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regular triangle (Definition)

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


\begin{pspicture}(-0.2,-0.2)(5.2,5.2) \pspolygon(0,0)(5,0)(2.5,4.33) \rput[b](2.... ...}{60} \psarc(5,0){0.5}{120}{180} \psarc(2.5,4.33){0.5}{240}{300} \end{pspicture}

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 $\displaystyle \frac{r^2\sqrt{3}}{4}$ .




"regular triangle" is owned by Wkbj79.
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See Also: triangle, isosceles triangle, equilateral triangle, equiangular triangle, equivalent conditions for triangles, regular polygon


Attachments:
compass and straightedge construction of regular triangle (Algorithm) by Wkbj79
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Cross-references: area, length, Euclidean geometry, opposite side, perpendicular bisector, median, height, angle, bisector, isosceles triangle theorem, regular polygons, interior angles, congruent, sides
There are 7 references to this entry.

This is version 3 of regular triangle, born on 2007-06-06, modified 2007-06-09.
Object id is 9538, canonical name is RegularTriangle.
Accessed 9091 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

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