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| [[Image:Triangle.png|right]]
| | {{uncommon identity}} |
| A '''triangle''' is a three-sided [[geometric]] [[shape]].
| | {{infobox identity |
| In [[Euclidean geometry]], each side of a triangle is perfectly straight, and the sum of the internal angles of a triangle is always 180º.
| | | name = Trigender |
| A triangle is defined by any three points that are not [[collinear]].
| | | flag = trigender.png |
| | | related = [[multigender]], [[polygender]], [[bigender]], [[pangender]] |
| | | percentage = 0.1 |
| | | gallery_link = Pride Gallery/Trigender |
| | }} |
| | '''Trigender''' is a [[gender identity]] under the [[multigender]] and [[transgender]] umbrella terms. Trigender people experience exactly three genders, either simultaneously or moving between the three (the latter one being under the [[genderfluid]] umbrella too).<ref>Leslie Feinberg, ''Trans Liberation: Beyond Pink Or Blue'', page 53-4, Beacon Press, 1999, ISBN 0-8070-7951-0, ISBN 978-0-8070-7951-5.</ref><ref>Alexia Elejalde-Ruiz, "[http://articles.chicagotribune.com/2009-11-18/news/0911180173_1_gender-born-layers For the young, gender is fluid]", ''Chicago Tribune'', November 18, 2009.</ref> These three genders can be any gender, either binary or nonbinary.<ref>Maurianne Adams, Lee Anne Bell, Pat Griffin, ''Teaching for diversity and social justice'', page 224,CRC Press, 2007, ISBN 0-415-95200-X, 9780415952002.</ref> |
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| ==Naming conventions== | | ==History== |
| 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.
| | Trigender was mentioned as one of many valid nonbinary identities in the 2013 text ''Sexuality and Gender for Mental Health Professionals: A Practical Guide''.<ref>{{cite book|isbn=9781446293133|title=Sexuality and Gender for Mental Health Professionals: A Practical Guide|last1=Richards|first1=Christina|last2=Barker|first2=Meg|year=2013|publisher=SAGE Publications}}</ref> |
| The angles are denoted by Greek letters, if possible, the letter of an angle will correspond to the letter of the adjacent vertex.
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| 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>.
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| Similarly, the angles are denoted as <math>\alpha = \angle CAB, \beta = \angle ABC, \gamma = \angle BCA</math>.
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| | == See also == |
| | * [[Multigender]] |
| | * [[Genderfluid]] |
| | * [[Bigender]] |
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| ==Types of triangles== | | == References == |
| A [[right triangle]] has one 90º angle. Right triangles have special properties (see [[trigonometry]]).
| | <references />{{Stub}} |
| | | [[Category:Nonbinary identities]] |
| An [[isosceles triangle]] has two equal angles, and two equal sides.
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| An [[equilateral triangle]] has three equal sides, and three 60º angles.
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| If a triangle is not one of the above, it is a '''scalene triangle''' -- that is, a triangle with no [[congruent]] angles.
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| An '''obtuse triangle''' has one angle that measures more than 90<sup>o</sup>.
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| {| class="wikitable"
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| |-
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| |<!--col1-->[[Image:Right-triangle.png|150px]]
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| |<!--col2-->[[Image:Isoscles-triangle.png|150px]]
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| |<!--col3-->[[Image:Equilateral-triangle.png|150px]]
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| |<!--col4-->[[Image:Obtuse-triangle.png|150px]]
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| |-
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| |<!--col1-->Right Triangle
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| |<!--col2-->Isosceles Triangle
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| |<!--col3-->Equilateral Triangle
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| |<!--col4-->Obtuse Triangle
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| |-
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| |<!--col1--><math>\angle CBA =90^\circ = \pi/2</math>
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| |<!--col2--><math>\angle BCA = \angle CAB </math>
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| |<!--col3--><math>\angle ABC = \angle BCA = \angle CAB</math>
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| |<!--col4--><math>\angle ACB > 90^\circ</math>
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| |}<!--end wikitable-->
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| ==Congruence of triangles==
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| Triangles can be proven [[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]]
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| *[[Pascal's triangle]]
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| *[[Sierpinski triangle]]
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| *[[Bermuda Triangle]]
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| [[Category:Geometry]] | |
