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 used if the quadrilateral is a right kite, since the denominator is zero in that case. If "M" and "N" are the midpoints of the diagonals, and "E" and "F" are the intersection points of the extensions of opposite sides, then the area of a bicentric quadrilateral is given by where "I" is the center of the incircle. The area of a bicentric quadrilateral can be expressed in terms of two opposite sides and the angle "θ" between the diagonals according to In terms of two adjacent angles and the radius "r" of the incircle, the area is given by