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
Napoleon's theorem outer Napoleon triangle has a length of The relation between the latter two equations is that the area of an equilateral triangle equals the square of the side times formula_5 The centers of regular n-gons constructed over the sides of an n-gon P form a regular n-gon if and only if P is an affine image of a regular n-gon. Napoleon's theorem In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the centres of those equilateral triangles themselves form an equilateral triangle. The triangle thus formed