在立体几何教学中,常遇到下面这个问题:已知m,n是两条异面直线,直线l上的任意一点到直线m,n的距离都相等,则满足条件的直线l有几条?一般的,我们容易想到以下两条直线,如图1所示:设m,n的公垂线段为AB,取线段AB的中点P,过点P作平面α与AB垂直,则必有:m//α,n//α,设m,n在平面α内的射影分别为m′,n′,m′∩n′=P,则m′、 In the three-dimensional geometry teaching, we often encounter the following problem: we know that m, n are two different straight lines, any point on the line l to the line m, n are the same distance, then there are several lines l to meet the conditions In general, we easily think of the following two straight lines, as shown in Fig. 1. Let m,n be the vertical line of AB, take the midpoint P of line AB, and pass point P for the planes α and AB, then there must be :m//α,n//α, Let m,n be the projections in the plane α as m′,n′,m′∩n′=P, then m′,