The Methods to Trisect an Acute Angle

Yi LIU, Gang LIU, Ruijie LIU, Rong TAN


This paper introduces the condition required to trisect an angle. The authors believe that, if you want to trisect the exterior angle of a triangle, the measures of two remote angles must have a proportion of 2:1. The deduction says that such triangle can be divided into two smaller isosceles triangles. One base angle of the first smaller isosceles triangle is the exterior angle of the other triangle. Construct this triangle with measures of the remote angles having a proportion of 2:1. There is a ray being the side of one isosceles triangle, as well as the base line of the other. The authors provide another method and predicts even more.


Internal angle; Ray; Angle trisection; Triangle; Characteristic supplementary angle triangle; Characteristic quadrangle; Isosceles triangle

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