# regular triangle

A regular triangle is one for which all sides are congruent and all interior angles are congruent.

All regular triangles are regular polygons. Also, by the isosceles triangle theorem, the bisector of any angle coincides with the height, the median and the perpendicular bisector of the opposite side.

The following statements hold in Euclidean geometry for a regular triangle.

• 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 regular triangle Canonical name RegularTriangle Date of creation 2013-03-22 17:12:52 Last modified on 2013-03-22 17:12:52 Owner Wkbj79 (1863) Last modified by Wkbj79 (1863) Numerical id 6 Author Wkbj79 (1863) Entry type Definition Classification msc 51-00 Related topic Triangle Related topic IsoscelesTriangle Related topic EquilateralTriangle Related topic EquiangularTriangle Related topic EquivalentConditionsForTriangles Related topic RegularPolygon