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
Ex-tangential quadrilateral the vertices "B" or "D", provided that the sides of the quadrilateral "ABCD" are "a" = "AB", "b" = "BC", "c" = "CD", and "d" = "DA". A way of combining these characterizations regarding the sides is that the absolute values of the differences between opposite sides are equal for the two pairs of opposite sides, These equations are closely related to the Pitot theorem for tangential quadrilaterals, where the sums of opposite sides are equal for the two pairs of opposite sides. If opposite sides in a convex quadrilateral "ABCD" intersect at "E" and "F", then The implication to