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

Answers (1)

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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