5.2.4.7 Various problems on the plane

Let \( P \) be the point of intersection of the diagonals of the trapezoid \( A B C D \). A straight line is drawn through the point \(P\), parallel to the bases of the trapezoid, intersecting the sides at the points \(M, N\). Prove that \( P \) is the midpoint of the segment \( M N \).