全等三角形在初中数学中的应用论文资料解读

曲靖师范学院

本科生毕业论文

论文题目: 全等三角形的证明在初中数学中的应用

作者、学号：李发蝌**********

学院、年级：数学与信息科学学院2011级

学科、专业：数学数学与应用数学

********

完成日期：2015年5月20日

曲靖师范学院教务处

全等三角形的证明在初中数学中的应用

摘要

“全等三角形的证明”是在初中数学平面几何中占重要内容之一，是研究图形性质的基础，而且在近几年的中考中都有出现，新课标的要求是“探索并掌握两个三角形全等的条件”，因此掌握三角形全等的证明及运用方法对初中生来说至关重要。其证明方法繁多，技巧性强，有一定的通法，所以研究范围极广，难度极大．论文整理和归纳了全等三角形证明的步骤及其注意事项，分别列举了几种常用的全等三角形的证明方法，让每一种方法兼有理论与实践性．旨在使学生对全等三角形证明及其应用问题有一个较为深入的了解，进而在解决相关全等三角形问题时能融会贯通、举一反三，达到事半功倍的效果，同时为从事教育的工作者提供参考．

关键词：全等三角形；初中数学；方法；应用

Prove congruent triangles used in in junior high school

mathematics

Abstract：“Entire and so on the triangle proofs” are account for one of important contents in the junior middle school mathematics plane geometry, is studies the graph nature the foundation, moreover tests in recent years all has the appearance, the new class sign request is “explores and grasps two triangles entire and so on the condition”, therefore the grasping triangle entire and so on the proof and said since birth using the method to the junior middle school very important.Its proof method is many, skillful, has certainly certainly passes the law, therefore the research scope is extremely broad, the difficulty is enormous. The paper reorganized and has induced entire and so on the triangle proof steps and the matters needing attention, has enumerated several kinds separately commonly used entire and so on the triangle proof methods, let each method have at the same time the theory and the practicality. Is for the purpose of making the student to entire and so on the triangles to prove and the application question has a more thorough understanding, then is connected entire when the solution and so on the triangle questions can achieve mastery through a comprehensive study of a subject, extrapolate, achieved the twice the result with half the effort effect, simultaneously for the worker who is engaged in the education provides the reference.

Key word: Entire and so on triangles; Junior middle school mathematics; Method; Using

目录

1引言 (1)

2文献综述 (1)

2.1国内研究现状 (1)

2.2国内研究现状评价 (2)

2.3提出问题 (2)

3证明全等三角形的知识梳理及注意事项 (2)

3.1全等三角形的知识梳理 (2)

3.2证明全等三角形的步骤及注意事项 (4)

4证明全等三角形的构造法 (4)

4.1构造全等三角形的常用方法 (5)

4.1.1截长补短法 (5)

4.1.2平行线法 (6)

4.1.3旋转法 (6)

4.1.4倍长中线法 (7)

4.1.5翻折法 (8)

4.2由角平分线构造全等三角形 (8)

4.3添加辅助线构造全等三角形 (9)

4.3.1直接证明线段（角）相等 (9)

4.3.2转移线段到一个三角形中证明线段相等 (10)

4.3.3转移线段到一个三角形中证明线段不等关系 (13)

5全等三角形的证明在初中数学中的应用 (14)

6总结 (18)

6.1主要发现 (19)

6.2启示 (19)

6.3局限性 (19)

6.4努力方向 (19)

参考文献 (20)