Definition:Quadrilateral/Trapezium

Definition

A trapezium is a quadrilateral with no parallel sides.

Also defined as

Outside the US (one of a few countries that use this definition), a trapezium is a quadrilateral which has one pair of sides parallel, that is, what the US defines as a trapezoid.

Also known as

Outside the US (one of a few countries that use this definition), this figure is known as a trapezoid.

In order to reduce confusion, when such a quadrilateral is intended, it is probably better to use the term irregular quadrilateral instead.

Euclid, in his definitions, did not distinguish between trapezia and trapezoids.

Euclid's Definitions

In the words of Euclid:

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

(The Elements: Book $\text{I}$: Definition $22$)

Linguistic Note

The plural of trapezium is trapezia.

The word comes from Latin, in which language it is a neuter noun of the second declension, hence its plural form.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): trapezium: 2. (mainly North American usage. UK term: trapezoid.)
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): trapezoid