在四棱锥P﹣ABCD中，AD∥BC，AD=AB=DC= 12 BC=1，E是PC的中点，面PAC⊥面ABCD．（Ⅰ）证明：ED∥面PAB；（Ⅱ）若PC=2，PA= 3 ，求二面角A﹣PC﹣D的余弦_刷题宝

题干

在四棱锥P﹣ABCD中，AD∥BC，AD=AB=DC=

1

2

BC=1，E是PC的中点，面PAC⊥面ABCD．

（Ⅰ）证明：ED∥面PAB；

（Ⅱ）若PC=2，PA= 3 ，求二面角A﹣PC﹣D的余弦值．

上一题下一题 0.0难度选择题更新时间:2014-06-16 04:13:00

答案(点此获取答案解析）

（Ⅰ）证明：取PB的中点F，连接AF，EF．

∵EF是△PBC的中位线，∴EF∥BC，且EF=

1

2

BC ．

又AD=BC，且AD=

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