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
Newton's theorem (quadrilateral) Newton's theorem (quadrilateral) In Euclidean geometry Newton's theorem states, that in any tangential quadrilateral other than a rhombus the center of its incircle lies on its Newton line. Let "ABCD" be a tangential quadrilateral with at most one pair of parallel sides. Furthermore, let "E" and "F" the midpoints of its diagonals "AC" and "BD" and "P" be the center of its incircle. Given such a configuration the point P is located on the Newton line, that is line "EF" connecting the midpoints of the diagonals. A tangential quadrilateral with two pairs of parallel sides is a rhombus. In this