Question

Prove that every cyclic parallelogram is a rectangle.

Answer 1

Given : ABCD is a cyclic parallelogram.

To prove : ABCD is a rectangle.

Proof :

STATEMENT REASON

1. $\angle$ABC = $\angle$ADC Opposite angles of a parallelogram are equal.

2. $\angle$ABC + $\angle$ADC = ${180}^{\circ }$ Sum of opposite $\angle$s of a cyclic quad. is ${180}^{\circ }$

3. $\angle$ABC = $\angle$ADC = ${90}^{\circ }$ From (1) and (2).

∴ ABCD is a rectangle A parallelogram opposite angles = ${90}^{\circ }$ is a rectangle.

Hence proved.