Prove that, any rectangle is a cyclic quadrilateral

Explanation:- 

Given: ▢ABCD is a rectangle.

To prove: ▢ABCD is a cyclic quadrilateral

Proof:

▢ABCD is a rectangle. ….[Given] Therefore, the angles of the rectangle satisfy: ∠A = ∠B = ∠C = ∠D = 90° ….[Angles of a rectangle]

Now, ∠A + ∠C = 90° + 90° Therefore, ∠A + ∠C = 180°

We know that if a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.

Therefore, ▢ABCD is a cyclic quadrilateral ….[Converse of cyclic quadrilateral theorem]

Hence, any rectangle is a cyclic quadrilateral.