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分类讨论是数学思想中的一种重要的思想,它使我们考察问题全面而合理.在解决相似三角形问题中就需用分类讨论.下面举例说明.一、对应角不确定时例1如图1,∠=40°,∠B=60°,一直线l与△ABC的边AC、AB分别相交于点D、E两点,当∠ADE为多少度时,△ABC与△ADE相似?分析:显然∠C=80°,∠A是△ABC和△ADE的公共角,如果∠ADE等于∠C或∠B,那么△ABC与△ADE相似.
Category discussion is an important idea in mathematical thinking, it allows us to examine the issue of a comprehensive and reasonable.To solve the problem of similar triangles need to use the classification discussion.Examples below.First, the corresponding angle is not the case of time 1 as shown in Figure 1 , ∠ = 40 °, ∠B = 60 °, the line AC and AB of the line l and △ ABC intersect at points D and E respectively. When ΔEAD is the number of degrees, △ ABC is similar to △ ADE. Analysis: Obviously ∠C = 80 °, ∠A is the common angle between △ ABC and △ ADE. If ∠ADE is equal to ∠C or ∠B, △ ABC is similar to △ ADE.