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
Quadrilateral terms of the sides and two opposite angles: where the sides in sequence are "a", "b", "c", "d", where "s" is the semiperimeter, and "A" and "C" are two (in fact, any two) opposite angles. This reduces to Brahmagupta's formula for the area of a cyclic quadrilateral when . Another area formula in terms of the sides and angles, with angle "C" being between sides "b" and "c", and "A" being between sides "a" and "d", is In the case of a cyclic quadrilateral, the latter formula becomes formula_7 In a parallelogram, where both pairs of opposite sides and angles