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Concept
Trapezoid
Summary
In geometry, a trapezoid (ˈtɹæpəzɔɪd) in USA and Canadian English, or trapezium (trəˈpiːziəm) in British and other forms of English, is a quadrilateral that has at least one pair of parallel sides.
The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast with the special cases below.
A trapezoid is usually considered to be a convex quadrilateral in Euclidean geometry, but there are also crossed cases. If ABCD is a convex trapezoid, then ABDC is a crossed trapezoid. The metric formulas in this article apply in convex trapezoids.
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").
Two types of trapezia were introduced by Proclus (412 to 485 AD) in his commentary on the first book of Euclid's Elements:
one pair of parallel sides – a trapezium (τραπέζιον), divided into isosceles (equal legs) and scalene (unequal) trapezia
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)
All 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. This mistake was corrected in British English in about 1875, but was retained in American English into the modern day.
The following is a table comparing usages, with the most specific definitions at the top to the most general at the bottom.
Official source
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