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Line 1: − + + + + + + + + + + + + − In [[Euclidean geometry]], each side of a triangle is perfectly straight, and the sum of the internal angles of a triangle is always 180º. Line 13:
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In political ideology, a triangle symbolizes change as the Greek delta symbol. Usually demands for change are to move towards socialism and away from the U.S. Constitution and principles of a constitutional republic.
A '''triangle''' is a three-sided [[geometric]] [[shape]], made by any three points that are not [[collinear]].
[[Image:Triangle.png|right]]
A '''triangle''' is a three-sided [[geometric]] [[shape]].
In [[Euclidean geometry]], each side of a triangle is perfectly straight, and the sum of the internal angles of a triangle is always 180º.
A triangle is defined by any three points that are not [[collinear]].
In political ideology, a triangle symbolizes change as the [[Greek]] delta symbol. Usually demands for change are to move towards [[socialism]] and away from the [[U.S. Constitution]] and principles of a [[constitutional republic]].
==Naming conventions==
Usually, the vertices of a triangle are counter-clockwise denoted by big Latin letters, while small Latin letters are used for the sides: Each side will have the same letter as the opposite vertex.
The angles are denoted by Greek letters, if possible, the letter of an angle will correspond to the letter of the adjacent vertex.
Often, the sides will be referenced by the adjacent vertices: in the triangle on top of this page, we have <math>a = \overline{BC} = \overline{CB}, b = \overline{CA} = \overline{CA}, c = \overline{BA} = \overline{AB} </math>.
Similarly, the angles are denoted as <math>\alpha = \angle CAB, \beta = \angle ABC, \gamma = \angle BCA</math>.
==Types of triangles==
==Types of triangles==
An '''obtuse triangle''' has one angle that measures more than 90<sup>o</sup>.
An '''obtuse triangle''' has one angle that measures more than 90<sup>o</sup>.
{| class="wikitable"
|-
|<!--col1-->[[Image:Right-triangle.png|150px]]
|<!--col2-->[[Image:Isoscles-triangle.png|150px]]
|<!--col3-->[[Image:Equilateral-triangle.png|150px]]
|<!--col4-->[[Image:Obtuse-triangle.png|150px]]
|-
|<!--col1-->Right Triangle
|<!--col2-->Isosceles Triangle
|<!--col3-->Equilateral Triangle
|<!--col4-->Obtuse Triangle
|-
|<!--col1--><math>\angle CBA =90^\circ = \pi/2</math>
|<!--col2--><math>\angle BCA = \angle CAB </math>
|<!--col3--><math>\angle ABC = \angle BCA = \angle CAB</math>
|<!--col4--><math>\angle ACB > 90^\circ</math>
|}<!--end wikitable-->
==Congruence of triangles==
==Congruence of triangles==