E and F are the midpoints of the sides BC and AD of the convex quadrilateral ABCD. Prove that the segment EF divides the diagonals AC and BD in the same ratio.
Source: 2004 Oral Moscow Geometry Olympiad grade 10 p1
Tags: geometry, ratio, midpoints
E and F are the midpoints of the sides BC and AD of the convex quadrilateral ABCD. Prove that the segment EF divides the diagonals AC and BD in the same ratio.