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含60°内角的三角形已被证明具有很多良好的几何性质,其中与三角形的外心和垂心相关的性质最为突出.而对于以120°为内角的钝角三角形,其外心和垂心都在形外,因此,它的距离关系和角度关系很难直观地从几何上获得和严格证明.所以,从代数角度建立反映几何关系的方程成为分析这类问题的一般手段.这种方法对于寻找几何关系成立的充要条件、探究几何关系之间的本质联系、研究问题的条件从特殊到一般等等都具有重要意义.从问题的发现过程而言,代数建立的方程可以在简化过程中调整问题初始给定的条件以达到最终结论.以下两个与120°内角有关的解三角形问题充分反映了这种方法的优势.
The triangle with an internal angle of 60° has been proven to have a lot of good geometric properties, among which the nature associated with the triangle’s center of gravity and the verticality is the most prominent. For an obtuse triangle with an internal angle of 120°, the external and vertical centers of the shape are outside the shape. Therefore, its distance relationship and angle relationship are difficult to obtain intuitively and rigorously. Therefore, the establishment of an equation reflecting the geometric relationship from the algebraic point of view has become a general approach to the analysis of this type of problem. This method is useful for finding geometric relationships. The necessary and sufficient conditions, the exploration of the essential relationship between geometric relationships, and the conditions for studying problems are of special significance from special to general. From the point of view of problem discovery, the equations established by algebra can be adjusted during the simplification process. The conditions are determined so as to reach the final conclusion. The following two solution triangle problems related to the internal angle of 120° fully reflect the advantages of this method.