<P> 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 (τραπεζοειδή, trapezoeidé, "table - like") was by Marinus Proclus (412 to 485 AD) in his Commentary on the first book of Euclid's Elements . </P> <P> This article uses the term trapezoid in the sense that is current in the United States and Canada . In many other languages using a word derived from the Greek for this figure, the form closest to trapezium (e.g. Portuguese trapézio, French trapèze, Italian trapezio, Spanish trapecio, German Trapez, Russian "трапеция") is used . </P> <P> There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids . Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms . Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition), making the parallelogram a special type of trapezoid . The latter definition is consistent with its uses in higher mathematics such as calculus . The former definition would make such concepts as the trapezoidal approximation to a definite integral ill - defined . This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid . This is also advocated in the taxonomy of quadrilaterals . </P> <P> Under the inclusive definition, all parallelograms (including rhombuses, rectangles and squares) are trapezoids . Rectangles have mirror symmetry on mid-edges; rhombuses have mirror symmetry on vertices, while squares have mirror symmetry on both mid-edges and vertices . </P>

When is a trapezoid also called a parallelogram
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