1 . 如图,在四棱锥
中,
底面
,
,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/1/24/2643070521409536/2644342555025408/STEM/5fa15c8580e14acfae967cdc41cec12e.png?resizew=192)
(1)求证:
平面
;
(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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/1/24/2643070521409536/2644342555025408/STEM/5fa15c8580e14acfae967cdc41cec12e.png?resizew=192)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
您最近一年使用:0次
名校
2 . 如图,在三棱锥
中,AO,OB,OC两两互相垂直,点D,E分别为棱BC,AC的中点,F在棱AO上,且满足
,已知
.
![](https://img.xkw.com/dksih/QBM/2021/1/22/2641640183218176/2643034324131840/STEM/f1c49806-b114-42a0-abbc-03e4eb1f5227.png)
(1)
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98140559ade34a1cc55b93b6c8f3991d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0affc564d1d6d0a72c32a4481108de0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c79c189c2d0563aa977377b1e42b6c3.png)
![](https://img.xkw.com/dksih/QBM/2021/1/22/2641640183218176/2643034324131840/STEM/f1c49806-b114-42a0-abbc-03e4eb1f5227.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fdb2b9d6a4a54ed1328c5b3adcf7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade6931be0db4f7a771bb764c88c80d9.png)
您最近一年使用:0次
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解题方法
3 . 如图,矩形
所在平面与半圆弧
所在平面垂直,
是
上异于
的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/bb294994-27ec-483e-99b1-e5771eef077d.png?resizew=175)
(1)证明:平面
平面
;
(2)在线段
上是否存在点
,使得
平面
?若不存在,说明理由,若存在请证明你的结论并说明
的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a5b099b9112ed6a9f71b4a65875ccf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/bb294994-27ec-483e-99b1-e5771eef077d.png?resizew=175)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb23a04ac9df27fb987126e7ba0f6c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3219a5fbe920e617eff32e558c0c6ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2021-01-23更新
|
468次组卷
|
3卷引用:宁夏银川市长庆高级中学2020-2021学年高一上学期期末考试数学试题
宁夏银川市长庆高级中学2020-2021学年高一上学期期末考试数学试题(已下线)专题11.4《立体几何初步》(B卷提升篇)-2020-2021学年高一数学必修第四册同步单元AB卷(新教材人教B版)江苏省南京市外国语学校2022-2023学年高一下学期5月月考数学试题
4 . 如图(1),已知梯形
,
,
,
,将
沿
向上翻折,构成如图(2)所示的四棱锥
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/12/29/2624859004608512/2632267762065408/STEM/3e307187-6be7-47d0-993a-4e4fab64171f.png?resizew=422)
(1)证明:
平面
;
(2)当四棱锥体积最大时,若二面角
的余弦值为
,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15164f8cfc92ef0bff64cc07d9116cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7099026716ee1821dd7d9f157dc055f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e98920101c174b991d7a8481707ab88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2020/12/29/2624859004608512/2632267762065408/STEM/3e307187-6be7-47d0-993a-4e4fab64171f.png?resizew=422)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
(2)当四棱锥体积最大时,若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48ca51b0c3fbf5d5624ea08b916e59a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
您最近一年使用:0次
2021-01-09更新
|
190次组卷
|
2卷引用:宁夏贺兰县景博中学2021届高三期末数学(理)试题
2020高三·全国·专题练习
名校
解题方法
5 . 如图,在四棱锥PABCD中,PA⊥平面ABCD,底面ABCD为菱形,E为CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/25b8c1ec-e5a2-4661-b2bb-39335139d0b4.png?resizew=148)
(1)求证:BD⊥平面PAC;
(2)若∠ABC=60°,求证:平面PAB⊥平面PAE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/25b8c1ec-e5a2-4661-b2bb-39335139d0b4.png?resizew=148)
(1)求证:BD⊥平面PAC;
(2)若∠ABC=60°,求证:平面PAB⊥平面PAE.
您最近一年使用:0次
2021-01-08更新
|
1042次组卷
|
14卷引用:宁夏银川市三沙源上游学校2022-2023学年高一下学期期末考试数学试题
宁夏银川市三沙源上游学校2022-2023学年高一下学期期末考试数学试题江西省南昌市八一中学2020-2021学年高二下学期期末数学(文)试题贵州省黔西南州同源中学2020-2021学年高二下学期期末数学(文)试题广东省梅州市丰顺县丰顺中学2022-2023学年高三上学期期末考试数学试题(已下线)专题8.5 直线、平面垂直的判定及性质 (精讲)-2021年高考数学(文)一轮复习学与练四川省广安市武胜烈面中学校2021-2022学年高二10月月考数学(理)试题上海外国语大学闵行外国语中学2021-2022学年高二上学期期中数学试题广东省广州市新塘中学2021-2022学年高二上学期期中数学试题(已下线)上海高二上学期期中【常考60题考点专练】(2)四川省遂宁中学校2022-2023学年高二上学期期中考试数学(文)试题青海省西宁市城西区海湖中学2020-2021学年高二下学期开学数学试题甘肃省兰州市第五十八中学2023年普通高中学业水平合格性考试数学试卷(已下线)第10章 空间直线与平面(常考、易错必刷30题7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(沪教版2020必修第三册)(已下线)期中真题必刷易错40题(17个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
20-21高二·全国·假期作业
名校
6 . 如图,在四棱锥
中,已知
是平行四边形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/da80e71d-d9dc-4454-8fb3-4e6ac2f9ad2a.png?resizew=172)
(1)求证:
平面
;
(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/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0998235b5aa3374d98636f28a929e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71c3c9fe52ad7ab87da571a72c4eea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eea328811717ab763fe1f97babcc754.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/da80e71d-d9dc-4454-8fb3-4e6ac2f9ad2a.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,四棱锥
的底面是正方形,
底面
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/e8a44b24-fe94-45d8-aa43-52e9863882fd.png?resizew=143)
(1)求证:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/e8a44b24-fe94-45d8-aa43-52e9863882fd.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8ed6acd96e5586ea7f2316669094c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d1190fdc8609b1e43957aaaaf4abbe.png)
您最近一年使用:0次
2020-12-17更新
|
776次组卷
|
5卷引用:宁夏海原县第一中学2021届高三上学期期末考试数学(文)试题
名校
解题方法
8 . 如图,在四棱锥
中,四边形
是直角梯形,且
,
,
⊥平面
,
,
,点
为线段
的靠近点
的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/bdb1067c-16d2-4656-accf-65a0e69e2c05.png?resizew=177)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
平面
;
(2)若异面直线
与
所成的角为
,求多面体
的体积.
![](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/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/bdb1067c-16d2-4656-accf-65a0e69e2c05.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cf3ef69ebbd5a3a7dbfa1ca62db26e.png)
您最近一年使用:0次
2020-12-04更新
|
780次组卷
|
2卷引用:宁夏石嘴山市第三中学2021届高三上学期期末考试数学(文)试题
9 . 如图,已知
平面
,四边形
为矩形,四边形
为直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/11/13/2592100518371328/2605582305214464/STEM/d972a812fa604e2b84970bf6a7eb836a.png?resizew=230)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](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/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768c2ebf7e4c39d125e6a95369c41b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/2020/11/13/2592100518371328/2605582305214464/STEM/d972a812fa604e2b84970bf6a7eb836a.png?resizew=230)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199098479c92e87304b91871172d46e0.png)
您最近一年使用:0次
2020-12-02更新
|
1770次组卷
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13卷引用:【全国百强校】宁夏银川一中2018-2019学年高一上学期期末考试数学试题
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10 . 已知空间中的三点
,
,
,设
,
.
(1)若
与
互相垂直,求
的值;
(2)求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540a5ea5c0f16bddb92e1416f4a103ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cce2129b649c3e954e0d53c7e7aa46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50cfc4a55697ae8ac7a8635d4dfd5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59eb47e19123a9bb10e19fd4065cfb4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9ec7ce95755fed0d64be3eaaa7b645.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e08d0ffb3a2147fb1ba5145471082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
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