如图,在正方体ABCD-A1B1C1D1中,求证:平面DBB1D1⊥平面A1BC1

问题描述:

如图,在正方体ABCD-A1B1C1D1中,求证:平面DBB1D1⊥平面A1BC1
请写出过程.

∵A1C1⊥B1D1,A1C1⊥BB1,BB1∩B1D1=B1,
∴A1C1⊥平面DBB1D1.
又A1C1在平面A1BC1内,
∴平面A1BC1⊥平面DBB1D1.