 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 three-dimensional counterpart of a parallelogram is a parallelepiped.