名校
解题方法
1 . 如图所示,在四棱锥
中,底面
时直角梯形,
,
为等边三角形,平面
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/5dd5c76d-c066-46ec-aa82-44d1f782bf53.png?resizew=217)
(1)证明:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8c12a6be7d9ec81631aca2c2b5074a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/5dd5c76d-c066-46ec-aa82-44d1f782bf53.png?resizew=217)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
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2 . 如图,在四棱锥S-ABCD中,底面ABCD是菱形,
,
为等边三角形,G是线段SB上的一点,且SD//平面GAC.
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412900907646976/2416012291588096/STEM/ad120724-3b23-4e3d-806e-96b20e8aa732.png)
(1)求证:G为SB的中点;
(2)若F为SC的中点,连接GA,GC,FA,FG,平面SAB⊥平面ABCD,
,求三棱锥F-AGC的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25df618ec33cee978f79d2eae62024f2.png)
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412900907646976/2416012291588096/STEM/ad120724-3b23-4e3d-806e-96b20e8aa732.png)
(1)求证:G为SB的中点;
(2)若F为SC的中点,连接GA,GC,FA,FG,平面SAB⊥平面ABCD,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
您最近一年使用:0次
2020-03-09更新
|
517次组卷
|
5卷引用:2020届湖北省武汉市高三下学期2月调考仿真模拟数学文科试题
3 . 如图所示,四棱锥
中,底面
为菱形,
底面
,
,
,E为棱
的中点,F为棱
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/2dcfb607-8ea6-43eb-b197-f709656fb164.png?resizew=191)
(1)求证:
平面
;
(2)若锐二面角
的正弦值为
,求点F的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/2dcfb607-8ea6-43eb-b197-f709656fb164.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40df8e474334faad849abb7cc6bbd12c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
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名校
解题方法
4 . 如图,点P是菱形ABCD所在平面外一点,且
平面ABCD,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/24cb8be5-10a8-4bd7-87c7-33f06a60d6c9.png?resizew=135)
(1)求证:平面
平面PCE;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202bdcbdc02deb43a861c501afafa55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e1636ee301839f397198139b72e5b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/24cb8be5-10a8-4bd7-87c7-33f06a60d6c9.png?resizew=135)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a67a4e9289c99c6ea017e928120988a.png)
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2020-02-21更新
|
332次组卷
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2卷引用:2019届湖北省宜昌市第一中学高三模拟训练(三)数学(理)试题
解题方法
5 . 如图,在直三棱柱
中,
,
,
,
,
分别为
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/409fc36e-b96c-4d05-a7c5-c23b3eaccaf8.png?resizew=153)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602cdfab573c9cb3ce030f8dba8a9390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/409fc36e-b96c-4d05-a7c5-c23b3eaccaf8.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047da2786ecd6c3b0248908e72593c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0278f9809e118b80c9946d9b9ae40c83.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0278f9809e118b80c9946d9b9ae40c83.png)
您最近一年使用:0次
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6 . 如图,四棱锥
中,
平面ABCD,底面ABCD是正方形,
,E为PC上一点,当F为DC的中点时,EF平行于平面PAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/f62a42fc-8213-4202-b2e2-53e2ff927791.png?resizew=180)
(Ⅰ)求证:
平面PCB;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99926bf272cd757f0985c69b390ebcce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/f62a42fc-8213-4202-b2e2-53e2ff927791.png?resizew=180)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eaa13915786802de6a540d56dec821b.png)
您最近一年使用:0次
2020-02-10更新
|
418次组卷
|
4卷引用:2020届湖北省部分重点中学高三第二次联考数学试卷理科试题
2020届湖北省部分重点中学高三第二次联考数学试卷理科试题(已下线)数学-6月大数据精选模拟卷02(山东卷)(满分冲刺篇)重庆市第一中学2019-2020学年高二下学期期中数学试题重庆市凤鸣山中学2020-2021学年高二下学期期中数学试题
名校
7 . 设
是给定的平面,
是不在
内的任意两点.有下列四个命题:
①在
内存在直线与直线
异面;②在
内存在直线与直线
相交;
③存在过直线
的平面与
垂直;④存在过直线
的平面与
平行.
其中,一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
③存在过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
其中,一定正确的是( )
A.①②③ | B.①③ | C.①④ | D.③④ |
您最近一年使用:0次
2020-01-29更新
|
627次组卷
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5卷引用:湖北省黄冈中学2020届高三下学期冲刺卷(二)理科数学试题
湖北省黄冈中学2020届高三下学期冲刺卷(二)理科数学试题2020届广东省东莞市高三期末调研测试文科数学试题2020届广东省东莞市高三期末调研测试理科数学试题2020届高三1月(考点07)(理科)-《新题速递·数学》(已下线)第32练 直线、平面垂直的判定与性质-2021年高考数学(理)一轮复习小题必刷
名校
8 . 在如图所示的三棱柱
中,
底面ABC,
.
![](https://img.xkw.com/dksih/QBM/2020/1/27/2386303741878272/2387060068728832/STEM/2ef26ec4f7324aefb9eda2ecd77f28f6.png?resizew=116)
(1)若
,证明:
;
(2)若底面ABC为正三角形,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220551e5754a52ab982f9f8b79bd9e5c.png)
![](https://img.xkw.com/dksih/QBM/2020/1/27/2386303741878272/2387060068728832/STEM/2ef26ec4f7324aefb9eda2ecd77f28f6.png?resizew=116)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7768503b1ad4775258b2f1a71c413086.png)
(2)若底面ABC为正三角形,求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
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2020-01-28更新
|
651次组卷
|
5卷引用:湖北省恩施州2022届高三上学期期末文科数学试题
名校
9 . 如图,在三棱锥P-ABC中,平面PAC⊥平面ABC,
和
都是正三角形,
, E、F分别是AC、BC的中点,且PD⊥AB于D.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/0178693f-cfc9-4ea6-b3b5-1d6d1e7d3539.png?resizew=164)
(Ⅰ)证明:直线
⊥平面
;
(Ⅱ)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/0178693f-cfc9-4ea6-b3b5-1d6d1e7d3539.png?resizew=164)
(Ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9f783884705e6092fd35fd9222dae1.png)
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2020-01-20更新
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451次组卷
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2卷引用:2020届湖北省荆州中学、宜昌一中等“荆、荆、襄、宜四地七校高三上学期期末考试数学(理)试题
10 . 已知菱形
的边长为
,
,
,将菱形
沿对角线
折起,使
,得到三棱锥
,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/f38648a0-ee99-4707-b306-97f6e5c97977.png?resizew=335)
(1)当
时,求证:
平面
;
(2)当二面角
的大小为
时,求直线
与平面
所成的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3d296e0d7154a170cb7d3ae42989b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/f38648a0-ee99-4707-b306-97f6e5c97977.png?resizew=335)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5b763032c085a1e60822d8dc1b3605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2020-01-17更新
|
592次组卷
|
3卷引用:2020届湖北省华师一附中高三2月月考数学(理)试题