Question

Prove that a cyclic parellelogram is a rectangle

Answer 1

hey!

given - ABCD is a cyclic ||gm

to prove - ABCD is a rectangle (

proof- property of rectangle is that is one angle is 90°

We know that sum of oppisite angles of a cyclic quadrilateral is 180°

<A+<C = 180°

we know that opposite angles of a || gm are equal

<A=<C

2<A = 180° ( <A+<C=180°)

<A = 180/2

<A=90°

hence one angle of ||ABCD is 90° so hence it is a rectangle

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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