∵ 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.