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 opposite sides intersect at "J" and "K", then the quadrilateral is also cyclic if and only if "JIK" is a right angle. Yet another necessary and sufficient condition is that a tangential quadrilateral "ABCD" is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral "WXYZ". (The Newton line of a quadrilateral is the line defined by the midpoints of its diagonals.) There is a simple method for constructing a bicentric quadrilateral: It starts with the incircle "C" around the centre "I" with the radius "r" and then draw two to each