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 a tangential quadrilateral into two polygons with equal areas and equal perimeters, then that line passes through the incenter. The inradius in a tangential quadrilateral with consecutive sides "a", "b", "c", "d" is given by where "K" is the area of the quadrilateral and "s" is its semiperimeter. For a tangential quadrilateral with given sides, the inradius is maximum when the quadrilateral is also cyclic (and hence a bicentric quadrilateral). In terms of the tangent lengths, the incircle has radius The inradius can also be expressed in terms of the distances from the incenter "I" to the vertices of the