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
Reuleaux triangle is possible to construct constant-width shapes based on irregular polygons that have an even number of sides. The Yanmouti sets are defined as the convex hulls of an equilateral triangle together with three circular arcs, centered at the triangle vertices and spanning the same angle as the triangle, with equal radii that are at most equal to the side length of the triangle. Thus, when the radius is small enough, these sets degenerate to the equilateral triangle itself, but when the radius is as large as possible they equal the corresponding Reuleaux triangle. Every shape with width "w", diameter "d",