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对于几何题的证明,习惯方法是根据几何的定义、定理、性质和添作适当的辅助线进行推理论证,这就是所谓的纯几何法。辩证唯物主义告诉我们,世界上的万事万物都是普遍联系的。这就启示我们,几何题也可以用非纯几何法——代数法、三角法等去解决。非纯几何法的最大特点就是能够减少许多添作辅助线的麻烦,从而使问题简单化。另外,用非纯几何法证几何题,对帮助学生沟通知识间的联系,培养学生综合运用知识的能力,提高解题技巧都大有益处。下面简略谈谈用三角法证几何题。一、应用三角函数定义证几何题当已知图形中多次出现直角时,可考虑用三角函数的定义证题。
For the proof of the geometrical problem, the customary method is based on the definition of the geometry, theorem, property, and add appropriate auxiliary lines for inference theory. This is the so-called pure geometric method. Dialectical materialism tells us that everything in the world is universally connected. This enlightens us that geometric problems can also be solved with non-pure geometry methods - algebraic methods, trigonometric methods, etc. The most important feature of the non-pure geometry method is that it can reduce the trouble of adding many auxiliary lines, thus simplifying the problem. In addition, the use of non-pure geometric methods to test geometric questions will help students communicate the connection between knowledge, develop students’ ability to use knowledge comprehensively, and improve problem-solving skills. The following briefly talks about the use of the triangle forensics geometry. First, the application of a trigonometric function to define a card geometry problem When there are multiple occurrences of a right angle in a known graph, consider using a trigonometric function to define the problem.