View source for Triangle

{{otheruses}}
[[File:Black triangle2.svg|thumb|A black triangle]]
A '''triangle''' is a [[shape]], or a part of [[2D|two dimensional]] [[Space (physics)|space]]. It has [[3 (number)|three]] straight [[side]]s and three [[Vertex (geometry)|vertices]]. The three [[angle]]s of a triangle always add up to 180° (180 [[Degree (angle)|degrees]]). It is the [[polygon]] with the least possible number of sides. A triangle with vertices ''A'', ''B'', ''C'' is written as <math>\triangle ABC</math>.<ref>{{Cite web|last=|first=|date=2020-04-17|title=List of Geometry and Trigonometry Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/geometry-trigonometry-symbols/|archive-url=|archive-date=|access-date=2020-09-01|website=Math Vault|language=en-US}}</ref><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Triangle|url=https://mathworld.wolfram.com/Triangle.html|access-date=2020-09-01|website=mathworld.wolfram.com|language=en}}</ref> The study of geometry related to triangles is called [[trigonometry]]. Modern [[computer]]s usually use triangles to make more complex [[graphic]] images or shapes.
== Types of triangles ==
[[File:Isosceles-right-triangle.jpg|thumb|This is an ''isosceles right triangle'', because it has a right angle and two of its sides have the same length.]]
Triangles can be grouped according to how many of their sides are equal:<ref name=":0">{{Cite web|title=Triangles - Equilateral, Isosceles and Scalene|url=https://www.mathsisfun.com/triangle.html|access-date=2020-09-01|website=www.mathsisfun.com}}</ref>
* if all the three sides of a triangle have the same length, then it is an '''[[equilateral triangle]]'''.
* if a triangle has two sides with the same length, then it is an '''[[isosceles triangle]]'''.
* if all the three sides of a triangle have different lengths, then we have a '''scalene triangle'''.
Triangles can also be grouped by their angles:<ref name=":0" />

* if a triangle has a [[right angle]], that is, if one of the angles of that triangle measures 90° (90 degrees), then it is a '''[[right triangle]]'''. The opposite side to the right angle is the [[hypotenuse]].
* if a triangle has an [[obtuse angle]], that is, if one of the angles of that triangle is larger than 90°, then it is an '''obtuse triangle'''.
* if a triangle has only [[Acute angle|acute angles]], that is, if all the angles of that triangle are less than 90°, then it is an '''acute triangle'''.

{| width=50%
|-
|
<gallery>
File:Triangle.Equilateral.svg|Equilateral triangle
File:Triangle.Isosceles.svg|Isosceles triangle
File:Triangle.Scalene.svg|Scalene triangle
File:Triangle.Right.svg|Right Angled triangle
File:Triangle.Obtuse.svg|Obtuse Angled triangle
File:Triangle.Acute.svg|Acute Angled triangle
</gallery>
|}
== Area ==
[[File:Triangle (acute) bh.PNG|thumb|''b'' is base and ''h'' is height]]
The [[area]] of a triangle is equal to base times height times one half.

<math>area= \frac{base \times height}{2}</math>

== Triangle Media ==
<gallery widths='160px' heights='100%' mode='traditional' caption=''>
File:Triangle illustration.svg|Triangle, a polygon with three corners (vertices) and three lines (sides)

File:Triangle sommeangles.svg|The measures of the interior angles of the triangle always add up to 180 degrees (same color to point out they are equal).

File:Triangle.GeometryArea.svg|The area formula for a triangle can be proven by cutting two copies of the triangle into pieces and rearranging them into a rectangle.

File:Triangle.TrigArea.svg|Applying trigonometry to find the altitude {{math|1=''h''}}

File:Lexell's theorem in the plane.png|Orange triangles {{math|△''ABC''}} share a base {{mvar|AB}} and area. The locus of their apex {{mvar|C}} is a line (dashed green) parallel to the base. This is the Euclidean version of [[Lexell's theorem]].

File:Structural rigidity basic examples.svg|Rigidity of a triangle and square

File:Triangulation 3-coloring.svg|Triangulation in a simple polygon

File:Calabi triangle.svg|The [[Calabi triangle]] and the three placements of its largest square. The placement on the long side of the triangle is inscribed; the other two are not.

File:Lemoine Hexagon.svg|The Lemoine hexagon inscribed in a triangle
</gallery>
== Related pages ==
* [[Law of sines]]
* [[Pythagorean theorem]]
* [[Sierpinski triangle]]
* [[Reuleaux triangle]]
== References ==
<references />


{{-}}
{{Math-stub}}
{{Polygons}}
{{shapes}}
[[Category:Polygons]]