Prove that a cyclic parallelogram is a rectangle.

Question

Philoid · Accepted Answer

Given that: ABCD is a cyclic quadrilateral

We have to prove that: ABCD is a rectangle

Proof: ∠1 + ∠2 = 180^o (Sum of opposite angles of a cyclic parallelogram)

We also know that, opposite angles of a cyclic parallelogram are equal

Therefore,

∠1 = ∠2

∠1 + ∠1 = 180^o

∠1 = 90^o

As,

One of the interior angle of the parallelogram is 90^o

Therefore, ABCD is a rectangle