# Q: 12     Prove that a cyclic parallelogram is a rectangle.

M mansi

Given: ABCD is a cyclic quadrilateral.

To prove: ABCD is a rectangle.

Proof :

In cyclic quadrilateral ABCD.

$\angle A + \angle C = 180 \degree$.......................1(sum of either pair of opposite angles of a cyclic quadrilateral)

$\angle A = \angle C$........................................2(opposite angles of a parallelogram are equal )

From 1 and 2,

$\angle A + \angle A = 180 \degree$

$\Rightarrow 2\angle A = 180 \degree$

$\Rightarrow \angle A = 90 \degree$

We know that a parallelogram with one angle right angle is a rectangle.

Hence, ABCD is a rectangle.

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