Editing Triangle (section)

== Definition, terminology, and types ==
A triangle is a figure consisting of three line segments, each of whose endpoints are connected.{{sfn|Lang|Murrow|1988|p=[https://books.google.com/books?id=pc_kBwAAQBAJ&pg=PA4 4]}} This forms a polygon with three sides and three angles. The terminology for categorizing triangles is more than two thousand years old, having been defined in Book One of Euclid's ''[[Euclid's Elements|Elements]]''.{{sfn|Byrne|2013|pp=xx–xxi}} The names used for modern classification are either a direct transliteration of Euclid's Greek or their Latin translations.

{{anchor|Type of triangles}}Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an [[equilateral triangle]],<ref>{{multiref
|{{harvnb|Lang|Murrow|1988|p=[https://books.google.com/books?id=pc_kBwAAQBAJ&pg=PA4 4]}}
|{{harvnb|Heath|1926|loc=Definition 20}}
}}</ref> a triangle with two sides having the same length is an [[isosceles triangle]],<ref>{{multiref
|{{harvnb|Lang|Murrow|1988|p=[https://books.google.com/books?id=pc_kBwAAQBAJ&pg=PA4 4]}}
|{{harvnb|Ryan|2008|p=[https://books.google.com/books?id=b_qM4HImlPgC&pg=PA91 91]}}
}}</ref>{{efn|1=The definition by Euclid states that an isosceles triangle is a triangle with exactly two equal sides.{{sfn|Heath|1926|loc=[https://hdl.handle.net/2027/uva.x001426155?urlappend=%3Bseq=207 p. 187, Definition 20]}} By the modern definition, it has at least two equal sides, implying that an equilateral triangle is a special case of isosceles triangle.{{sfn|Stahl|2003|loc=[https://books.google.com/books?id=jLk7lu3bA1wC&pg=PA37 p. 37]}}}} and a triangle with three different-length sides is a ''scalene triangle''.<ref>{{multiref
|{{harvnb|Ryan|2008|p=[https://books.google.com/books?id=b_qM4HImlPgC&pg=PA91 91]}}
|{{harvnb|Usiskin|Griffin|2008|page=4}}
}}</ref> A triangle in which one of the angles is a [[right angle]] is a [[right triangle]], a triangle in which all of its angles are less than that angle is an [[acute triangle]], and a triangle in which one of it angles is greater than that angle is an [[obtuse triangle]].<ref>{{multiref
|{{harvnb|Lang|Murrow|1988|p=[https://books.google.com/books?id=pc_kBwAAQBAJ&pg=PA44 44]}}
|{{harvnb|Ryan|2008|p=[https://books.google.com/books?id=b_qM4HImlPgC&pg=PA96 96]}}
}}</ref> These definitions date back at least to [[Euclid]].{{sfn|Heath|1926|loc=Definition 20, Definition 21}}
<gallery widths=180 heights=180 class="center" >
 Triangle.Equilateral.svg|[[Equilateral triangle]]
 Triangle.Isosceles.svg|[[Isosceles triangle]]
 Triangle.Scalene.svg|Scalene triangle
</gallery>
<gallery widths=180 heights=180 class="center" >
 Triangle.Right.svg|[[Right triangle]]
 Triangle.Acute.svg|[[Acute triangle]]
 Triangle.Obtuse.svg|[[Obtuse triangle]]
</gallery>