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82问答网 > 如图，在直三棱柱ABC--A1B1C1中，AC⊥BC，点D是AB的中点

如图，在直三棱柱ABC--A1B1C1中，AC⊥BC，点D是AB的中点

2025-04-03 19:00:21

推荐回答（1个）

回答1：

证明：（1）在直三棱柱ABC--A1B1C1中，有：BB1⊥平面ABC
又AC在平面ABC，那么：BB1⊥AC
而已知：AC⊥BC，这就是说直线AC垂直于平面BCC1B1内的两条相交直线BB1.BC
所以由线面垂直的判定定理可得：
AC⊥平面BCC1B1
又BC1在平面BCC1B1内，所以：AC⊥BC1
（2）设侧面矩形BCC1B1对角线BC1与B1C交于点O，连结OD
则易知点O是对角线BC1的中点
又点D是AB的中点，那么在△ABC1中：
中位线OD//AC1
又OD在平面B1CD内，AC1不在平面B1CD内
所以由线面平行的判定定理可得：
AC1∥平面B1CD

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