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代数与几何问题的互相转化是中学数学学习与研究中运用广泛,意义深刻的一种思维方法。以“形”研究“数”,会使问题直观形象,解法灵活简便。因此在解某些较复杂的代数问题时,可根据题目的特征,构造出一些简单的几何图形,把所求的问题转化为一个几何问题,然后运用几何等知识和方法求出所求问题的结果,本文将通过以下例题的分析,介绍在初中数学教学中,如何构造常见图形,直观简捷解题。例1 已知△ABC的三边长为
The mutual transformation of algebraic and geometric problems is a widely used and profoundly thought method in the study and research of middle school mathematics. To study “number” with “form” will make the problem intuitively visible and the solution is flexible and simple. Therefore, when solving some of the more complex algebraic problems, some simple geometrical figures can be constructed according to the features of the questions, and the problem can be transformed into a geometric problem. Then the knowledge and methods of geometry are used to solve the problem. As a result, through the analysis of the following examples, this article will introduce how to construct common graphs in mathematics teaching in junior high school and make them intuitive and easy to solve. Example 1 It is known that the three sides of △ABC are