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
Saccheri quadrilateral (orbifold notation), and include: Saccheri quadrilateral A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri, who used it extensively in his book "Euclides ab omni naevo vindicatus" (literally Euclid Freed of Every Flaw) first published in 1733, an attempt to prove the parallel postulate using the method Reductio ad absurdum. The first known consideration of the Saccheri quadrilateral was by Omar Khayyam in the late 11th century, and it may occasionally be referred to as the Khayyam-Saccheri quadrilateral. For a Saccheri quadrilateral