Points A, B, C, D do not lie in the same plane, K, M, P are the midpoints of segments AB, BC, CD, respectively.

Points A, B, C, D do not lie in the same plane, K, M, P are the midpoints of segments AB, BC, CD, respectively. Prove that the plane KMP is parallel to the lines AC, BD

Consider a triangle ABC, it is obvious that KM is its midline and is parallel to AC by the property of the midline. Similarly, in the triangle BCD – MP – the middle line and parallel to BD. On the basis of parallelism of a straight line and a plane, a plane is parallel to a straight line if it contains a straight line parallel to the given one. According to the above, AC and BD are parallel to the CMR.