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我们在解某些代数问题时,当发现问题条件中有明显的“a~2+b~2=c~2(a、b、c均为正数)的数量关系,我们可以优先考虑构造直角三角形求解。通过已知作图,将题设条件及数量关系直接在直角三角形中显示出来,然后借助直角三角形的性质寻求所解的结论。这种利用直角三角形的知识解代数问题的方法比较特殊,但非常巧妙,且直观、清楚、简洁易于理解。现举几例说明如下:
When we solve some algebraic problems, when we find that there are obvious quantitative relationships between ”a~2+b~2=c~2 (a, b, and c are all positive numbers), we can give priority to the construction of The right-angle triangle is solved by knowing the graph, and the condition and quantity relations of the problem are directly displayed in the right-angle triangle, and then the solution result is found by means of the properties of the right-angle triangle.The method of solving the algebraic problem using the right-angled triangle is compared. Special, but very clever, intuitive, clear, concise and easy to understand. Here are a few examples to illustrate: