![]() ![]() 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). Triangles are assumed to be two- dimensional plane figures, unless the context provides otherwise (see § Non-planar triangles, below). 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 fact, all equilateral triangles, because all of the angles are exactly 60 degrees, all equilateral triangles are actually acute. You could have an equilateral acute triangle. And this right over here would be a 90 degree angle. In non-Euclidean geometries three straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. In this situation right over here, actually a 3, 4, 5 triangle, a triangle that has lengths of 3, 4, and 5 actually is a right triangle. More generally, several points in Euclidean space of arbitrary dimension determine a simplex. 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. 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. 30-60-90 Theorem: If a triangle has angle measures 30 30, 60 60 and 90 90, then the sides are in the ratio x: x 3: 2x x: x 3: 2 x. One of the two special right triangles is called a 30-60-90 triangle, after its three angles. A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. Hypotenuse equals twice the smallest leg, while the larger leg is 3 3 times the smallest. ![]()
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