![]() ![]() The measures of the interior angles of the triangle always add up to 180 degrees (same color to point out they are equal). Elementary facts about triangles were presented by Euclid, in books 1–4 of his Elements, written around 300 BC. In rigorous treatments, a triangle is therefore called a 2- simplex (see also Polytope). The 454590 right triangle, which appears in the tetrakis square tiling, is isosceles. The latter definition would make all equilateral triangles isosceles triangles. Triangles are assumed to be two- dimensional plane figures, unless the context provides otherwise (see § Non-planar triangles, below). Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.Ī triangle with vertices A, īasic facts A triangle, showing exterior angle d. A curvilinear triangle is a shape with three curved sides, for instance a circular triangle with circular-arc sides. A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides which are straight relative to the surface. In non-Euclidean geometries three straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. More generally, several points in Euclidean space of arbitrary dimension determine a simplex. All isosceles triangles are not similar for a couple of reasons. ![]() In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points, when non- collinear, determine a unique triangle situated within a unique flat plane. There is the special case where all three sides are equal which is called a equilateral triangle. ![]() Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex. The triangle's interior is a two-dimensional region. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. ![]()
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