论文部分内容阅读
直线和平面垂直是空间直线和平面位置关系中非常重要的一种情况。而直线和平面垂直判定定理,是立体几何的一个教学难点之一,该定理的传统证法对大多数同学而言,理解上存在一个很大的的困难,所以在现行的人教版“普通高中课程标准实验教科书”——《数学》(必修)2中,就删去了定理的证明(见第二章65页)。近几年来,对该定理的证明也出现了不少新的方法。而随着空间向量的知识在中学教材中的引入,逐步将立体几何问题代数化,也就成为了可能。在高教版的“中等职业教育国家规划教材”——《数学》(基础版)第二册(见157页)中,所给出的定理证明就非常简明扼要,学生也容易接受。其证明过程利用了平面向量的分解定理和两个非零向量垂直的充要条件。本文不用平面向量的分解定理,而是引入了向量的坐标,利用向量代数的方法,根据两个非零向量垂直的充要条件,证明了直线和平面垂直的判定定理和三垂线定理。
Straight lines and plane vertical is a very important situation in the relationship between the space line and the plane. The straight line perpendicular to the plane and decision theorem, is one of the difficulties of teaching a three-dimensional geometry, for most students, it’s a lot of difficulty understanding the traditional proofs of theorems, so PEP in the current “ In the General High School Curriculum Standard Experimental Textbook ”-“ Mathematics ”(compulsory) 2, the proof of the theorem is deleted (see Chapter 2, p. 65). In recent years, there have been many new ways to prove this theorem. With the introduction of the knowledge of space vector in middle school textbooks, it is possible to gradually solve the problem of geometric geometry. In the higher education edition of the “Secondary Vocational Education National Planning Textbook” - “Mathematics” (Basic Edition) Volume II (see page 157), the proof given theorem is very concise, students are also easy to accept. It proves that the process takes advantage of the theorem of decomposition of the plane vector and the necessary and sufficient conditions of two non-zero vector verticals. Herein without decomposition theorem vector plane, but the introduction of the vector coordinates using vector algebra method according Sufficient Conditions two nonzero vector perpendicular to prove the theorem of linear and is determined perpendicular to the plane and three perpendicular theorem.