名校
1 . 在四棱锥
中,平面
平面
,底面
为矩形,
,
,
,
、
分别为线段
、
上一点,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/bf50abb3-4d68-451c-a41d-14c579f5d2ad.png?resizew=187)
(1)证明:
;
(2)证明:
平面
,并求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e05d8681a679bd31922e62480f69d55.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251387023641ec1af5b58801666ecda2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bac9bf01e282af11adc5b45044a499b.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348fb71fbc47fd87e9ce011652ef4186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3505caf94539d51c4edba53a78ad0d3b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/bf50abb3-4d68-451c-a41d-14c579f5d2ad.png?resizew=187)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ab924e3692515bd8be4c36472a959a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16835e3f230ba3f543b6804e445e283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2990ef24039c6be7643cb582062503a.png)
您最近一年使用:0次
2019-03-28更新
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1363次组卷
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7卷引用:四川省成都市棠湖中学2018-2019学年高二下学期期末考试数学(文)试题
2 . 如图,在四棱锥
中,底面ABCD是矩形,
,E,F分别为BC,CD的中点,且
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437d19406753ee07f403ef7a4094d605.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e3ead519-07f3-45da-8d7d-7371f658be91.png?resizew=201)
求证:
平面PBD;
平面PEF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed4f2b8f2f8fced0fd7f6784117247d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104175a41a6bbd4531822cd53d69cce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437d19406753ee07f403ef7a4094d605.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e3ead519-07f3-45da-8d7d-7371f658be91.png?resizew=201)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b5fe221a99803ddb64b87bf35cda47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b601f45feea9f13175129e66072a1237.png)
您最近一年使用:0次
名校
3 . 如图,四棱锥
的底面为正方形,
底面
,则下列结论中不正确的是
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/8e07666a-6800-4def-960d-4cb990d7498f.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/8e07666a-6800-4def-960d-4cb990d7498f.png?resizew=170)
A.![]() |
B.![]() ![]() |
C.平面![]() ![]() |
D.![]() ![]() ![]() ![]() |
您最近一年使用:0次
2019-02-28更新
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1007次组卷
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4卷引用:山西省运城市景胜中学2019-2020学年高二上学期12月月考数学(文)试题
名校
4 . 如图,在直四棱柱ABCD-A1B1C1D1中,底面是边长为
的正方形,AA1=3,点E在棱B1B上运动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b9a2dd49-3a93-413b-9ae9-d6e32cfb4bc0.png?resizew=160)
(1)证明:AC⊥D1E;
(2)若三棱锥B1-A1D1E的体积为
时,求异面直线AD,D1E所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b9a2dd49-3a93-413b-9ae9-d6e32cfb4bc0.png?resizew=160)
(1)证明:AC⊥D1E;
(2)若三棱锥B1-A1D1E的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0e7bfbd56fe73dfe04c04da749d942.png)
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2019-02-08更新
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341次组卷
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4卷引用:山东省东营市广饶县第一中学三校区2022-2023学年高二9月月考数学试题
山东省东营市广饶县第一中学三校区2022-2023学年高二9月月考数学试题(已下线)第一章 空间向量与立体几何(易错必刷40题14种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)2015届湖北省武汉市武昌区高三元月调研考试文科数学试卷(已下线)章末检测2(课后作业)-2018-2019版数学创新设计课堂讲义同步系列(人教A版必修2)
18-19高一·全国·单元测试
名校
5 . 如图,四边形ABCD为矩形,DA⊥平面ABE,AE=EB=BC=2,BF⊥平面ACE于点F,且点F在CE上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/c1669e1a-ea7e-41e5-940a-2d55e6238bd4.png?resizew=170)
(1)求证:AE⊥BE;
(2)求三棱锥D-AEC的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/c1669e1a-ea7e-41e5-940a-2d55e6238bd4.png?resizew=170)
(1)求证:AE⊥BE;
(2)求三棱锥D-AEC的体积.
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2019-02-08更新
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528次组卷
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4卷引用:四川省自贡市田家柄中学教育集团2021-2022学年高二上学期期中考试数学试题
四川省自贡市田家柄中学教育集团2021-2022学年高二上学期期中考试数学试题2023年广东省普通高中学业水平合格性考试模拟(五)数学试题甘肃省民勤县第一中学2023-2024学年高二下学期开学考试数学试题(已下线)章末检测2(课后作业)-2018-2019版数学创新设计课堂讲义同步系列(人教A版必修2)
名校
解题方法
6 . 如图,在四棱锥
中,
,
,
,
,
分别是
和
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/517972d2-397c-4d5f-927b-d9decdc43676.png?resizew=172)
(1)证明:
;
(2)证明:平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502a46021ff0bd64fc4cd3bad7d8a826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1161e0345b3646c71365430dccbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/517972d2-397c-4d5f-927b-d9decdc43676.png?resizew=172)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d103e9cd501065d24ab94b5fd6cb37.png)
您最近一年使用:0次
2019-02-05更新
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1299次组卷
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6卷引用:安徽省安庆市桐城市第八中学2019-2020学年高二下学期期初检测文科数学试题
9-10高一下·云南昆明·期末
名校
7 . 如图,在正方体
中,M是
的中点,O是底面ABCD的中心,P是
上的任意点,则直线BM与OP所成的角为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b77a03d567bafae72d7b14e69bace81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc689a0bf91e6384ca0bd3fb3fbfa0ac.png)
您最近一年使用:0次
2019-01-30更新
|
1110次组卷
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10卷引用:2011年四川省绵阳中学高二下学期第一次月考数学试卷
(已下线)2011年四川省绵阳中学高二下学期第一次月考数学试卷(已下线)2010-2011年四川省绵阳中学高二下学期第一次月考数学试卷北京市十一学校2016-2017学年高二上学期期中考试数学(理)试题(已下线)第十一课时 课后 1.4.2.2 夹角问题(已下线)第3讲 用空间向量研究距离、夹角问题-2021-2022学年高二数学上学期高频考点专题突破(人教A版2019选择性必修第一册)山东省聊城市第二中学2022-2023学年高二上学期开学考试数学试题上海市嘉定区第一中学2021-2022学年高二上学期期末数学试题(已下线)1.4.2 用空间向量研究距离、夹角问题【第一课】(已下线)09-10学年昆明三中高一下学期期末数学试卷(已下线)2010年吉林一中高一下学期期末考试数学卷
8 . 在四棱锥
中,
平面
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/32cda40b-59c4-4001-9866-b2d1c6897211.png?resizew=147)
(1)求证:
.
(2)当
时,求此四棱锥的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ee7ec207528fdd7f22287dafc2dcd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/32cda40b-59c4-4001-9866-b2d1c6897211.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
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9 . 在三棱柱
中,平面
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/929825ec-dd81-4486-98b1-2103bd357105.png?resizew=174)
(1)证明:
;
(2)若
,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/2623e1c4ecbd65ae5e0285c0453ffd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e793c52fdd16cc602eaf753964ec02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd9abf9ec52d85bfe36188e95e6ad6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/929825ec-dd81-4486-98b1-2103bd357105.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403ec256d712cf32d21ed51d71648c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e975f6c9fafab8fd7639dc0cd0f70a4.png)
您最近一年使用:0次
名校
10 . 如图,在三棱锥
中,
,
,
,
,
,
分别为线段
,
上的点,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/7b450a34-8cb3-451c-9f80-d35ae0238ac3.png?resizew=131)
(1)证明:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7c18f9db65fcd840b39d7bbd3028c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28597da489dc639750523c83fbc11c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e99aae9fa3f0cd6405461b8db163e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/1aabee6b0c633ffd42f01af2e1fb8a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75dc7cef548ba1fda2b082733baae52.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/7b450a34-8cb3-451c-9f80-d35ae0238ac3.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb0f9de2f087af7ef18ee9184d88b51.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69fbd5a9df4c0210604cf1ae2fa7e0c.png)
您最近一年使用:0次
2019-01-23更新
|
508次组卷
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5卷引用:娄底市2018-2019学年高二上学期期末考试数学(理)试题