triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted

{\displaystyle \triangle ABC}

.

Triangle
A triangle
Edges and vertices	3
Schläfli symbol	{3} (for equilateral)
Area	various methods; see below
Internal angle (degrees)	60° (for equilateral)

In Euclidean geometry any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space), in other words, there is only one plane that contains that triangle and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it, however, in higher dimensional Euclidean spaces this is no longer true. This article is about triangles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.

Types of triangle

Euler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides, i.e. equilateral triangles are isosceles.

By lengths of sides

Triangles can be classified according to the lengths of their sides:

• An equilateral triangle has all sides the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.
• An isosceles triangle has two sides of equal length.An isosceles triangle also has two angles of the same measure, namely the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides.The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles.
• A scalene triangle has all its sides of different lengths.Equivalently, it has all angles of different measure.

Equilateral	Isosceles	Scalene