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高级中学《立体几何》第11面有一道长期来只被人们当作论证两直线异面必须采用反证法的范例,而忽视其使用价值的例题: 命题1 平面内一点与平面外一点的连线,和平面内不经过该点的直线是异面直线。通过本文的应用例子,可看出,此命题的使用价值:给论证两直线异面及线面关系问题提供一个新工具,可以活跃解题思路。为应用方便现将它改述为如下等价命题
The 11th surface of the high school “Three-Dimensional Geometry” has long been used as a paradigm for demonstrating that two straight lines must use counter-evidence, but ignores examples of their use value: Proposition 1 is a point in the plane and a point outside the plane, The straight line that does not pass this point in the plane is a straight line. Through the application example of this article, we can see that the use value of this proposition: to provide a new tool for the argumentation of the two linear heterogeneity and line surface relationship problems, can be active to solve problem ideas. For application convenience, it is rephrased as the following equivalent proposition