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 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. The shape is often called an irregular quadrilateral. 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) This mistake was corrected in British English in about 1875, but was retained in American English into the modern day. no parallel sides – trapezoid (τραπεζοειδή, trapezoeidé, literally trapezium-like ( εἶδος means 'resembles'), in the same way as cuboid means cube-like and rhomboid means rhombus-like)Īll European languages follow Proclus's structure as did English until the late 18th century, until an influential mathematical dictionary published by Charles Hutton in 1795 supported without explanation a transposition of the terms.one pair of parallel sides – a trapezium (τραπέζιον), divided into isosceles (equal legs) and scalene (unequal) trapeziums.

Two types of trapezia were introduced by Proclus (412 to 485 AD) in his commentary on the first book of Euclid's Elements: Ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια ( trapezia literally 'a table', itself from τετράς ( tetrás), 'four' + πέζα ( péza), 'a foot end, border, edge').

Isosceles trapezoid definition