Prove that a para

We will prove by negation

i.e. If ABCD is a cyclic parallelogram then it is a rectangle

Proof:

∠ A + ∠ C = 180° (ABCD is a cyclic quadrilateral) …(1)

Since ∠ A = ∠ C (Opposite angles of a parallelogram) …(2)

⇒ ∠ A + ∠ A = 180° (from (1) and (2))

⇒ 2∠ A = 180°

⇒ ∠ A = 90°

Thus, ABCD is a rectangle.

That is a parallelogram which is not a rectangle is not cyclic.