# Definition:Triangle (Geometry)/Right-Angled

## Definition

A right-angled triangle is a triangle in which one of the vertices is a right angle. Note that in order to emphasise the nature of the right angle in such a triangle, a small square is usually drawn inside it.

Note the following nomenclature in the context of a right-angled triangle:

### Hypotenuse

In a right-angled triangle, the opposite side to the right angle is known as the hypotenuse.

In the above figure, the side labeled $b$ is the hypotenuse.

In a right-angled triangle, for a given non-right angled vertex, the adjacent side which is not the hypotenuse is referred to as the adjacent.

In the above figure:

the adjacent to vertex $A$ is side $c$
the adjacent to vertex $C$ is side $a$.

### Opposite

In a right-angled triangle, for a given non-right angled vertex, the opposite side is referred to as the opposite.

In the above figure:

the opposite to vertex $A$ is side $a$
the opposite to vertex $C$ is side $c$.

### Legs

In a right-angled triangle, the two sides which are not the hypotenuse are referred to as its legs.

## Euclid's Definition

In the words of Euclid:

Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute.

## Also known as

A right-angled triangle is also often referred to as a right triangle.

## Also see

• Results about right triangles can be found here.