A convex hexagon ABCDEF satisfies the following conditions:
1) AB∥DE, BC∥EF, and CD∥FA.
2) The distances between these pairs of parallel lines are the same.
3) \angle FAB \equal{} \angle CDE \equal{} 90^\circ
Prove that the diagonals BE and CF of the hexagon intersect with angle 45 degrees.
∙ Thank you dear Babis Stergiou for your translation. :P geometry unsolvedgeometry