名校
解题方法
1 . 如图,在四棱锥
中,底面
是平行四边形,
,
底面
,
,E、F分别为BC、AD的中点,点M在线段
上.
(1)求证:
平面
;
(2)设
,若直线
与平面
所成的角
的正弦值为
,求
的值.
![](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/6e901c430af74f7bbce43364bd4f2e47.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/d65ae5cb9089acf47572c33f312f3ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/56672792-0120-477c-9af0-0c66e7905c5b.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d2fd826237dd9250d4e9eb92a1e657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9786d2ec9acadce968ce77d33d120d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
2 . 如图,在四棱锥
中,底面
为矩形,
平面
,垂足为O,E为PC的中点,
平面
.
(1)证明:
.
(2)若
,
,PC与平面
所成的角为
,求平面
与平面
夹角的余弦值.
![](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/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a04ea8ebc597fd1f5d6bb8df181a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/1527497e-8a18-4660-88a9-2ae1e128484b.png?resizew=180)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585288e61871608f6ff8f7e4a0beafbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49bdf1dcfe6c344dd2442669e72c44b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
3 . 如图,在四棱锥
中,底面
是矩形,
是
的中点,
平面
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/ee2b26db-04bb-4488-bf81-f8e26d6b8d2a.png?resizew=138)
(1)求证:
;
(2)求二面角
的余弦值.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4720bd0e6a1d47a84e19b60d4ea36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/ee2b26db-04bb-4488-bf81-f8e26d6b8d2a.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e81c256be76e1d0a71a09a75fe91d8.png)
您最近一年使用:0次
名校
4 . 如图所示,在梯形
中,
,
,
.四边形
为矩形,且
平面
.
平面
;
(2)若直线
与
所成角的正切值为
,点
在线段
上运动,当点
在什么位置时,平面
与平面
所成的锐二面角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f18f1b5ebe17b068fe79bdf30d6effc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1674add0f4a1a24f5ed893b1c5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e108d5c61e85e0741ec2c484fc5768.png)
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2024-01-31更新
|
1201次组卷
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5卷引用:新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二下学期数学开学考试数学试卷
新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二下学期数学开学考试数学试卷四川省攀枝花市普通高中2023-2024学年高二上学期教学质量监测数学试题卷2024届高三新改革适应性模拟测试数学试卷二(九省联考题型)(已下线)第5讲:立体几何中的动态问题【练】(已下线)黄金卷04(2024新题型)
名校
解题方法
5 . 如图,在长方体
中,
为棱
的中点,
为四边形
内(含边界)的一个动点.且
,则动点
的轨迹长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/cd1708d9-73db-42e6-aeb8-4558867c1c54.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e477427d7d9daf0cb3c31d7b3c58bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3db208cdc38ae7acbd6a866bf494b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/cd1708d9-73db-42e6-aeb8-4558867c1c54.png?resizew=137)
A.5 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-22更新
|
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3卷引用:新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二下学期数学开学考试数学试卷
名校
解题方法
6 . 如图,在多面体中,平面
平面
,四边形
为正方形,四边形
为梯形,且
,
.
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)线段
![](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/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6114761b369162cda06f08e31c23fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258ed4f5282317bb067a41104d559222.png)
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2024-01-21更新
|
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2卷引用:新疆昌吉回族自治州第一中学2024届高三下学期3月月考数学试题
名校
解题方法
7 . 已知直线
、m、n与平面
、
,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-12更新
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3卷引用:2024年高考数学二轮复习测试卷(新题型地区专用)
(已下线)2024年高考数学二轮复习测试卷(新题型地区专用)内蒙古呼和浩特市2024届高三上学期学业质量监测数学(文)试题福建省永春一中、培元中学、石光中学、季延中学2024届高三下学期第二次联合考试数学试题
8 . 如图,在直三棱柱中,若
,
,
是棱
的中点,则下列说法正确的是( )
A.点![]() ![]() ![]() |
B.![]() ![]() |
C.点![]() ![]() ![]() |
D.![]() |
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6卷引用:新疆维吾尔自治区阿克苏地区第一中学2023-2024学年高二上学期期末数学试题
新疆维吾尔自治区阿克苏地区第一中学2023-2024学年高二上学期期末数学试题江苏省2023-2024学年高二上学期期末迎考数学试题(B卷)江苏省2023-2024学年高二上学期期末迎考数学试题(R版B卷)河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(四)(已下线)专题13 空间向量的应用10种常见考法归类(4)(已下线)第四章 立体几何解题通法 专题二 体积法 微点3 体积法综合训练【基础版】
名校
9 . 已知四棱锥的底面
为等腰梯形,
,
,
,
平面
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4710f75c66f19825a3e44b48f78bbac.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
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6卷引用:新疆维吾尔自治区石河子市第一中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
10 . 如图,在三棱柱中,
,
,
为
的中点,平面
平面
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a446b91e73b181f9f4d56264dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d8afb6a50406ba4c6621f4976c8dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f25c5543b39190dc2499aa66f939659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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2024-01-31更新
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7卷引用:新疆伊犁州华·伊高中联盟2023-2024学年高二上学期期中数学试题