∵ is a cube ∴BD is perpendicular to AC, BD is perpendicular to BF.

∫BF parallel AE

∴BD vertical AE

∫AC∩AE = A

∴BD vertical AEGC

∵BD∈ flat bed

∴ AEGC on vertical plane of plane bed

Proving that planes are parallel means proving that straight lines are parallel, and all the questions are the same idea.