# Definition:Quadrilateral/Rhombus

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## Definition

A **rhombus** is a parallelogram whose sides are all the same length.

Its angles *may or may not* all be equal.

## Also known as

A **rhombus** is also known as a **rhomb**.

Particularly when it is oriented so that the longer diagonal is a vertical line, a **rhombus** is often referred to as a **diamond**.

Some sources give the word **lozenge**, but this is old-fashioned, and nowadays brings with it an association with throat medication.

## Also see

- A square is a
**rhombus**all of whose angles are equal to a right angle.

## 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 **rhombus** is properly **rhombi**, although you may occasionally see the technically incorrect **rhombuses**.

The adjectival form of **rhombus** is **rhombic**, meaning:

*shaped like, or appertaining to, a***rhombus**.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**parallelogram** - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**rhombus**,**rhomb**,**diamond**or**lozenge** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**rhombus (rhomb)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**rhombus (rhomb)** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**rhombus (rhombi)** - 2021: Richard Earl and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(6th ed.) ... (previous) ... (next):**rhombus (rhombi)**