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 sides in its contact quadrilateral intersect at "L" and "M", then the four points "J", "L", "K" and "M" are collinear. If the incircle is tangent to the sides "AB", "BC", "CD", "DA" at "T", "T", "T", "T" respectively, and if "N", "N", "N", "N" are the isotomic conjugates of these points with respect to the corresponding sides (that is, "AT" = "BN" and so on), then the "Nagel point" of the tangential quadrilateral is defined as the intersection of the lines "NN" and "NN". Both of these lines divide the perimeter of the quadrilateral into two equal parts. More