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在解几何题时,若遇到角平分线、线段的垂直平分线、倍角三角形等问题,可巧妙构造等腰三角形,借助等腰三角形的有关性质,往往能够迅速找到解题的途径,使问题化难为易,迎刃而解.那么如何构造等腰三角形呢?现举几例解析如下.一、“角平分线和平行线”构造等腰三角形当一个三角形中出现角平分线和平行线时,我们可以寻找到等腰三角形.如图1(1)中,若AD平分∠BAC,AD∥EC,则△ACE是等腰三角形;如图1(2)中,AD平分∠BAC,DE∥AC,则△ADE是等腰三角形;
In solving geometric problems, if you encounter the angle bisector, the line bisect the vertical line, multiplying triangle and other issues, you can skillfully construct isosceles triangles, with the nature of the isosceles triangle, often can quickly find a solution to the problem, the problem How to construct isosceles triangle? Here are a few examples as follows: First, “angle bisector and parallel line ” to construct the isosceles triangle When a triangle appears bisect and parallel lines, As shown in Figure 1 (1), if AD is divided by ACBAC, AD∥EC, △ ACE is an isosceles triangle; as shown in Figure 1 (2), AD is divided by ∠BAC, DE∥AC , Then △ ADE is isosceles triangle;