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在解答几何问题时,我们经常要求学生注意问题的一般性,谨防特殊代替一般的错误。但解题实践告诉我们,仅强调这一面是不对的,有些几何问题,巧妙地应用满足题设条件的特殊元素,常能收到事半功倍之效,因此在教学中我们也必须引导学生去研究另一面——问题中的特殊情况。现按所取特殊元素的不同,举例归纳如下,供教学时参考。一、取特殊值例1 如图1,在Rt△ABC中,AC=BC,DEF弧的圆心为A,如果图中的两个阴影部分的面积相等,那么
When answering geometric questions, we often ask students to pay attention to the generality of the problem and guard against special errors instead of ordinary ones. However, the problem-solving practice tells us that it is wrong to emphasize only this aspect. Some geometric problems, and the clever use of special elements that satisfy the condition of the questions, often can be effective. Therefore, in teaching, we must also guide students to study One side - a special case of the problem. According to the different special elements adopted, examples are summarized below for reference when teaching. First, take the special value Example 1 In Figure 1, in Rt △ ABC, AC = BC, the center of the DEF arc is A, if the area of the two shaded parts in the figure is equal, then