Trapezium
as defined by Euclid, any quadrilateral except a square, an oblong, a rhombus, and a rhomboid. Later Greek geometers seem to have used the word in the more restricted sense of a quadrilateral with one pair of parallel sides; and the word trapezoid was introduced to describe a quadrilateral which had no two sides parallel. On the Continent the words are so distinguished to this day. By English geometers and writers on mensuration the words got interchanged as regards their significance, so that with us a trapezoid is generally defined as a quadrilateral with two parallel sides. Thus English writers have retained trapezium in the broader sense, and have used trapezoid in the restricted sense of a Euclidean trapezium with two sides parallel. The continental custom is historically and etymologically the better. There is, however, hardly a necessity for both words, since the word quadrilateral is now invariably used by modern geometers for a four-sided figure which is not a parallelogram.