Math Help - Convex quadrangle ABCD, midpoints of its sides, diagonals

1. Convex quadrangle ABCD, midpoints of its sides, diagonals

In a convex quadrangle ABCD points M and N are respectively centres of sides AB and CD. E is the point of intersection of the quadrangle's diagonals. Prove that the line containing bisector of $ is perpendicular to the line MN only if $AC=BD.$

2. I find it funny how this is the exact same question except with M, N and X, Y switched. http://www.mathhelpforum.com/math-he...al-155234.html
(My reply to this question remains the same as the other one.)