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
Triangle of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality. Three given angles form a non-degenerate triangle (and indeed an infinitude of them) if and only if both