equivalent conditions for triangles
It suffices to show that is equilateral if and only if it is equiangular.
Sufficiency: Assume that is equilateral.
Since , SSS yields that . By CPCTC, . Hence, is equiangular.
Necessity: Assume that is equiangular.
By the theorem on determining from angles that a triangle is isosceles, we conclude that is isosceles with legs and that is isosceles with legs . Thus, . Hence, is equilateral. ∎
|Title||equivalent conditions for triangles|
|Date of creation||2013-03-22 17:12:46|
|Last modified on||2013-03-22 17:12:46|
|Last modified by||Wkbj79 (1863)|