Difference between revisions of "Triangle"

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(congruence of triangles)
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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.
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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]]
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==Congruence of triangles==
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Triangle can be proven [[congruence|congruent]] in the following ways:
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'''Side-Angle-Side (SAS)''': If two sides are equal and the included angle is equal to another triangle, then the triangles are congruent.<br>
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'''Side-Side-Side (SSS)''': If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.<br>
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'''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>
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'''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>
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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.
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==See also==
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*[[polygon]]
  
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Revision as of 17:39, 20 May 2007

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.

A right triangle has one 90º angle. Right triangles have special properties (see trigonometry).

Congruence of triangles

Triangle can be proven 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.
Side-Side-Side (SSS): If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
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.
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.
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