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. Thus,

ABCD is a rectangle.

solution

Answer 2

Step-by-step explanation:

Given:

PQRS is a parallelogram inscribed in a circle.

To prove: PQRS is a rectangle.

image

Proof:

Since, PQRS is a cyclic quadrilateral.

Thus, + = ...(i)

(Since, Sum of opposite angles in a cyclic quadrilateral is )

But, = ...(ii)

(Since, in a parallelogram, opposite angles are equal)

from eq. (i) and (ii), we get,

= =

Similarly,

= =

Thus, Each angle of PQRS is .

Hence, it is proved that PQRS is a rectangle.