如图,正方体ABCD-ABCD中,点E在AB上,点F在BD上,且BE等于BF,求证：EF∥平面BCCB

Question

如图,正方体ABCD-ABCD中,点E在AB上,点F在BD上,且BE等于BF,求证：EF∥平面BCCB

Answer 1

图,正方体ABCD~A1B1C1D1中,E在AB1上,F在BD上,且B1E=BF.(1)求证：EF平形平面BB1C1C. （若正方体棱长为4.且B1E=根号2.求三棱锥E~ABF的体积,(1)证明：如图所示：∵正方体ABCD~A1B1C1D1中,B1E=BF
∴BD=AB1==>BF/BD=EB1/AB1
过F作FG//AD交AB于G ,连接EG
∴BF/BD=BG/AB==> BG/AB=EB1/AB1
∴EG//BB1==>BB1//面EFG
∵BB1⊥底面ABCD
∴面EFG⊥底面ABCD
又面BB1C1C⊥底面ABCD
∴面EFG//面BB1C1C
∴EF//面BB1C1C