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 "c", "d" respectively and the extensions of the adjacent two sides for each side. Several more characterizations are known in the four subtriangles formed by the diagonals. The eight "tangent lengths" ("e", "f", "g", "h" in the figure to the right) of a tangential quadrilateral are the line segments from a vertex to the points where the incircle is tangent to the sides. From each vertex there are two congruent tangent lengths. The two "tangency chords" ("k" and "l" in the figure) of a tangential quadrilateral are the line segments that connect points on opposite sides where the incircle is