The midpoints of the sides CD and AB of the parallelogram ABCD lie in the plane L and

The midpoints of the sides CD and AB of the parallelogram ABCD lie in the plane L and the side BC does not lie in L. prove that AD are parallel to the plane L

Let point N be the middle of side AB, point O – the middle of side CD. Then the segment NO is the middle line of the parallelogram ABCD.

АN // ОD and АN = ОD, therefore the segments NO and AD are also parallel.

thus, if a plane passes through the segment NO, then according to the theorem, any straight line (not lying in this plane) and parallel to the segment NO will be parallel to this plane.