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
Bicentric quadrilateral and cosine functions the following formulas holds: The angle "θ" between the diagonals can be calculated from The inradius "r" of a bicentric quadrilateral is determined by the sides "a", "b", "c", "d" according to The circumradius "R" is given as a special case of Parameshvara's formula. It is The inradius can also be expressed in terms of the consecutive tangent lengths "e", "f", "g", "h" according to These two formulas are in fact necessary and sufficient conditions for a tangential quadrilateral with inradius "r" to be cyclic. The four sides "a", "b", "c", "d" of a bicentric quadrilateral are