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equilateral triangle : ウィキペディア英語版
equilateral triangle

a^2
| angle = 60°}}
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.
==Principal properties==


Denoting the common length of the sides of the equilateral triangle as ''a'', we can determine using the Pythagorean theorem that:
* The area is A=\frac a^2
* The perimeter is p=3a\,\!
* The radius of the circumscribed circle is R = \frac} a or r=\frac
* The geometric center of the triangle is the center of the circumscribed and inscribed circles
* And the altitude (height) from any side is h=\frac a.


Many of these quantities have simple relationships to the altitude ("h") of each vertex from the opposite side:
* The area is A=\frac
* The radius of the circle circumscribing the three vertices is R=\frac
* The radius of the inscribed circle is r=\frac


In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors and the medians to each side coincide.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「equilateral triangle」の詳細全文を読む



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