Definition:Quadrilateral/Trapezoid

Definition

A trapezoid is a quadrilateral which has exactly one pair of sides parallel:

Thus, by this definition, a parallelogram is not a trapezoid.

Base

The bases of a trapezoid are its $2$ parallel sides.

In the above diagram, the bases of the given trapezoids are $AB$ and $DC$, $EF$ and $HG$, and $IJ$ and $KL$.

Leg

The legs of a trapezoid are its $2$ sides adjacent to the bases.

In the above diagram, the legs of the given trapezoids are $AD$ and $BC$, $EH$ and $FG$, and $IK$ and $JL$.

Height

The height of a trapezoid is defined as the length of a line perpendicular to the bases.

In the above diagram, the heights of the given trapezoids are indicated by the letter $h$.

Also defined as

Outside the US (one of a few countries that use this definition), a trapezoid is a quadrilateral with no parallel sides, that is, what the US defines as a trapezium.

Also known as

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

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

Also see

• Results about trapezoids can be found here.

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 $22$)

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): trapezium: 1. (mainly UK usage. North American term: trapezoid.)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trapezium (US: trapezoid)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trapezium (US: trapezoid)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): trapezium (trapezia)