Question

Prove that cyclic parallelogram is always a rectangle.

Answer 1

in a cyclic quadrilateral, opp angles are supplementary

in a parallelogram, opp angles are equal

⇒x+x=180

⇒x=90

and opp sides are equal

⇒the parallelogram is a rectangle

Answer 2

Given, that ABCD is a parallelogram

∠A = ∠C

∠B = ∠D


To find, ABCD is a rectangle


Solution :- ABCD is a cyclic parallelogram

Cyclic parallelogram measures upto 180°

∠A + ∠C = 180°

∠B + ∠D = 180°

∠B + ∠B = 180°

2m∠B = 180°

m∠B = $\dfrac{180}{2}$

m∠B = 90°


If, m∠B = 90° then m∠D = 90°

Opposite angles of rectangle are congruent

If, m∠A = m∠C

and m∠A = 90°

So, m∠C = 90°




∴ ABCD is a rectangle as all sides measures 90°