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 three-cornered shape of the Reuleaux triangle may be seen both as a symbol of the Trinity, and as "an act of opposition to the form of the circle". The Reuleaux triangle has also been used in other styles of architecture. For instance, Leonardo da Vinci sketched this shape as the plan for a fortification. A modern high-rise building, the Kölntriangle in Cologne, Germany, was built with a Reuleaux triangle cross-section. Together with the circular shape of its core, this gives varied depths to the rooms of the building. Another early application of the Reuleaux triangle, by Leonardo da Vinci circa