Prove that the non-rectangular parallelogram is not a cyclic quadrilateral.
Consider the non-rectangular parallelogram, ABCD.
We know that opposite angles of a parallelogram are equal.
∴ ∠A = ∠C … (1)
Let us suppose that ABCD is a cyclic quadrilateral.
We know that opposite angles of a cyclic quadrilateral are supplementary.
⇒ ∠A + ∠C = 180°
⇒ ∠A + ∠A = 180° (From equation (1))
⇒ 2∠A = 180°
⇒ ∠C = 90°
This is a contradiction to the given condition that ABCD is a non-rectangular parallelogram.
Thus, our supposition was wrong.
Hence, a non- rectangular parallelogram is not a cyclic quadrilateral.