Question

Prove that a cyclic parallelogram is a rectangle

Answer 1

in an cyclic quad. sum of opposite angle is 180 and in parallelogram opposite angles are equal so,
angle 1+ angle 2 = 180
but angle 1 is equal to angle 2 because they are opposite angle of cyclic quadrilateral
twice angle 1 = 180
so angle 1 is equal to 90 there for a parallelogram with one angle 90 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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