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 the midpoints of the diagonals. This is possible when using Euler's quadrilateral theorem in the above formulas. Whence and Note that the two opposite sides in these formulas are not the two that the bimedian connects. In a convex quadrilateral, there is the following dual connection between the bimedians and the diagonals: The four angles of a simple quadrilateral "ABCD" satisfy the following identities: and Also, In the last two formulas, no angle is allowed to be a right angle, since tan 90° is not defined. If a convex quadrilateral has the consecutive sides "a", "b", "c", "d" and the