A **triangle** is a three-sided figure.

In Euclidean geometry, each side of a triangle is perfectly straight, and the sum of the internal angles of a triangle is always 180º.

A right triangle has one 90º angle. Right triangles have special properties (see trigonometry).

## Congruence of triangles

Triangle can be proven congruent in the following ways:

**Side-Angle-Side (SAS)**: If two sides are equal and the included angle is equal to another triangle, then the triangles are congruent.

**Side-Side-Side (SSS)**: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

**Angle-Side-Angle (ASA)**: If two angles and the included side of one triangle are equal the ones of another triangle, then the triangles are congruent.

**Angle-Angle-Side (AAS)**: If two angles and a side that is not included are equal to the ones of another triangle, then the triangles are congruent.

The SSA (Side-Side-Angle) cannot prove triangles congruent unless it is a right angle, where it is known as the HL (Hypotenuse-Leg) Theorem. AAA (Angle-Angle-Angle) cannot prove triangles congruent either. In hyperbolic geometry, however, it does prove congruence.