Question

How can I prove that a parallelogram ( which is not a rectangle ) is not cyclic????

Answer 1

For a quadrilateral to be cyclic, the sum of the opposite angles should be 180 deg. In case of a square and a rectangle the sum of the opposite angles is always. Therefore, a square and a rectangle are cyclic.
On the other hand in case of a parallelogram the sum of the opposite angles is never 180. Therefore, a parallelogram is not quadrilateral cyclic. Same is the case with a rhombus, a trapezium and a kite.