View source for Triangle

''in the Euclidean plane''

Three points (the vertices) and the straight line segments (the sides) with ends at these points. Sometimes the definition of a triangle refers to the convex part of the plane that is bounded by the sides of the triangle (the solid triangle).

The notion of a triangle can be introduced in manifolds different from the Euclidean plane. A triangle is usually defined as three points and three geodesic segments with ends at these points. Such are e.g. spherical triangles in [[Spherical geometry|spherical geometry]], and triangles in the hyperbolic or Lobachevskii plane (see [[Non-Euclidean geometries|Non-Euclidean geometries]]).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  H.S.M. Coxeter,   S.L. Greitzer,   "Geometry revisited" , Math. Assoc. Amer.  (1975)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  H.S.M. Coxeter,   "Introduction to geometry" , Wiley  (1969)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  S.I. Zetel',   "A new geometry of triangles" , Moscow  (1962)  (In Russian)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  J. Hadamard,   "Leçons de géométrie élémentaire. Géométrie plane" , J. Gabay, reprint  (1990)  pp. Chapt. 1</TD></TR><TR><TD valign="top">[5]</TD> <TD valign="top">  D. Efremov,   "A new geometry of triangles" , Odessa  (1902)  (In Russian)</TD></TR></table>



====Comments====
For relations between angles and sides of a triangle see [[Plane trigonometry|Plane trigonometry]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,   "Geometry" , '''1–2''' , Springer  (1987)  pp. Chapt. 9  (Translated from French)</TD></TR></table>