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 formula in the same way. The exradius for an ex-tangential quadrilateral with consecutive sides "a", "b", "c", "d" is given by where "K" is the area of the quadrilateral. For an ex-tangential quadrilateral with given sides, the exradius is maximum when the quadrilateral is also cyclic (and hence an ex-bicentric quadrilateral). These formulas explain why all parallelograms have infinite exradius. If an ex-tangential quadrilateral also has a circumcircle, it is called an ex-bicentric quadrilateral. Then, since it has two opposite supplementary angles, its area is given by which is the same as for a bicentric quadrilateral. If "x" is the