Question

prove that a cyclic Parallelogram is a rectangle

Answer 1

According to a theorem the opposite angles of a cyclic quadrilateral are supplementary.

The opposite angles of a parallelogram are equal.

So let the angle be x
2x = 180
x = 180 ÷ 2
x = 90

So a parallelogram with angles 90 degree is a rectangle

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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.☺

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