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 "l" connects the sides of lengths "b" = "f" + "g" and "d" = "h" + "e". The squared ratio of the tangency chords satisfies The two tangency chords The tangency chord between the sides "AB" and "CD" in a tangential quadrilateral "ABCD" is longer than the one between the sides "BC" and "DA" if and only if the bimedian between the sides "AB" and "CD" is shorter than the one between the sides "BC" and "DA". If tangential quadrilateral "ABCD" has tangency points "W" on "AB" and "Y" on "CD", and if tangency chord "WY" intersects diagonal "BD" at