Okay, here we have this:
We can see that the given parallelogram is ABCD, so as it's a parellelogram and the diagonals of it are congruent we have the following:
AC=BD (Given)
AB=DC (Definition of parallelogram)
AD=AD (Common side)
Then by congruence we obtain that:
ΔACD≅ΔABD (SSS Congruent Postulate)
∠CDA≅∠BAD (The CPCTC theorem)
And as by definition the adjacent angles of a parallelogram are supplementary:
∠CDA+∠BAD=180
And as they are congruent and supplementary this mean that are right triangles.
So, as ∠CDA≅∠BAD, we can replace in the last equation ∠BAD with ∠CDA, getting the following:
∠CDA+∠BAD=180
∠CDA+ ∠CDA=180
2 ∠CDA=180
∠CDA=180/2
∠CDA=90° (It's a right angle)
Therefore since if a parallelogram has a right angle then it must be a rectangle.