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1 . 已知底面ABCD为菱形的直四棱柱,被平面AEFG所截几何体如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/594b9562-51ce-470a-90d9-8686b0d06bec.png?resizew=232)
(1)若
,求证:
;
(2)若
,
,三棱锥GACD的体积为
,直线AF与底面ABCD所成角的正切值为
,求锐二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/594b9562-51ce-470a-90d9-8686b0d06bec.png?resizew=232)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4da6d55f36613f4c677d479358fce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a67d05f2f5e3e6fd43fb60e8c53d4f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f4f259d60ade01bd9bf6632238e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b98d08cb05a894f940009f56c74d83c.png)
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2022-06-07更新
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4卷引用:重庆市实验中学校2021-2022学年高二下学期期末复习数学试题
名校
2 . 如图,四棱锥
中,平面
平面
,
,
,
,
,
,
.
是
中点,
是
上一点.
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992864283205632/2996212997742592/STEM/7fadf429-64dc-42da-89c8-bcf2d78177fd.png?resizew=256)
(1)是否存在点
使得
平面
,若存在求
的长.若不存在,请说明理由;
(2)二面角
的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8107edcdc8423834966183d84976b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e68018750dcdcb6a346761c96a45cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992864283205632/2996212997742592/STEM/7fadf429-64dc-42da-89c8-bcf2d78177fd.png?resizew=256)
(1)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8126878fd2a06f3a0dd13decb07e60f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b1e52dfd144ab4afda4d4aa5a92c1f.png)
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1051次组卷
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5卷引用:重庆市实验中学2021-2022学年高二下学期期末复习(二)数学试题
重庆市实验中学2021-2022学年高二下学期期末复习(二)数学试题贵阳第一中学2022届5月高三高考适应性月考卷(八)数学(理)试题(已下线)专题32 空间向量及其应用-5(已下线)7.3 空间角(精练)(已下线)第五章 破解立体几何开放探究问题 专题二 立体几何开放题的解法 微点3 立体几何开放题的解法综合训练【培优版】
名校
3 . 如图,在四面体ABCD中,G为△ABC的重心,E,F分别在棱BC,CD上,平面
平面EFG.
![](https://img.xkw.com/dksih/QBM/2022/5/5/2973090481995776/2973803743371264/STEM/51ee699b2c9641f3b5c66c5436c34160.png?resizew=251)
(1)求
的值;
(2)若
平面BCD,
,且
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709b04a9b3c364e1a9c5fddcdbacda27.png)
![](https://img.xkw.com/dksih/QBM/2022/5/5/2973090481995776/2973803743371264/STEM/51ee699b2c9641f3b5c66c5436c34160.png?resizew=251)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80df7738deea20c3b835f1496910e2d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67585d2e2a0a8c12bcda212252cfd144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8b25d0f7e74ecef0b830b6056305b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7f9eca6d2aabe3f9e0f39b46106ce4.png)
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解题方法
4 . 如图,正方体ABCD−A1B1C1D1的边长为2,点F为棱CC1的中点,过直线AF作一平面,与棱BB1,DD1分别交于E,G两点.
![](https://img.xkw.com/dksih/QBM/2022/3/27/2945397921021952/2946120025210880/STEM/caec9052-7a00-4f22-9046-8f02ac795cec.png?resizew=158)
(1)求证:四边形AEFG为平行四边形;
(2)求四棱锥C1−AEFG的体积;
(3)若
,且直线AC1与平面AEFG所成角的正弦值为
,求
的值.
![](https://img.xkw.com/dksih/QBM/2022/3/27/2945397921021952/2946120025210880/STEM/caec9052-7a00-4f22-9046-8f02ac795cec.png?resizew=158)
(1)求证:四边形AEFG为平行四边形;
(2)求四棱锥C1−AEFG的体积;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0877f117860c2904f8d4bb51692d5c17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec42ae1010746324df9d5d883413526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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