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 tangent to these sides. These are also the diagonals of the "contact quadrilateral". The area "K" of a tangential quadrilateral is given by where "s" is the semiperimeter and "r" is the inradius. Another formula is which gives the area in terms of the diagonals "p", "q" and the sides "a", "b", "c", "d" of the tangential quadrilateral. The area can also be expressed in terms of just the four tangent lengths. If these are "e", "f", "g", "h", then the tangential quadrilateral has the area Furthermore, the area of a tangential quadrilateral can be expressed in terms of the