Question

Prove that a cyclic parallelogram is a rectangle

Answer 1

Opposite angles in a parallelogram are congruent, while opposite angles in acyclic quadrilateral are supplementary. Congruent supplementary angles are right angles, so opposite angles in acyclic parallelogram are right angles. Thus all four angles are right angles, and it's a rectangle.

Answer 2

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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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