两外角平分线相等的三角形性质的探讨

Investigation on Triangle Properties with Two Equal Exterior Angle Bisector

"两外角平分线相等的三角形是否是等腰三角形"的问题,可以分解为两外角平分线在第三边的同侧与两外角平分线在第三边的两侧两种情况分别用纯几何证法与肯否法证明,由此可得出这样的结论:两外角平分线在第三边的同侧,且两外角平分线相等的三角形是等腰三角形;两外角平分线在第三边的两侧,且外角平分线相等在第三边两侧的三角形是非等腰三角形.

The problem whether triangles with two equal exterior angle bisectors are isosceles triangles or not can be solvedthrough the pure geometric method and the positive and negative method. It can be decomposed into two cases. One is that twoexterior angle bisectors and the third side are on the same side and the other is that two exterior angle bisectors are on the oppositesides of the third side. So we can conclude that： when the two exterior angle bisectors and the third side are on the same side andthe two exterior angle bisectors are equal,the triangle is isosceles triangle;when the two exterior angle bisectors are equal and onthe opposite sides of the third side,the triangle is not isosceles triangle.