α∥β,直线AB交α,β于A,B,直线CD交α,β于C,D,M,N分别在AB,CD上,且AM／MB=CN／ND,求证MN∥平面β

分别作A、C、M、N到平面β的垂线,垂足分别为A'、C'、M'、N‘；则有：AA'∥CC'∥MM'∥NN'；可得：AA'/MM' = AB/MB ,CC'/NN' = CD/ND ；已知,α∥β ,则AA'和CC'都是α、β两平行平面之间的距离,可得：AA' = CC' ；已...