已知:在直四棱柱ABCD-A1B1C1D1中,底面ABCD是菱形. 求证:(1)平面B1AC∥平面DC1A1; (2)平面B1AC⊥平面B1BDD1.

问题描述:

已知:在直四棱柱ABCD-A1B1C1D1中,底面ABCD是菱形.
求证:(1)平面B1AC∥平面DC1A1
(2)平面B1AC⊥平面B1BDD1

证明:(1)因为ABCD-A1B1C1D1是直四棱柱,所以,A1C1∥AC,而A1C1⊄平面B1AC,AC⊂平面B1AC,所以A1C1∥平面B1AC.(3分)同理,A1D∥平面B1AC.(5分)因为A1C1、A1D⊂平面DC1A1,A1C1∩A1D=A1,所以平面B1AC∥平...