名校
解题方法
1 . 在等腰梯形
中,
,
,将它沿着两条高
,
折叠成如图所示的四棱锥
(
,
重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/93fe1829-bf0a-4bb4-9a6a-10d3176be62e.png?resizew=368)
(1)求证:
;
(2)设点
为线段
的中点,试在线段
上确定一点
,使得
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b06f824f3779f910448ae3a80f483d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3b9fe94b261d634f275a92d8b8cd2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/93fe1829-bf0a-4bb4-9a6a-10d3176be62e.png?resizew=368)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c182a9d9fd0a7023b710cd671d9468e7.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f332555e65843f32f4c623098c6adc72.png)
您最近一年使用:0次
2020-11-26更新
|
2869次组卷
|
4卷引用:辽宁省盘锦市第二高级中学2020-2021学年高二第一学期第一次阶段性考试数学试题
辽宁省盘锦市第二高级中学2020-2021学年高二第一学期第一次阶段性考试数学试题(已下线)第六章 立体几何初步(能力提升)-2020-2021学年高一数学单元测试定心卷(北师大2019版必修第二册)江西省遂川中学2021-2022学年高二上学期第二次月考数学(理)试题(B卷)云南省北大附中云南实验学校2020-2021学年高一下学期期中考试数学试题
名校
2 . 如图,
是边长为
的等边三角形,四边形
为菱形,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/0334c950-7d0c-46d3-a8b0-44e738a91f93.png?resizew=170)
(1)求证:
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c99e6d75d606b5cae9392ecca969200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59567dbf014b5608475254efb2cf2c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a8d8fe0503af1c8f8d04eaf211bac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70abed7faf55deb24162255c5ad59577.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/0334c950-7d0c-46d3-a8b0-44e738a91f93.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
名校
3 . 如图,正方形
和直角梯形
所在平面互相垂直,
,
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/5196057a-6554-4001-8019-85ac67b33f8b.png?resizew=123)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ea9d3df7c2bcdf135dedd1554fb82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce38d8a8a7043586aad206f8153d0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a77f26a7be722e00baa984f769ec8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce84f6062f12bf6ef42d7b733cd2248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/5196057a-6554-4001-8019-85ac67b33f8b.png?resizew=123)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc521258fcaeaf7acffc5ae98c3af6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646084b7f3902efa4c462ed67599265a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a34e44c5d7e1d22521fb293994f5b0.png)
您最近一年使用:0次
2022-09-06更新
|
1013次组卷
|
6卷引用:辽宁省沈阳市东北育才学校2023-2024学年高二上学期期中数学试题
名校
解题方法
4 . 如图,已知点P是平行四边形ABCD所在平面外一点,M、N分别是AB、PC的中点
平面PAD;
(2)在PB上确定一个点Q,使平面MNQ
平面PAD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)在PB上确定一个点Q,使平面MNQ
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
您最近一年使用:0次
2021-09-09更新
|
1617次组卷
|
8卷引用:辽宁省沈阳市新民市第一高级中学2021-2022学年高一上学期期末考试数学试题
名校
解题方法
5 . 如图,已知四棱锥
中,平面
平面
,底面
为矩形,且
,
,
,O为棱AB的中点,点E在棱AD上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8eb491b9-25ff-4831-8f9d-42d4f31afc2f.png?resizew=172)
(1)证明:
;
(2)在棱PB上是否存在一点F使
平面
?若存在,请指出点F的位置并证明;若不存在,请说明理由.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7005932de8ace6e3c78a754c35466d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940099db7ffe6b3f7e70afcfba66750a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8eb491b9-25ff-4831-8f9d-42d4f31afc2f.png?resizew=172)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5ffe436f8eb53a211abf95baed8ca9.png)
(2)在棱PB上是否存在一点F使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e447c70f2ad6d6a38afd6cad312007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
您最近一年使用:0次
2022-07-13更新
|
886次组卷
|
5卷引用:辽宁省锦州市2021-2022学年高一下学期期末数学试题
辽宁省锦州市2021-2022学年高一下学期期末数学试题辽宁省鞍山市一般高中协作校(含矿山高级中学、文化学校等)2022-2023学年高一下学期6月月考数学试题(已下线)第03讲 空间直线、平面的平行 (精讲)-2江西省遂川中学2022-2023学年高二上学期期末考试数学试题(已下线)模块四 专题1 期末重组综合练(辽宁)(人教B)
名校
解题方法
6 . 如图,在四棱锥
中,底面ABCD是平行四边形,E,F分别是CD,PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/a7594f3f-1235-449f-abc9-c2ebee1a4fcc.png?resizew=140)
(1)证明:
平面PAD.
(2)若四棱锥
的体积为32,
的面积为4,求B到平面DEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/a7594f3f-1235-449f-abc9-c2ebee1a4fcc.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
您最近一年使用:0次
2022-12-03更新
|
850次组卷
|
5卷引用:辽宁省沈阳市第一二〇中学2022-2023学年高一下学期第三次质量监测数学试题
名校
解题方法
7 . 如图,在三棱柱
中,四边形
为菱形,
,平面
平面
﹐Q在线段AC上移动,P为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/c4b7a15c-4f94-4d35-a9ba-ea41b93ccf29.png?resizew=207)
(1)若H为BQ中点,延长AH交BC于D,求证:
平面
﹔
(2)若二面角
的平面角的余弦值为
,求点P到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0d0e78101fef36a75b70ac7e7cf5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e20ab4f192002c79ccb7ff7f9d63ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e2385ec6765cff01b2d00664d4aad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/c4b7a15c-4f94-4d35-a9ba-ea41b93ccf29.png?resizew=207)
(1)若H为BQ中点,延长AH交BC于D,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5edfe97aeab0cf16b40fa9d2e15f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ffba8658b0023316117e1536cbf806.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39eefa58485e43a86a1931a2aa7222a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fed1f54c1b008a633326db4f20288c5.png)
您最近一年使用:0次
2022-05-27更新
|
789次组卷
|
12卷引用:辽宁省沈阳市2022届高三三模考试数学试题
辽宁省沈阳市2022届高三三模考试数学试题辽宁省大连市大连育明高级中学2022-2023学年高二上学期期中数学试题河北省衡水中学2018届高三考前适应性训练6月1日第3天数学(理)试题人教A版(2019) 选择性必修第一册 必杀技 第一章 空间向量与立体几何 素养检测人教B版(2019) 选择性必修第一册 必杀技 第一章 空间向量与立体几何 素养检测北师大版(2019) 选修第一册 必杀技 第三章 素养检测湖南省邵阳市第二中学2021-2022学年高二下学期入学考试数学试题章节综合测试-空间向量与立体几何山东省东营市广饶县第一中学2022-2023学年高三上学期12月月考数学试题北师大版(2019) 选修第一册 章末检测卷(三) 空间向量与立体几何(已下线)第一章 空间向量与立体几何(单元提升卷)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)四川省宜宾市叙州区第二中学校2024届高三一模数学(理)试题
名校
解题方法
8 . 如图甲,在平面五边形ABCDE中,
,
,
,
,
,
,
,
,垂足为H,将
沿AD折起(如图乙),使得平面
平面ABCD.
(1)求证:
平面ABCD;
(2)在线段BE上是否存在点M,使得
平面CDE?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5740c2a631f14c695386ec8178bf853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10b6175fb056760a9357936d14ffe82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ba3109534912d40dc277aa0c2a8fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/8fac5393-4033-4d85-afd1-451364fef3c0.png?resizew=143)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/bdbafdee-dd06-456b-ab18-2e4c86cea3f2.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2dc4bf4fdbfebc9ef6822aa37790a6.png)
(2)在线段BE上是否存在点M,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3869b3d43cd1d050dac2baecc169f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd8a98e03f6bb5601c91e72e9102e44.png)
您最近一年使用:0次
名校
解题方法
9 . 如图甲,直角梯形
中,
,
,
为
中点,
在
上,且
,已知
,现沿
把四边形
折起(如图乙),使平面
平面
.
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888496258179072/2889214410678272/STEM/3b9e4a2c-ccf1-4c12-a2ed-2de244a39bd1.png?resizew=378)
(1)求证:
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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1834434d91637d8ae88834465f18e2ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f3df5713a423887c16e6355236372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9b8345fc4d52e1a9377cf98b429be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888496258179072/2889214410678272/STEM/3b9e4a2c-ccf1-4c12-a2ed-2de244a39bd1.png?resizew=378)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
您最近一年使用:0次
2022-01-07更新
|
594次组卷
|
3卷引用:辽宁省沈阳市郊联体2021-2022学年高三上学期期中考试数学试题
10 . 如图多面体
,正方形
的边长为
,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/827e856e-520d-44fd-9897-dc041f1e721a.png?resizew=200)
(1)求证:
平面
;
(2)若二面角
的大小为
,且
,求
长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](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/6a22d6b860f06fe23618b0d3de6768fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc39144b305c67d44410d41053a1d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8139d9fd5c670c91aa7dc485366dd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745873876f2186144d6318ba4824ce3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/827e856e-520d-44fd-9897-dc041f1e721a.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a8123abd239549f7b0b1c98ff21133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a986c4642414bdbe41f2c59f7991bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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