Parallelogram Parallelogram In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The
Cyclic quadrilateral have the same area. Specifically, for sides , , , and , side could be opposite any of side , side , or side . The area of a cyclic quadrilateral with successive sides , , , and angle between sides and can be expressed as or where is either angle between the diagonals. Provided is not a right angle, the area can also be expressed as Another formula is where is the radius of the circumcircle. As a direct consequence, where there is equality if and only if the quadrilateral is a square. In a cyclic quadrilateral with successive