# Definition:Triangle (Geometry)/Isosceles

## Definition

An **isosceles triangle** is a triangle in which two sides are the same length.

### Base

The base of an isosceles triangle is specifically defined to be the side which is a different length from the other two.

In the above diagram, $BC$ is the **base**.

### Base Angles

The two (equal) vertices adjacent to the base of an isosceles triangle are called the **base angles**.

In the above diagram, $\angle ABC$ and $\angle ACB$ are the **base angles**.

### Apex

The vertex opposite the base of an isosceles triangle is called the **apex** of the triangle.

In the above diagram, $A$ is the **apex**.

### Legs

The sides of an isosceles triangle which are adjacent to the apex are called the **legs** of the triangle.

In the above diagram, $AB$ and $AC$ are the **legs**.

## Also defined as

Some sources require that in an **isosceles triangle**, the third side has to be specifically of a different length than the two defined as being equal.

Hence, under such a definition, an equilateral triangle would *not* be classified as **isosceles**.

## 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 see

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

## Linguistic Note

The word **isosceles** comes from the Greek: $\iota \sigma \omicron \sigma \kappa \epsilon \lambda \epsilon \varsigma$, that is: from **iso** meaning **equal**, and **skelos** meaning **leg**.

Thus an **isosceles triangle** is literally an **equal-leg triangle**.

It is pronounced **eye- sos-ell-eez**, that is, with the emphasis on the second syllable. Note that the

**c**is silent.

The word **skeleton** comes from the same linguistic root.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**triangle**(Euclidean geometry) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**isosceles triangle** - 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):**isosceles 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):**isosceles triangle**