Question

Prove that a cyclic parallelogram is a rectangle​

Answer 1

Answer:

Given,

ABCD is a cyclic parallelogram.

To prove,

ABCD is a rectangle.

Proof:

∠1+∠2=180° ...Opposite angles of a cyclic parallelogram

Also, Opposite angles of a cyclic parallelogram are equal.

Thus,

∠1=∠2

⇒∠1+∠1=180°

⇒∠1=90°

One of the interior angle of the parallelogram is right angled.

Answer 2

rectangle is a parallelogram with angle 90

we have to prove that angle is 90

draw a cyclic parallelogram

consider its opposite angles <A,<C

opposite angles of a parallelogram is are equal

<A=<C

sum of angles in a cyclic quadrilateral is 180

<A+<C=180. =<A+<A=180

=2<A=180

=<A=180/2

=<A=90

hence proved