百科知识

如图,在正三棱柱ABC-A1B1C1中,AB=AA1,D是棱BB?

2009-08-12 19:02:36F***
如图,在正三棱柱ABC—A1B1C1中,AB=AA1,D是棱BB1中点。求证:平面A1DC⊥平面AA1C1C。如图,在正三棱柱ABC—A1B1C1中,AB=AA1,D是棱BB1中点。求证:平面A1DC⊥平面AA1C1C。:连接AC1 则AC1⊥A1C 做AC1在面A?

最佳回答

  • 连接AC1 则AC1⊥A1C 做AC1在面AA1B1B上的射影为AE 则E为A1B1中点 又因为D为BB1的中点 所以AE⊥A1D 根据三垂线定理得AC1⊥A1D AC1⊥A1C,AC1⊥A1D A1C交A1D于A1 得AC1⊥平面A1DC AC1属于平面AA1C1C 得平面A1DC⊥平面AA1C1C
    2009-08-12 19:09:21
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