectangle.