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Triangle
Shape with three sides / From Wikipedia, the free encyclopedia
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. The triangle's interior is a two-dimensional region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex.
Triangle | |
---|---|
![]() A triangle | |
Edges and vertices | 3 |
Schläfli symbol | {3} (for equilateral) |
Area | various methods; see below |
Internal angle (degrees) | 60° (for equilateral) |
![triangle, tri, three, angle](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Tri_plus_angle.png/640px-Tri_plus_angle.png)
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. More generally, several points in Euclidean space of arbitrary dimension determine a simplex.
In non-Euclidean geometries three straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides which are straight relative to the surface. A curvilinear triangle is a shape with three curved sides, for instance a circular triangle with circular-arc sides. This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.
A triangle with vertices
and
is denoted
In describing metrical relations within a triangle, it is common to represent the length of the edge opposite each vertex using a lower-case letter, letting
be the length of the edge
the length of
and
the length of
; and to represent the angle measure at each corner using a Greek letter, letting
be the measure of angle
the measure of
and
the measure of