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 true: If the incircle is tangent to the sides "AB", "BC", "CD", "DA" at "W", "X", "Y", "Z" respectively, then a tangential quadrilateral "ABCD" is also cyclic (and hence bicentric) if and only if any one of the following conditions hold: The first of these three means that the "contact quadrilateral" "WXYZ" is an orthodiagonal quadrilateral. A tangential quadrilateral is bicentric if and only if its inradius is greater than that of any other tangential quadrilateral having the same sequence of side lengths. If the incircle is tangent to the sides "AB" and "CD" at "W" and "Y" respectively, then