Prove that a cyclic parallelogram is a rectangle.

Given: Quadrilateral ABCD is a cyclic quadrilateral.
To Prove: ABCD is a rectangle.
Proof: In cyclic quadrilateral ABCD
∠A + ∠C = 180° …(1)
[∵ The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.]
But ∠A = ∠C …(2)
[∵ Opposite angles of a parallelogram are equal]
From the equation (1) and (2).
∠A + ∠A = 180°
⇒ 2∠A = 180°
⇒ ∠A = 180°/2 = 90°
We know that, a parallelogram with one angle right angle, is a rectangle.
Hence, ABCD is a rectangle.