名校
1 . 如图,在四边形
中,
,点E,F分别在
上运动,且
,现将四边形
沿
折起,使平面
平面
.
(1)若E为
的中点,求证:
平面
;
(2)求三棱锥
体积的最大值,并求此时直线AE与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432ec7c0fdfbcc8c2b210ed18f3dc64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46c696ff5f123a482bae81cf9a1b570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25eff69a4a0dc7a7ab183843303d333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f3df5713a423887c16e6355236372.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/28/18b5bf98-d92c-4cfc-8ff0-c21805296dc7.png?resizew=341)
(1)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68744081315689b14c9c7a2b74100f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
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解题方法
2 . 在长方体
中,
,
,点M、N分别在线段
,
上,且
,
.
(1)求直线
与平面
所成角的正弦值;
(2)若直线
与平面
相交于点P,求线段DP的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5282dc0f3e18f35495d775e83694943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcf08c283a57c03de8db6d64b1e2218.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/28/2a0a26ad-6fd5-4d69-a820-ecf01cce90bb.png?resizew=114)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
您最近一年使用:0次
2023-09-24更新
|
492次组卷
|
2卷引用:四川省绵阳市绵阳南山中学实验学校2023-2024学年高二上学期10月月考数学试题
3 . 四棱锥
的底面是边长为1的菱形,
,E是CD的中点,
,
平面
.
(1)求直线
与平面
所成角;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/ad47c662-8ca9-4620-9afc-3ba686fd3edb.png?resizew=150)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a26a7784c7419d8359fb119c8ecc03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
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4 . 图①是由矩形
和梯形
组成的一个平面图形,其中
,
,点
为
边上一点,且满足
,现将其沿着
折起使得平面
平面
,如图②.
(1)在图②中,当
时,
(ⅰ)证明:
平面
;
(ⅱ)求直线
与平面
所成角的正弦值;
(2)在图②中,记直线
与平面
所成角为
,平面
与平面
的夹角为
,是否存在
使得
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe457d83a45da9c3af435a1a1319b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7882853e3d1122a57cc4beb8eecafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca8d94c6437cdd63c48c05760ef6705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/6afff234-fbdc-4cd1-af2c-c39acc2c7bed.png?resizew=356)
(1)在图②中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071159cac13097ea0928285bc1be66d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dc8826770249f3996b8a188c03da92.png)
(ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)在图②中,记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90131175c3fb6a3837a22d7d5bbc268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/382184a43e2155e54abfa48ce96ad364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
5 . 如图,四面体
中,
、
分别是
、
的中点,
,
.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6559aabe16c2318687089e7cc498b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/a0acc81c-8980-4cc0-b42e-961f4aab97f5.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
名校
6 . 如图,多面体
中,四边形
为平行四边形,
,
,四边形
为梯形,
,
,
,
,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/24/5ad85ab5-0687-4a02-b424-7c57e08cf6ca.png?resizew=240)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](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/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921a71040d18df8b33bc41995675a586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d5a164bf56f8fb92527ad78bc10ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dced11455b3e31a9090915f80a046fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6370d6c626bdabf1fc694501ee6c714f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56512504254ab7f574a717dd6830fb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f82cd6b3572de264a1fbf7f39f0afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/24/5ad85ab5-0687-4a02-b424-7c57e08cf6ca.png?resizew=240)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
您最近一年使用:0次
7 . 已知平面
与
所成锐二面角的平面角为
,
为二面角内一定点(
不在平面
与
内),过点
作与平面α,β所成的角都是
的直线
,则这样的直线
有且仅有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b112f474fc4e1da5e8c0b326c595ce78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052e6bb57f7a823b0896680c32c5fa18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.1条 | B.2条 | C.3条 | D.4条 |
您最近一年使用:0次
名校
8 . 图,在棱长为2的正方体
中,点E,F分别是线段AC,
上的动点,
,
,且
.记
与
所成角为
,
与平面
所成角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64f1d0b5e4a6ebf4405b98a21a1ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2424068d330c491cff2f947e7b5ff93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf89344ded4d4ebb94edf2b8d42ed8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.对于任意![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2023-09-07更新
|
948次组卷
|
4卷引用:四川省眉山市东坡区多悦高级中学校等2023-2024学年高二上学期期中联考数学试题
四川省眉山市东坡区多悦高级中学校等2023-2024学年高二上学期期中联考数学试题(已下线)通关练07 空间向量与立体几何章末检测(二)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)江苏省苏州市2024届高三上学期期初调研考试数学试题广东省广州市广东实验中学2024届高三下学期教学情况测试(二)数学试卷B
2011·河北唐山·一模
名校
9 . 如图,在四棱锥
中,
平面
,
,
,且
,
,
.
;
(2)在线段
上,是否存在一点M,使得二面角
的大小为
,如果存在,求
与平面
所成角的正弦值,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2478a116f8ff83c8477094e97c4211cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5bb4978fdc23a8220f68fe41d28829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
您最近一年使用:0次
2023-09-06更新
|
1155次组卷
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23卷引用:四川省遂宁中学校2022-2023学年高二上学期10月月考数学(理)试题
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解题方法
10 . 如图,在正方体
中,
为
的中点( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/20/8c8f7e77-7ebf-455e-abed-af395e505003.png?resizew=153)
A.![]() ![]() ![]() |
B.![]() |
C.若正方体的棱长为1,则点![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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2023-08-19更新
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5卷引用:四川省德阳中学校2023-2024学年高二上学期10月月考数学试题