alternative proof of necessity direction of equivalent conditions for triangles (hyperbolic and spherical)
The following is a proof that, in hyperbolic geometry and spherical geometry, an equiangular triangle is automatically equilateral (http://planetmath.org/EquilateralTriangle) (and therefore regular (http://planetmath.org/RegularTriangle)). It better the proof of sufficiency supplied in the entry equivalent conditions for triangles and is slightly shorter than the proof of necessity supplied in the same entry.
Assume that is equiangular.
Since , AAA yields that . By CPCTC, . Hence, is equilateral.
|Title||alternative proof of necessity direction of equivalent conditions for triangles (hyperbolic and spherical)|
|Date of creation||2013-03-22 17:12:55|
|Last modified on||2013-03-22 17:12:55|
|Last modified by||Wkbj79 (1863)|