If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Let's suppose that we have a parallelogram ABCD with AC=BC.
We need to prove that it is a rectangle.
(Opposite sides of a parallelogram are equal)
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.