**If the diagonals of a parallelogram are equal, then show that it is a rectangle.**

**Solution:**

Let's suppose that we have a parallelogram ABCD with AC=BC.

We need to prove that it is a rectangle.

In and

** (Given)**

** (Opposite sides of a parallelogram are equal)**

**(Common)**

Therefore, by **SSS** congruence rule,

It means we have, **(Corresponding parts of congruent triangles are equal) (1)**

But ,we also have ** (Co-interior angles because )**

Putting **(1)** in the above equation, we get

Similarly, we can prove that all the angles of a given parallelogram ABCD are but there is no need to do so because once we have proved that one angle is equal to in a given parallelogram then it can be considered as rectangle.

Therefore, ABCD is a rectangle.