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
Tangential quadrilateral in another way using calculus. Another formula for the area of a tangential quadrilateral "ABCD" that involves two opposite angles is where "I" is the incenter. In fact, the area can be expressed in terms of just two adjacent sides and two opposite angles as Still another area formula is where "θ" is either of the angles between the diagonals. This formula cannot be used when the tangential quadrilateral is a kite, since then "θ" is 90° and the tangent function is not defined. As indirectly noted above, the area of a tangential quadrilateral with sides "a", "b", "c", "d"