# equilateral triangle

An equilateral triangle is one for which all 3 sides are congruent.

The following statements hold in Euclidean geometry for an equilateral triangle.

• It is a regular polygon.

• The bisector of any angle coincides with the height, the median and the perpendicular bisector of the .

• If $r$ is the length of the side, then the height is equal to $\displaystyle\frac{r\sqrt{3}}{2}$.

• If $r$ is the length of the side, then the area is equal to $\displaystyle\frac{r^{2}\sqrt{3}}{4}$.

 Title equilateral triangle Canonical name EquilateralTriangle Date of creation 2013-03-22 11:44:04 Last modified on 2013-03-22 11:44:04 Owner Mathprof (13753) Last modified by Mathprof (13753) Numerical id 22 Author Mathprof (13753) Entry type Definition Classification msc 51-00 Classification msc 81-00 Classification msc 08-01 Related topic Triangle Related topic IsoscelesTriangle Related topic EquivalentConditionsForTriangles Related topic EquiangularTriangle Related topic RegularTriangle