名校
1 . 如图所示的几何体是由一个直三棱柱和半个圆柱拼接而成.其中,
,点
为弧
的中点,且
四点共面.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/7a4e298c-07e9-4350-b1c6-31b239b59f4c.png?resizew=138)
(1)证明:
四点共面;
(2)若平面
与平面
夹角的余弦值为
,求
长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fea25b3a66048a7df4b36687407fded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5f01b6bc45dceed966d91d0f6f0c91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/7a4e298c-07e9-4350-b1c6-31b239b59f4c.png?resizew=138)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadeaa994b8065400aa2f8b251843f87.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90131175c3fb6a3837a22d7d5bbc268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae015b0d4134a91faa1ab01bbb00fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2024-01-25更新
|
910次组卷
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7卷引用:江苏省南京师范大学附属中学2021届高三下学期模拟考试数学试题
江苏省南京师范大学附属中学2021届高三下学期模拟考试数学试题河北省衡水市冀州中学2024届高三第一次调研数学试题广东省惠州市博罗县2023-2024学年高二上学期期末数学试题广东省惠州市2023-2024学年高二上学期1月期末数学试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)微考点5-2 新高考新试卷结构立体几何解答题中与旋转体有关的问题
2 . 如图,直三棱柱
,
,
点M,N分别为
和
的中点.
(Ⅰ)证明:
∥平面
;
(Ⅱ)若二面角
为直二面角,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d8fd172a3638b435e758f2bf40e2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e737bc35da650eda3825d29799b5f86f.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06faea49d957a5bab3fe0582f76ff23.png)
(Ⅱ)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca78edfd819b3b675455e9f7897f0d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://img.xkw.com/dksih/QBM/2012/7/5/1570916308729856/1570916314087424/STEM/fe8797518c5d4106a830946620f8440a.png?resizew=265)
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2019-01-30更新
|
1675次组卷
|
3卷引用:江苏省南通市如皋市部分学校2021届高三下学期6月份临门一脚考试数学试题
江苏省南通市如皋市部分学校2021届高三下学期6月份临门一脚考试数学试题(已下线)2013届陕西省西安市西北工业大学附中高三第十二次适应性训练理数学卷2012年全国普通高等学校招生统一考试理科数学(辽宁卷)
3 . 如图,在直三棱柱
中,
,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/2017/2/4/1619478440148992/1619478440525824/STEM/2056a0789fce4f738c2e1646cef7a4bb.png)
(1)求证:
∥平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2017/2/4/1619478440148992/1619478440525824/STEM/2056a0789fce4f738c2e1646cef7a4bb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2017-02-08更新
|
1275次组卷
|
5卷引用:2017届江苏南京市盐城高三一模考试数学试卷
4 . 如图, 在四棱锥
中,
是线段
的中点.
(1)求证:
平面
;
(2)若
,平面
平面
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa495186bc69ac1dd4318d5ac59c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf1d2c64950a4ae3c7d2a7cbfdeddd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://img.xkw.com/dksih/QBM/2017/11/6/1811431649705984/1813487455125504/STEM/91a0266ae5f54ff5894ad574bb34833b.png?resizew=141)
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2016-12-04更新
|
724次组卷
|
2卷引用:2016届江苏省清江中学高三考前周练模拟数学试卷
5 . 如图,在四棱锥
中,底面
是菱形,侧面
是直角三角形,
,点
是
的中点,且平面
平面
.证明:
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572660084457472/1572660090650624/STEM/c51055ed8d5a4d8ebef12c4c57a4b8f6.png)
(1)
平面
;
(2)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153163fecdf3f410411048428ccaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7c28e1964509d008de51a26920f777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6975ec118f40dc2feb16fb2dcde3285c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572660084457472/1572660090650624/STEM/c51055ed8d5a4d8ebef12c4c57a4b8f6.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d8677ae5ca7acf874d93789425d172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932fa5b69598e262129c5be86ed64376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
您最近一年使用:0次
6 . 如图,在直三棱柱ABC-A1B1C1中,D为棱BC上一点.
![](https://img.xkw.com/dksih/QBM/2016/5/20/1572643402964992/1572643408707584/STEM/3cb5d56911ad45a8892aab067ac17bb0.png?resizew=182)
(1)若AB=AC,D为棱BC的中点,求证:平面ADC1⊥平面BCC1B1;
(2)若A1B∥平面ADC1,求
的值.
![](https://img.xkw.com/dksih/QBM/2016/5/20/1572643402964992/1572643408707584/STEM/3cb5d56911ad45a8892aab067ac17bb0.png?resizew=182)
(1)若AB=AC,D为棱BC的中点,求证:平面ADC1⊥平面BCC1B1;
(2)若A1B∥平面ADC1,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/501dc6babe43bd4d7e669b5dcea40945.png)
您最近一年使用:0次
2016-12-04更新
|
978次组卷
|
4卷引用:2016届江苏省南京市高三第三次模拟考试数学试卷
2016届江苏省南京市高三第三次模拟考试数学试卷江苏省南通中学2018届高三10月月考数学试题(已下线)专题07 空间几何体的平行于垂直-《巅峰冲刺2020年高考之二轮专项提升》(江苏)福建省福州市八县(市)协作校2021-2022学年高一下学期期末联考数学试题
7 . 在如图多面体中,
底面
,
,
,
是
的中点.
(1)
平面
;
(2)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef5ff8e198b340ab2b5a2abe48e0e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cba7d2ce69e27c561fd17d9eceb3a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96bc9a285172c48e4726ee6492670ef.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d0df73a49d4348a5c1e3aaa149cc8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://img.xkw.com/dksih/QBM/2018/6/4/1959978964992000/1961015858610176/STEM/06efe1533128400f92d3e43febb2baab.png?resizew=168)
您最近一年使用:0次
2016-12-04更新
|
827次组卷
|
2卷引用:2016届江苏省清江中学高三考前一周模拟二数学试卷
8 . 如图,已知直三棱柱
的侧面
是正方形,点
是侧面
的中心,
,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572472770240512/1572472776351744/STEM/67fc9a998f6e48edb31552b24930574f.png)
(1)求证:
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e612b79595292d25bcb611f2cd592044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2016/2/15/1572472770240512/1572472776351744/STEM/67fc9a998f6e48edb31552b24930574f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280247d7df395bb9ea78c51e67b458d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73fcf70859f620a7492e1351327725c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2016-12-04更新
|
505次组卷
|
3卷引用:2016届江苏省南京市、盐城市高三第一次模拟考试数学试卷
9 . 如图,边长为2的正方形
是圆柱的中截面,点
为线段
的中点,点
为圆柱的下底面圆周上异于
,
的一个动点.
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572176667361280/1572176673226752/STEM/847e0b86ab674e92a74ff48c88bf2b0b.png)
(1)在圆柱的下底面上确定一定点
,使得
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572176667361280/1572176673226752/STEM/847e0b86ab674e92a74ff48c88bf2b0b.png)
(1)在圆柱的下底面上确定一定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c541a26748f3c5f2c0cbd2c08029968e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2811b8da5672debf9929e51d5b43e32.png)
您最近一年使用:0次
10 . 在四棱锥
中,
平面
,
是边长为4的正三角形,
与
的交点
恰好是
中点,又
,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572104921440256/1572104926822400/STEM/404276c2494643d380e695e7a2ff3de3.png)
(1)求证:
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153163fecdf3f410411048428ccaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb18e947166d2fb0110967c885abe358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950d90f852dc2881b29cf4ee7fd853ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692c7ee52fd507ca5ec79ae9631847b9.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572104921440256/1572104926822400/STEM/404276c2494643d380e695e7a2ff3de3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aacb89c9441afb299130f0ac59a761.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
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