Prove that, any rectangle is a cyclic quadrilateral. Given: ABCD is a rectangle. To prove: ABCD is a cyclic quadrilateral.

Question

Prove that, any rectangle is a cyclic quadrilateral. 

Answer 1

Given: ABCD is a rectangle. 

To prove: ABCD is a cyclic quadrilateral.

Proof:

⟂XBCD is a rectangle. [Given] 

∴ ∠A = ∠B = ∠C = ∠D = 90° [Angles of a rectangle] 

Now, ∠A + ∠C = 90° + 90° 

∴ ∠A + ∠C = 180° 

∴ ⟂ABCD is a cyclic quadrilateral. [Converse of cyclic quadrilateral theorem