As shown in the figure, let ABCD and abef be parallelograms, they are not in the same plane, m and N are the points on the diagonal AC and BF respectively, and am: FN = AC: BF (Continued), prove: Mn ‖ plane bec

As shown in the figure, let ABCD and abef be parallelograms, they are not in the same plane, m and N are the points on the diagonal AC and BF respectively, and am: FN = AC: BF (Continued), prove: Mn ‖ plane bec

Am: AC = FN: FB is obtained from am: FN = AC: BF
Take point G on AB so that am: AC = FN: FB = Ag: ab
Then mg is parallel to BC, GN is parallel to AF
The plane MGN is parallel to the plane bec
So Mn is parallel to the plane bec