Solving plane geometry problems with method （解决平面几何问题的方法）.pdfVIP

Solving plane geometry problems with method of three-dimensional geometry Team member: Haihao Lu, Jiawei Zang Advisor: Xianfu Yan School: Qingdao No.2 Middle School Preface Generally speaking, when we deal with the three-dimensional geometry problems, we used to transfer them into the plane geometry first. However, I cannot agree with the idea that we should always transfer the three-dimensional geometry problems into the plane geometry mode. In the following article, we solve the problem in an opposite way, which means solving the problems of a total of three points or three planes by using the three-dimensional geometry. The main idea is simple: if three points both are on two planes, they are in line; if three lines are the interception lines of three different planes which intercept each other, they have a common point. The key to this point is how to construct the two or three planes. It follows that we provide three methods to construct the planes, and independently prove some basic theories and properties. (1) transferring plane graphs into three-dimensional graphs (2) using proportional relationship and similarity (3) symestrically finding out two planes which do not parallel to the base Therefore, let’s walk into the three-dimensional world, and research the common problems in a different vision. First of all, let’s see a familia problem: Prove that the three midlines of a triangle pass though the same point. Proof : ′ ′ Move ⊿ABC upwards by the length CC1 , then the quadrangle CBB C is a parallelogram.