Prove that a cyclic parallelogram is a rectangle.

Given: ABCD is a cyclic parallelogram.
To Prove: ABCD is a rectangle.

Proof: ∵ ABCD is a cyclic quadrilateral
∴ ∠1 + ∠2 = 180°    ...(1)
| ∵ Opposite angles of a cyclic quadrilateral are supplementary
∴ ABCD is a parallelogram
∴ ∠1 = ∠2    ...(2)
| Opp. angles of a || gm
From (1) and (2),
∠1 = ∠2 = 90°
∴ || gm ABCD is a rectangle.