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equiangular triangle∗
Wkbj79†
2013-03-21 23:08:20
An equiangular triangle is one for which all three interior angles are congruent.
A
B
C
By the theorem at determining from angles that a triangle is isosceles, we
can conclude that, in any geometry in which ASA holds, an equilateral triangle
is regular. In any geometry in which ASA, SAS, SSS, and AAS all hold, the
isosceles triangle theorem yields that the bisector of any angle of an equiangular
triangle coincides with the height, the median and the perpendicular bisector of
the opposite side.
The following statements hold in Euclidean geometry for an equiangular
triangle.
• The triangle is determined by specifying one side.
√
r 3
• If r is the length of the side, then the height is equal to
.
2
√
r2 3
• If r is the length of the side, then the area is equal to
.
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∗ hEquiangularTrianglei
created: h2013-03-21i by: hWkbj79i version: h39537i Privacy
setting: h1i hDefinitioni h51-00i
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