名校
1 . 如图,在平行六面体
中,每一个面均为边长为2的菱形,平面
底面
,
,
分别是
,
的中点,
是
的中点.
平面
;
(2)若侧棱
与底面
所成的角为60°,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e884ca9429486026caa5e2310b0e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f5d29c352ddf9c57274b1b53342056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ac7cf883a6e586d06e3f33875bd95b.png)
(2)若侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b32fbb09df3cc6bdd32fd47d56942ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
您最近一年使用:0次
2022-11-19更新
|
457次组卷
|
3卷引用:重庆市第一中学校2023届高三上学期期中数学试题
名校
2 . 如图,在四棱锥
中,底面
是正方形,
是等边三角形,平面
平面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/98675300-9a0b-49fe-9a1a-0940f868083c.png?resizew=175)
(1)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1c1db5140a973d87e2646d25ed4f91.png)
(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/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/98675300-9a0b-49fe-9a1a-0940f868083c.png?resizew=175)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1c1db5140a973d87e2646d25ed4f91.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8424bdcf257367472c217c92d559f39f.png)
您最近一年使用:0次
2022-11-18更新
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1102次组卷
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8卷引用:重庆市南开中学校2022-2023学年高二上学期网课质量检测数学试题
名校
解题方法
3 . 刍甍,中国古代数学中的一种几何体.中国传统房屋的顶部大多都是刍甍.《九章算术》中记载:“刍甍者,下有袤有广,而上有袤无广.刍,草也.甍,屋盖也.”翻译为“底面有长有宽为矩形,顶部只有长没有宽为一条棱.刍甍字面意思为茅草屋顶”.如图下面的五面体为一个刍甍,其五个顶点分别为A,B,C,D,E,F,四边形ABCD为正方形,
,
平面ABCD,
,
,平面
平面ABCD,O为BC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/050f4d5f-ec4e-4bf5-aea4-82d76fc4e4f5.png?resizew=177)
(1)求证:
平面
;
(2)求平面
和平面
所成的锐二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a5a1579e41e7404e97d535297102aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2d28f1e7a6b17401c19c34beddcbe0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/050f4d5f-ec4e-4bf5-aea4-82d76fc4e4f5.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7ea432599108b34a0ccaa0f2c75e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
您最近一年使用:0次
2022-11-06更新
|
596次组卷
|
2卷引用:重庆市南开中学校2023届高三上学期第三次质量检测数学试题
名校
4 . 如图,在由三棱锥
和四棱锥
拼接成的多面体
中,
平面
,平面
平面
,且
是边长为
的正方形,
是正三角形.
(1)求证:
平面
;
(2)若多面体
的体积为16,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03962e215c034bbe273c45843e212fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2d28f1e7a6b17401c19c34beddcbe0.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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/c962b9a4-e26a-424b-ae5b-4f0858d2c7c0.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2023-07-04更新
|
543次组卷
|
7卷引用:重庆市第一中学2019-2020学年高三下学期期中数学(理)试题
重庆市第一中学2019-2020学年高三下学期期中数学(理)试题重庆市经开礼嘉中学2020届高三下学期期中数学(理)试题(已下线)考点24 空间直线、平面的平行、垂直问题-2021年新高考数学一轮复习考点扫描江西省上高二中2021届高三年级全真模拟考试数学(理)试题第三章空间向量与立体几何 章末测评卷-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)第一章 空间向量与立体几何 章末测试(提升)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)黑龙江省饶河县高级中学2022-2023学年高二下学期期末考试数学试题
名校
5 . 如图,在菱形
中,
,
,将
沿对角线
翻折到
位置,连结
,则在翻折过程中,下列说法不正确 的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/ac866f67-8b8e-4bde-ac33-9c7c8102e804.png?resizew=346)
![](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/f7dbf31dfd36aa456a63bafea8bc1985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/ac866f67-8b8e-4bde-ac33-9c7c8102e804.png?resizew=346)
A.存在某个位置,使得![]() |
B.当二面角![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.存在某个位置,使得![]() ![]() ![]() |
您最近一年使用:0次
2022-07-15更新
|
743次组卷
|
3卷引用:重庆市第七中学校2021-2022学年高一下学期期末数学试题
名校
6 . 四棱锥
中,四边形
为菱形,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/29/1529d48c-dbc9-4bb9-95bb-4161869432ae.png?resizew=218)
(1)证明:
;
(2)若
,且PA与平面ABCD成角为60°,在棱PC上是否存在点E,使二面角
的平面角的余弦值为
?若存在,求出PE的长;若不存在,说明理由.
![](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/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a46dc0bb5d8fa33583817e530a5d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/29/1529d48c-dbc9-4bb9-95bb-4161869432ae.png?resizew=218)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6f1d672d4d7775a81ccf0464a8d742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954795d1842974a705f9468f3b952ab1.png)
您最近一年使用:0次
2022-07-13更新
|
992次组卷
|
2卷引用:重庆市南开中学校2021-2022学年高一下学期期末数学试题
名校
7 . 如图所示,四棱锥
中,△
为正三角形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892076218064896/2923249386692608/STEM/f0ea3c3e6ba742ce8b31e6228523723b.png?resizew=211)
(1)求四棱锥
的体积;
(2)求
与面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2550fca125b1f9e31f65701e4d0637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34f4a1d4e690ccc0efb3e38d8261aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490f0c21a0bfecc1447d54803af0b119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/379b96bd6556f8b3f1f6f331d24e8283.png)
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892076218064896/2923249386692608/STEM/f0ea3c3e6ba742ce8b31e6228523723b.png?resizew=211)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2022-02-24更新
|
1373次组卷
|
3卷引用:重庆市南开中学2022届高三下学期高考模拟数学试题
名校
8 . 如图,在四棱锥
中,
,
,
是等边三角形,平面
平面
,
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/2022/1/24/2901456358277120/2909832154554368/STEM/bc5bfc6c-9105-41d2-a8d4-3e6568e5b8a8.png?resizew=243)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcac3b256b269b824d8738bb081f8ad.png)
![](https://img.xkw.com/dksih/QBM/2022/1/24/2901456358277120/2909832154554368/STEM/bc5bfc6c-9105-41d2-a8d4-3e6568e5b8a8.png?resizew=243)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
2022-02-05更新
|
478次组卷
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5卷引用:重庆市第八中学2021-2022学年高二下学期第一次月考数学试题
名校
解题方法
9 . 在四棱锥
中,底面ABCD为正方形,平面
平面ABCD,点M在线段PB上,
平面MAC,
.
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967237236064256/2997813252128768/STEM/511909ee-20f2-4935-9774-01d35d4f0050.png?resizew=303)
(1)判断M点在PB的位置并说明理由;
(2)记直线DM与平面PAC的交点为K,求
的值;
(3)若异面直线CM与AP所成角的余弦值为
,求二面角
的平面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a36ac578a3a35859c23e5a3a03487c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967237236064256/2997813252128768/STEM/511909ee-20f2-4935-9774-01d35d4f0050.png?resizew=303)
(1)判断M点在PB的位置并说明理由;
(2)记直线DM与平面PAC的交点为K,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da959c0ba06e6e3817ba8adafdac1c6.png)
(3)若异面直线CM与AP所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e468f168f3657d84d44be5eb89a62d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daffe333e60992bb4590370b79b806d5.png)
您最近一年使用:0次
2022-06-09更新
|
811次组卷
|
5卷引用:重庆市南开中学校2021-2022学年高一下学期7月月考数学试题
重庆市南开中学校2021-2022学年高一下学期7月月考数学试题浙江省宁波市2020-2021学年高一下学期期末数学试题山东省济南市章丘区第四中学2021-2022学年高一下学期4月月考数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)上海市南洋模范中学2021-2022学年高二上学期12月月考数学试题
名校
10 . 如图,在四棱锥
中,底面
为直角梯形,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/c3214260-742e-4575-b67b-cbc0bc183c06.png?resizew=188)
(1)证明:
平面
;
(2)已知
,
,
,且直线
与平面
所成角的正弦值为
,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/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/c3214260-742e-4575-b67b-cbc0bc183c06.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c54d01623f09f23103f03ba1135fc6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
2022-01-11更新
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1089次组卷
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5卷引用:重庆市第七中学校2023-2024学年高二上学期第一次月考数学试题