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正方体是学生早已熟悉的简单的几何体,它包含立体几何中研究的点、线、面元素,教材第一章中各种元素之间的关系都可以在正方体模型中找到。它制作简便,是立体几何教学不可缺少的教具,本文主要谈谈它在《立体几何》第一章的学习中的应用。 一、正方体中平面的基本性质 正方体有6个直观面,如图1,正方体AC_1中,直线AB上有两点A、B在平面AC内,直线AB就在平面AC内;直线AA_1只有一个点在平面AC内,直线A_1B_1和平面AC_1没有公共点,直线AA_1、A_1B_1都不在平面AC内. 平面AC和平面AB_1有一个公共点A,则平面AC
The cube is a simple geometry already familiar to the students. It contains the points, lines, and surfaces of the elements studied in the three-dimensional geometry. The relationship between various elements in the first chapter of the textbook can be found in the cube model. It is easy to make, and it is an indispensable teaching aid for solid geometry teaching. This article mainly talks about its application in the first chapter of the “Three-Dimensional Geometry”. First, the basic properties of the square plane The cube has six visual surfaces, as shown in Fig. 1. In the cube AC_1, there are two points A and B in the plane AC on the straight line AB, and the straight line AB lies in the plane AC; there is only one point on the straight line AA_1. In the plane AC, the straight line A_1B_1 and the plane AC_1 have no common point, and the straight lines AA_1, A_1B_1 are not within the plane AC. The plane AC and the plane AB_1 have a common point A, and the plane AC