If a parallelogram is cyclic, then it is a rectangle. Justify.

Write the converse and decide whether the converse is true or false. (vii) If vertices of a parallelogram lie on a circle then it is a rectangle.

If the diagonals of a parallelogram are equal, show that it is a rectangle.

If the diagonals of a parallelogram are equal, then show that it is rectangle .

Rewrite each of the following statements in the form ''p if and only if q'' r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Parallelogram ABCD and rectangle ABEF are on the base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Let F_1 be the set of parallelograms , F_2 the set of rectangles, F_3 the set of rhombuses , F_4 the set of squares and F_5 the set of trapeziums in a plane. Then F_1 may be equal to :

Prove that a cyclic parallelogram is a rectangle.

In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that DeltaAFD~=DeltaBEC .

Statement 1: If | vec a+ vec b|=| vec a- vec b|,t h e n vec aa n d vec b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.