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
Integer triangle inequality. An important characteristic of the automedian triangle is that the squares of its sides form an arithmetic progression. Specifically, formula_91 so formula_92. A triangle family with integer sides formula_93 and with rational bisector formula_94 of angle A is given by with integers formula_99. There exist infinitely many non-similar triangles in which the three sides and the bisectors of each of the three angles are integers. There exist infinitely many non-similar triangles in which the three sides and the two trisectors of each of the three angles are integers. However, for "n" > 3 there exist no triangles in which