平面几何中添加辅助线的技巧.doc

平面几何中添加辅助线的技巧 摘 要 平面几何是中学数学中很重要的一门基础课，平面几何中有很多复杂的问题是需要添加一些合适的辅助线来解决的，辅助线是平面几何中沟通已知和未知的桥梁.因此，怎样添加辅助线对于解决平面几何问题就显得尤其重要，同时它也是初中学生学习的难点、教师教学的重点. 笔者在任教期间发现许多初中学生在解决平面几何问题时对几何图形中辅助线的添加技巧不能熟练的应用，因此经过查资料写了本论文，从而为在以后教学中提高学生解题技巧做铺垫.本论文主要研究了平面几何中一些常见的辅助线添加技巧在考试解题中的应用，并对辅助线的添加技巧在不同几何图形中进行了分类，这样有助于学生加深理解，提高解题的速度.这不论是对学生学习解题还是老师教授学习方法，都有重要的意义，因此具有一定的研究价值. 【关键词】平面几何 辅助线 三角形 梯形 圆 Plane geometry in add auxiliary line skills Abstract Plane geometry is an important basic course in secondary school mathemati- cs, there are many complicated problems need to add some suitable auxiliary lines to be solved in plane geometry, auxiliary line is the communication bridge of known and unknown. Therefore, how to add auxiliary lines to solve the prob- lems in plane geometry appears especially important, at the same time it is also the junior middle school students learning difficulties and teaching focus. The author in the teaching of junior middle school found many students in solving problems in plane geometry of geometric graphics auxiliary lines in add skills can not be used, so the author wroe this thesis after checking the information, which makes bedding to improve students problem solving skills in later teaching.The thesis mainly studies the geometry of some common auxiliary line adding skills in examination problem solving application, and the auxliary line added skills in different geometry were classified, such it is helpful for students to deepen understanding and enhance problem-solving speed. This is not only for students learning problem solving but also for professor of learning methods, are of great significance, so it has certain research value. 【Key Words】plane geometry auxiliary line triangle trapezoid circle 目录 一、绪论 (4) 二、平面几何辅助线的添加原则……………………………………………………. (4) 三、平面几何中添加辅助线的技巧………………………………………………………(4) ㈠ 三角形中辅助线的添加技巧 ……………………………………………………………(4) ㈡ 梯形中辅助线的添加技巧…………………………………………………………… (10) ㈢ 圆中辅助线的添加技巧………………………………………………………… （14） 四、结论…………………………………………………………………………………（17） 参考文献 （18）