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A '''triangle''' is a three-sided figure.
A '''triangle''' is a three-sided figure.
In Euclidean geometry, each side of a triangle is perfectly straight, and the sum of the internal angles of a triangle is always 180º.
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 [[right triangle]] has one 90º angle. Right triangles have special properties (see [[trigonometry]]).
A [[right triangle]] has one 90º angle. Right triangles have special properties (see [[trigonometry]]).
See: [[polygon]]
==Congruence of triangles==
Triangle can be proven [[congruence|congruent]] in the following ways:
'''Side-Angle-Side (SAS)''': If two sides are equal and the included angle is equal to another triangle, then the triangles are congruent.<br>
'''Side-Side-Side (SSS)''': If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.<br>
'''Angle-Side-Angle (ASA)''': If two angles and the included side of one triangle are equal the ones of another triangle, then the triangles are congruent.<br>
'''Angle-Angle-Side (AAS)''': If two angles and a side that is not included are equal to the ones of another triangle, then the triangles are congruent.<br>
The SSA (Side-Side-Angle) cannot prove triangles congruent unless it is a right angle, where it is known as the HL (Hypotenuse-Leg) Theorem. AAA (Angle-Angle-Angle) cannot prove triangles congruent either. In [[hyperbolic geometry]], however, it does prove congruence.
==See also==
*[[polygon]]
[[Category:Geometry]]
[[Category:Geometry]]