In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides (see definition below) is referred to as a trapezoid in American English and as a trapezium in English outside North America. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides. A scalene trapezoid is a trapezoid with no equal sides or angles, in contrast to the special cases below. A trapezoid with vertices ABCD is denoted ABCD.
This article uses the term trapezoid in the sense that is current in the United States (and sometimes in some other English-speaking countries). In all other languages using a word derived from the Greek for this figure, the form closest to trapezium (e.g. French trapèze, Italian trapezio, German Trapez, Russian трапеция) is used.
The term trapezium has been in use in English since 1570, from Late Latin trapezium, from Greek τραπέζιον (trapézion), literally "a little table", a diminutive of τράπεζα (trápeza), "a table", itself from τετράς (tetrás), "four" + πέζα (péza), "a foot, an edge". The first recorded use of the Greek word translated trapezoid (τραπέζοειδη, trapézoeide, "table-like") was by Marinus Proclus (412 to 485 AD) in his Commentary on the first book of Euclid's Elements.
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