Editing Isosceles triangle (section)

{{Short description|Triangle with at least two sides congruent}}
{{good article}}
{{redirect|Isosceles}}
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{{Infobox Polygon
| name       = Isosceles triangle
| image      = Triangle.Isosceles.svg
| imagesize  = 100px
| caption    = Isosceles triangle
| type       = [[triangle]]
| edges      = 3
| symmetry   = [[Dihedral symmetry|Dih<sub>2</sub>]], [ ], (*), order 2
| schläfli   = (&nbsp;) ∨ {&nbsp;}
| wythoff    = 
| coxeter    = 
| area       = 
| dual       = Self-dual
| properties = [[convex polygon|convex]], [[Cyclic polygon|cyclic]]
}}

In [[geometry]], an '''isosceles triangle''' ({{IPAc-en|aɪ|ˈ|s|ɒ|s|ə|l|iː|z}}) is a [[triangle]] that has two [[Edge (geometry)|sides]] of equal length and two [[angle]]s of equal measure. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter version thus including the [[equilateral triangle]] as a [[special case]].
Examples of isosceles triangles include the [[isosceles right triangle]], the [[Golden triangle (mathematics)|golden triangle]], and the faces of [[bipyramid]]s and certain [[Catalan solid]]s.

The mathematical study of isosceles triangles dates back to [[ancient Egyptian mathematics]] and [[Babylonian mathematics]]. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the [[pediment]]s and [[gable]]s of buildings.

The two equal sides are called the ''legs'' and the third side is called the [[base (geometry)|''base'']] of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has [[reflection symmetry]] across the [[perpendicular bisector]] of its base, which passes through the opposite [[vertex (geometry)|vertex]] and divides the triangle into a pair of [[Congruence (geometry)|congruent]] [[right triangle]]s. The two equal angles at the base (opposite the legs) are always [[acute angle|acute]], so the classification of the triangle as acute, right, or [[obtuse triangle|obtuse]] depends only on the angle between its two legs.