Question

Prove that the cyclic parallelogram is always rectangle

Answer 1

Answer:

Step-by-step explanation:

We know that the sum of the opposite angles of a parallelogram is 180 degrees..again the adjacent angles of a parallelogram sum up to make 180 degrees...so when a pair of adjacent angles are equal and sum upto make 180 degrees we can conclude that each angle is 90 degrees...hence this parallelogram is 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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