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
|
7卷引用:河北省衡水市冀州中学2024届高三第一次调研数学试题
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 . 如图所示的几何体P—ABCD中,四边形ABCD为菱形,∠ABC=120°,AB=a,PB=
a,PB⊥AB,平面ABCD⊥平面PAB,AC∩BD=O,E为PD的中点,G为平面PAB内任一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/a5282e53-3ac8-417e-83c4-54cf3853eb91.png?resizew=161)
(1)在平面PAB内,过G点是否存在直线l使OE∥l?如果不存在,请说明理由,如果存在,请说明作法;
(2)过A,C,E三点的平面将几何体P—ABCD截去三棱锥D—AEC,求剩余几何体AECBP的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/a5282e53-3ac8-417e-83c4-54cf3853eb91.png?resizew=161)
(1)在平面PAB内,过G点是否存在直线l使OE∥l?如果不存在,请说明理由,如果存在,请说明作法;
(2)过A,C,E三点的平面将几何体P—ABCD截去三棱锥D—AEC,求剩余几何体AECBP的体积.
您最近一年使用:0次
2019-12-05更新
|
255次组卷
|
9卷引用:河北省衡水中学2017届高三押题II卷文数试卷
河北省衡水中学2017届高三押题II卷文数试卷河北省衡水中学2018年高考押题(二)文科数学(已下线)河北省衡水中学2019年高考押题数学(文)试题(二)【全国百强校】山东省淄博实验中学2019届高三第二学期第一次(4月)教学诊断考试数学(文)试题辽宁省2020届高三(5月份)高考数学(文科)押题试题(已下线)专题8.6 立体几何 (单元测试)(测)【文】-《2020年高考一轮复习讲练测》(已下线)专题8.6 立体几何(单元测试)(测)-江苏版《2020年高考一轮复习讲练测》(已下线)专题20+立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)(已下线)专题20 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)
3 . 已知平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
平面
,平面
平面
,平面
平面
,则下列命题:
①若
,则
,
;②若
,则
;③若
,
,则
.
其中正确的命题是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66854bb5784c29a27075e884e10e392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ccd6a2f9117c17049cf60631bdefcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138ca330a165c68e865cacd35c18a665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f23dd10fa2b7596fb842c67ca5db387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769cedbb48a28a76eb5b965224dfac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2be868c3222edf35a0d5f5fcb47535.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fbc714c63815dad9a27418f6492f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347347d0147894ec926890e1eef45de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289f5bc5fc3b73b5fb509109da0d6cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29c72e53105c5dc97a1bae4b39faf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf3fd703ffdb0c509b754cffa0c9b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057cdb4057bca398a838e868efd360f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4fc47a5814493cc5facdc3ab296dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2293799d379200cf746e8450ebd5744f.png)
其中正确的命题是
A.①②③ | B.②③ | C.①③ | D.①② |
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4 . 如图,四棱锥
的底面
为矩形,
,
,点
在底面上的射影在
上,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/9f08252966ce45ca93055d404a10d283.png)
(I)证明:
平面
;
(II)在
边上是否存在点
,使得
平面
?若存在,求出
的值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/29963f8a84274eed812977e92e2128ae.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/f68a0e4a03d94a4899300f5e55025f9c.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/e3bdc2a31b134a86a464fdcab06d1d42.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/6c9b188421a44246bb429cb936d6cf7e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/df2d72be93a84b63a45b3e18fb3f49bc.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/5fb7e65ab16844f18cc0adb15245e84d.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/5342f53cad8941cdbecc1187e90a4b32.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/1ec223493c824ee6a06c1b583253b80d.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/3b2551184b79495c99002311efbf6554.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/9f08252966ce45ca93055d404a10d283.png)
(I)证明:
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/181f32a8ff0d402fb34f5b19167a5f31.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/fdc5f327c73e40e6971e1fde16773fa0.png)
(II)在
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/f945931b43d5407499d2043248ad077c.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/2cd9b6cfd9014cceba2b5af8aa541793.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/61b050057b6a4b08865934fd3b8fe996.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/56b01e772215450b9fafb046a4e32b0e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663768809472/1572663774420992/STEM/d3cc38a761a144c585114ec4fed67f14.png)
您最近一年使用:0次
5 . 如图所示,在四棱锥
中,底面
为正方形,侧棱
底面
,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/3/29/1572561717133312/1572561722908672/STEM/168b32c85f344e7eb0e1a698b05b9b3d.png)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](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/551e4cd76a93de89ea2750160fe74923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b3c6e67d78d10080826ecd81dbc2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f9b30a2d396adfd0aef8d2a0373379.png)
![](https://img.xkw.com/dksih/QBM/2016/3/29/1572561717133312/1572561722908672/STEM/168b32c85f344e7eb0e1a698b05b9b3d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
6 . 已知
为空间中两条不同的直线,
为空间中两个不同的平面,下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
7 . 已知直三棱柱
的三视图如图所示,且
是
的中点.
(Ⅰ)求证:
∥平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)试问线段
上是否存在点
,使
与
成
角?若存在,确定
点位置,若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2012/4/27/1570845596786688/1570845602471936/STEM/45b6c8e76c5244689830cda117df6aad.png)
![](https://img.xkw.com/dksih/QBM/2012/4/27/1570845596786688/1570845602471936/STEM/df937833bb314e479773b2b7098a35cf.png)
![](https://img.xkw.com/dksih/QBM/2012/4/27/1570845596786688/1570845602471936/STEM/929fc70f3e8748f4b05a35a28d6065de.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1f7b595b05c5ad8446cd7f9ce3bbcd.png)
(Ⅲ)试问线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2012/4/27/1570845596786688/1570845602471936/STEM/7703f64a244246d28f42400d4eb91d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdccc23f0f0f511a29ebae43d194f5be.png)
![](https://img.xkw.com/dksih/QBM/2012/4/27/1570845596786688/1570845602471936/STEM/7703f64a244246d28f42400d4eb91d1e.png)
![](https://img.xkw.com/dksih/QBM/2012/4/27/1570845596786688/1570845602471936/STEM/a642e84255c648f68eddbf00dae851f9.png)
您最近一年使用:0次
8 . .(本小题满分12分)
如图,在四棱锥P-ABCD中,底面为正方形,PA丄平面ABCD,且PA=AD,E为棱PC上的一点,PD丄平面ABE.
(I)求证:E为PC的中点;
(II)若N为CD的中点,M为AB上的动点,当直线MN与平面ABE所成的角最大时,求二面角C-EM-N的大小.
如图,在四棱锥P-ABCD中,底面为正方形,PA丄平面ABCD,且PA=AD,E为棱PC上的一点,PD丄平面ABE.
(I)求证:E为PC的中点;
(II)若N为CD的中点,M为AB上的动点,当直线MN与平面ABE所成的角最大时,求二面角C-EM-N的大小.
![](https://img.xkw.com/dksih/QBM/2011/3/9/1570031669428224/1570031674843136/STEM/8157e8dd5f904661a589eb6f7085bbfd.png?resizew=181)
您最近一年使用:0次