Question

prove that a cyclic Parallelogram is a rectangle​

Answer 1

In parallelogram ABCD, angle a = angle c (opposite sides of parallelogram) and angle a + angle c = 180degree (cyclic quad.) so angle a + angle a = 180degree 2 angle a = 180degree angle a = 180/2 angle a = 90 hence it is a rectangle (In a parallelogram if one angle is 90,then it is a rectangle)

Answer 2

Step-by-step explanation:

let the cyclic quadrilateral be ABCD

<A=<C (in a parallelogram opposite angles are equal

<A+<C=180°( in a cyclic quadrilateral opposite angles are supplementary)

<A+<C=180°

<A+<A=180

2<A=180°

<A=180/2

<A=90°

similarly <A, B, C, D=180°

in a rectangle all angles are 90 degree

therefore a cyclic Parallelogram is a rectangle

hope it is helpful