Also in spherical geometry, a triangle has these additional requirements: It must be strictly contained in a hemisphere of the sphere that is serving as the model for spherical geometry, and all of its angles must have a measure strictly less that .
Triangles can be classified according to the number of their equal sides. So, a triangle with 3 equal sides is called equilateral (http://planetmath.org/RegularTriangle), a triangle with 2 equal sides is called isosceles, and finally a triangle with no equal sides is called scalene. Notice that an is also isosceles, but there are isosceles triangles that are not equilateral.
In Euclidean geometry, triangles can also be classified according to the of the greatest of its three (inner) angles. If the greatest of these is acute (and therefore all three are acute), the triangle is called an acute triangle. If the triangle has a right angle, it is a right triangle. If the triangle has an obtuse angle, it is an obtuse triangle.
Area of a triangle
There are several ways to a triangle’s area.
In hyperbolic and spherical , the area of a triangle is equal to its defect (measured in radians).
For the rest of this entry, only Euclidean geometry will be considered.
Many for the area of a triangle exist. The most basic one is , where is its base and is its height. Following is a of another for the area of a triangle.
The last is known as Heron’s formula.
With the coordinates of the vertices , , of the triangle, the area may be expressed as
(cf. the volume of tetrahedron (http://planetmath.org/Tetrahedron)).
Angles in a triangle
Special geometric objects for a triangle
|Date of creation||2013-03-22 11:43:51|
|Last modified on||2013-03-22 11:43:51|
|Last modified by||Wkbj79 (1863)|