# 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)**