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
Ex-tangential quadrilateral Ex-tangential quadrilateral In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the "extensions" of all four sides are tangent to a circle outside the quadrilateral. It has also been called an exscriptible quadrilateral. The circle is called its "excircle", its radius the "exradius" and its center the "excenter" ("E" in the figure). The excenter lies at the intersection of six angle bisectors. These are the internal angle bisectors at two opposite vertex angles, the external angle bisectors (supplementary angle bisectors) at the other two vertex angles, and the external angle bisectors at the angles formed where the extensions