Triangle their internal angles, measured here in degrees. A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral. Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a "2-simplex" (see also Polytope). Elementary facts about triangles were presented by Euclid in books 1–4
Equilateral pentagon relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane. When the equilateral pentagon is dissected into triangles, two of them appear as isosceles (triangles in orange and blue) while the other one is more general (triangle in green). We assume that we are given the adjacent angles formula_1 and formula_2. According to the law of sines the length of the line dividing the green and blue triangles is: The square of the length of the line dividing the orange and green triangles is: According to the law of cosines, the cosine