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添辅助线是几何证题的一大难点。教学中应引导学生把证题的需要和辅助线的作用结合起来思考,便可作出恰到好处的辅助线;另一方面,启发学生将各类证题进行归纳,找出作辅助线的一般规律,就可以化难为易了。本文介绍添辅助线的一个技巧,作过顶平行线。对于三角形内有关比例线段的证题,大都可用此法。利用过顶平行线,能巧妙地转移线段比式,把已知和未知沟通起来,从而揭示题目的已知条件和欲证结论之间的内在联系,获得最优解法。利用过顶平行线可以证有关线段和角的相等、和差倍分、
Adding auxiliary lines is a major challenge for geometrical test questions. Teaching should guide students to think about the needs of the testimony and the role of the auxiliary line to think about it, then they can make a proper auxiliary line; on the other hand, inspire students to summarize various types of test questions and find out the general rules for the auxiliary line. It can be difficult to change. This article describes a technique for adding helper lines and makes top parallel lines. Most of the questions on proportional lines in the triangle can be used in this method. Using overhead parallel lines, one can skillfully transfer the line segment ratios to communicate the known and the unknown, thereby revealing the intrinsic link between the known conditions of the problem and the conclusions of the claim, and obtaining the optimal solution. The use of overlying parallel lines can be used to prove that the relevant line segments and angles are equal, and difference times,