This is also advocated in the taxonomy of quadrilaterals. This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid. The latter definition is consistent with its uses in higher mathematics such as calculus. 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. Some sources use the term proper trapezoid to describe trapezoids under the exclusive definition, analogous to uses of the word proper in some other mathematical objects. Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids. Two parallel sides, and no line of symmetry Two parallel sides, and a line of symmetry ![]() Opposite sides and angles equal to one another but not equilateral nor right-angled Proclus (Definitions 30-34, quoting Posidonius) The following table compares usages, with the most specific definitions at the top to the most general at the bottom. This was reversed in British English in about 1875, but it has been retained in American English to the present.
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