# Definition:Quadrilateral/Rectangle

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## Definition

A **rectangle** is a quadrilateral all of whose angles are equal to a right angle, and whose sides *may or may not* all be the same length.

### Containment

In the words of Euclid:

*Any rectangular parallelogram is said to be***contained**by the two straight lines containing the right angle.

(*The Elements*: Book $\text{II}$: Definition $1$)

## Also see

- Rectangle is Parallelogram: A
**rectangle**is a parallelogram all of whose angles are equal to a right angle.

Euclid, in Book $\text{II}$ Definition $1$: Containment of Rectangle, refers to this as a **rectangular parallelogram**.

- Definition:Equiangular Polygon, of which the
**rectangle**is an example.

## 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):**parallelogram** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**rectangle** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**rectangle** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**isogon**