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
.
In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted.
Types of triangle
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.