# Definition:Triangle (Geometry)/Equilateral

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## Definition

An **equilateral triangle** is a triangle in which all three sides are the same length:

That is, a regular polygon with $3$ sides.

Thus it can be seen that an **equilateral triangle** can be considered to be a special case of an isosceles triangle.

## Euclid's Definition

In the words of Euclid:

*Of trilateral figures, an***equilateral triangle**is that which has its three sides equal, an**isosceles triangle**that which has two of its sides alone equal, and a**scalene triangle**that which has its three sides unequal.

(*The Elements*: Book $\text{I}$: Definition $20$)

## Also known as

An **equilateral triangle** is also less commonly known as an **equiangular triangle**.

## Also see

- Results about
**equilateral triangles**can be found**here**.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**triangle**(Euclidean geometry) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**triangle** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**triangle** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**equilateral**