Question

Prove that any cyclic parallelogram is rectangle.

Answer 1

To Prove :- any cyclic parallelogram is rectangle.

Proof :-

Here we will use the properties of parallelogram and cyclic quadrilateral.


‘In a parallelogram, opposite angles are equal’

Also,

‘In a cyclic quadrilateral, opposite angles are supplementary’
=> sum of opposite angles in a cyclic quadrilateral = 180°

Let the angle be a

Now, since opposite angles are equal, opposite angle would also be of "a"

Since the ||gm is cyclic, opposite angles would be supplement.

=> a + a = 180°

=> 2a = 180°

=> a = 180/2

=> a = 90°

Now, we got that the angle is of 90°.

We know that a parallelogram with an angle of 90° is a rectangle. Hence, a cyclic quadrilateral is always a rectangle.

Hence Proved :)

Answer 2

Hello mate ☺

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Solution:

➡It is given that parallelogram ABCD is cyclic. We need to prove that ABCD is a rectangle.

∠B=∠D   (Opposite angles of a parallelogram are equal) ....(1)

∠B+∠D=180°   ...... (2)  

(Sum of opposite angles of a cyclic quadrilateral is equal to 180°)                    

Using equation (1) in equation (2), we get

∠B+∠B=180°

⇒2∠B=180°

⇒∠B=180/2=90°      …...(3)

➡Therefore, ABCD is a parallelogram with ∠B=90° which means that ABCD is a rectangle.

I hope, this will help you.☺

Thank you______❤

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