平面α∩平面β=直线EF,AB⊥α于点B,AC⊥β于C，CD⊥α于D.求证 BD⊥EF不会做...谢谢....
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证AB⊥a,EF在a内,得AB⊥EF,AC⊥β,EF在β内,AC⊥EF,故EF⊥平面ABC. CD⊥a,AB⊥a故CD∥AB,ABCD共面,而EF⊥平面ABCD,BD在平面ABCD内,所以EF⊥BD
平面α∩平面β=直线EF,AB⊥α于点B,AC⊥β于C，CD⊥α于D.求证 BD⊥EF不会做...谢谢....
证AB⊥a,EF在a内,得AB⊥EF,AC⊥β,EF在β内,AC⊥EF,故EF⊥平面ABC. CD⊥a,AB⊥a故CD∥AB,ABCD共面,而EF⊥平面ABCD,BD在平面ABCD内,所以EF⊥BD