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
Quadrilateral quadrilateral are concurrent and are all bisected by their point of intersection. In a convex quadrilateral with sides "a", "b", "c" and "d", the length of the bimedian that connects the midpoints of the sides "a" and "c" is where "p" and "q" are the length of the diagonals. The length of the bimedian that connects the midpoints of the sides "b" and "d" is Hence This is also a corollary to the parallelogram law applied in the Varignon parallelogram. The lengths of the bimedians can also be expressed in terms of two opposite sides and the distance "x" between