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空间两条直线有相交、平行、不共面三种可能的相互位置。我们知道,空间两条直线的夹角或交角的概念是从平面两直线的夹角或交角概念推广而来的,空间里平行线的传递性也是由平面内平行线的传递性直接推导的,事实上,将平面内直线之间相互位置的某些概念和性质推广引伸到空间去,可以相应地得到与其平行的结果,本文试图从平面到空间,用类比的方法,论证几个异面直线的性质定理。为了叙述简便起见,我们约定,MN为异面直线l_1、l_2的公垂线,M、N分别是l_1及l_2上的垂足,l_1和l_2的交角是θ(0〈θ≤1/2π)。
There are three possible mutual positions where the two lines of space are intersected, parallel, and not coplanar. We know that the concept of the included angle or intersection angle of two lines in space is generalized from the concept of the included angle or intersection angle of plane two lines. The transitivity of parallel lines in space is also directly derived from the transitivity of parallel lines in plane. In fact, extending some of the concepts and properties of the mutual positions between planes to the space can be parallelized with the corresponding results. This paper attempts to demonstrate several straight lines from plane to space using an analogy method. The nature of the theorem. To simplify the narrative, we agree that MN is the perpendicular line of the straight lines l_1, l_2, and M, N are the perpendicular feet on l_1 and l_2, and the intersection angles of l_1 and l_2 are θ (0<θ≤1/2π). .