How to prove that 2 faces are parallel in three-dimensional geometry.

Proof: In rectangular ABCD-A1B1C1D1, AB=CD,AB∥CD and E,F are the midpoints of AB,CD

∴AE=CN ,AE∥CN

∴Quadrilateral AECN is a parallelogram

∴AE∥CE

And ∵CE is not contained in the surface AB1E, AE is contained in the surface AB1E

In triangle ABB1 N,O respectively. AB1E

∴CE∥Face AB1E

In triangle ABB1, N,O are the midpoints of AB and AB1 respectively

∴NO is the median of triangle ABB1

∴NO∥AB1

Similarly, NO∥Face AEB1

And ∵CN∩NO≡N

CN NO ∥NOC

CN∥AB1E NO∥AB1E

∴AB1E∥NOC

(Note: the plane is parallel to the plane of the judgment - a plane of the two intersecting straight lines are parallel to another plane, then the two planes are parallel)