Let's break down the problem step by step:Cyclic Parallelogram: A cyclic parallelogram is a quadrilateral whose opposite angles are supplementary and all its vertices lie on a single circle.Parallelogram: A parallelogram is a quadrilateral with opposite sides parallel.To prove that a cyclic parallelogram must be a rectangle, we need to show that all its angles are right angles (90 degrees).Here's the proof:In a cyclic quadrilateral, opposite angles are supplementary, meaning the sum of the measures of the opposite angles is 180 degrees.Let's label the angles of the cyclic parallelogram as A, B, C, and D.In a parallelogram, opposite angles are equal. So, let's say angle A is equal to angle C, and angle B is equal to angle D.Now, if we add the measures of angle A and angle C, and the measures of angle B and angle D, the sum should be 180 degrees, because the opposite angles in a cyclic quadrilateral are supplementary.So, ( A + C = 180^\circ ) and ( B + D = 180^\circ ).Since A = C and B = D, we can substitute:[ A + A = 180^\circ ] and [ B + B = 180^\circ ].Thus, ( A = 90^\circ ) and ( B = 90^\circ ), which implies all angles in the parallelogram are right angles.Therefore, the cyclic parallelogram is a rectangle.