Question

prove that a cyclic Parallelogram is a rectangle

Answer 1

Step-by-step explanation:

Given: PQRS be a cyclic parallelogram.

Prove: PQRS is a rectangle.

(i)

Sum of opposite angles of a quadrilateral is 180°.

⇒ ∠PSR + ∠PQR = 180°

(ii)

Opposite angles of a parallelogram is equal.

⇒ ∠PSR = ∠PQR

From (i) & (ii), we get

⇒ ∠PSR = ∠PQR = 90°

Therefore, cyclic parallelogram is rectangle.

Hope it helps!

Answer 2

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°

hope it helps u