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平行和垂直问题是立体几何问题中的一个重要组成部分,是每年高考必考查的内容, 毫无疑问,课本中的有关平行和垂直的判定定理和性质定理是解决有关平行与垂直问题的主要方法.本人从长期教学中发现学生对这些定理背的很熟,但解决起问题来常感到束手无策.究其原因,就是对定理没有真正掌握,只知道盲目地记忆,不会依据定理作辅助图,殊不知定理中蕴涵着“作图过程”,下面举两个最常见的例子:
The parallel and vertical problems are an important part of the three-dimensional geometry problem and must be examined every year. There is no doubt that the parallel and vertical decision theorems and property theorems in textbooks are the main methods to solve the parallel and vertical problems. I found out from the long-term teaching that students are well acquainted with these theorems, but they often feel helpless when they solve problems. The reason is that they have no real mastery of the theorem. They only know the memory blindly, and do not rely on the theorem as an auxiliary map. It is important to note that the theorem implies a “drawing process.” Here are the two most common examples: