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
Orthodiagonal quadrilateral "M", "N" are the feet of these normals, then "ABCD" is orthodiagonal if and only if the eight points "K", "L", "M", "N", "R", "S", "T" and "U" are concyclic; the "second eight point circle". A related characterization states that a convex quadrilateral is orthodiagonal if and only if "RSTU" is a rectangle whose sides are parallel to the diagonals of "ABCD". There are several metric characterizations regarding the four triangles formed by the diagonal intersection "P" and the vertices of a convex quadrilateral "ABCD". Denote by "m", "m", "m", "m" the medians in triangles "ABP", "BCP", "CDP", "DAP" from