<P> 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 . </P> <P> Triangles can be classified according to the lengths of their sides: </P> <Ul> <Li> An equilateral triangle has all sides the same length . An equilateral triangle is also a regular polygon with all angles measuring 60 ° . </Li> <Li> 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 . </Li> <Li> A scalene triangle has all its sides of different lengths . Equivalently, it has all angles of different measure . </Li> </Ul> <Li> An equilateral triangle has all sides the same length . An equilateral triangle is also a regular polygon with all angles measuring 60 ° . </Li>

What are the three types of triangles classified by sides