1 . 如图,在四棱柱
中,底面ABCD是菱形,AB=2,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/6bccdd56-07f7-4937-8056-2289194dbae3.png?resizew=189)
(1)求证:平面
平面ABCD;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebecdc0f0f815ff0083d85d3f539b36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b046a91816b74aab46ff92889ae6eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da3a51130be3a7757fc07f709b58c7d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/6bccdd56-07f7-4937-8056-2289194dbae3.png?resizew=189)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686e56830bfadfdde4e09d299f3738f9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48414158019504a81bdfa3a8836b84b.png)
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2012高三·广东肇庆·专题练习
名校
解题方法
2 . 如图,已知△
中,∠
=90°,
,且
=1,
=2,△
绕
旋转至
,使点
与点
之间的距离
=
.
(1)求证:
⊥平面
;
(2)求二面角
的大小;
(3)求异面直线
与
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf468f5132e14ee1d8cc766808b11af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971cd0358b49f1661adc674801bd6ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26552dfc6fd1c06859940cbb36e6ef3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4167feb456b79187e3582a90bdc0ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5427b3e28d3a34a59e2f7ceacd3d5f0b.png)
![](https://img.xkw.com/dksih/QBM/2012/2/9/1570725467234304/1570725472755712/STEM/84a336be38504a12aac70955f27dfa2c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251face19753cbbe1d24e185e3d0eebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26552dfc6fd1c06859940cbb36e6ef3f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470b575ff8c4466b820756f9a630fbeb.png)
(3)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d80d617cab2850dd9c7397ca458456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2012/2/9/1570725467234304/1570725472755712/STEM/c8014740af7246f79dd86f9818df58e5.png)
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