名校
1 . 如图,在棱长为4的正方体
中,点
是
的中点.
(1)求证:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/545f7283-6566-4b23-98c6-72b912d91588.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5441a4e71b599d31c45940a7d2614f3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f3750c0616ecc1d9dc8d905e26a9cc.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在边长为
的正方体
中,
为
中点,
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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://staticzujuan.xkw.com/quesimg/Upload/formula/0f11f1840eb8b17e7b07c3fe7e987a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0625187f35c80fb49277693e6b41b021.png)
您最近一年使用:0次
2024-04-24更新
|
2835次组卷
|
21卷引用:河北省邯郸市大名县第一中学2021-2022学年高一下学期开学考试数学试题
河北省邯郸市大名县第一中学2021-2022学年高一下学期开学考试数学试题河北省唐山市滦南县第一中学2020-2021学年高一下学期期中数学试题重庆市梁平中学2023-2024学年高二上学期入学考试数学试题广西桂林市第十八中学2019-2020学年高一上学期期中数学试题湖南省邵阳市第二中学2021-2022学年高一下学期期中数学试题河南省信阳市信阳高级中学2021-2022学年高一下学期第四次月考数学试题新疆昌吉回族自治州昌吉市昌吉州行知学校2022-2023学年高三上学期1月学业水平考试数学试题云南省(新教材)2021-2022学年高一春季学期期末普通高中学业水平考试数学试题贵州省黔西南州2022-2023学年高一下学期期末教学质量检测数学试题浙江省绍兴蕺山外国语学校2022-2023学年高一下学期期中数学试题福建省永春第二中学2022-2023学年高一下学期5月月考数学试题云南省文山州砚山县第三高级中学2022-2023学年高二下学期5月月考数学试题专题07B立体几何解答题(已下线)第03讲 直线、平面平行的判定与性质(八大题型)(讲义)(已下线)8.5.2 直线与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)第13章 立体几何初步(提升卷)-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)(已下线)第8.5.2讲 直线与平面平行-同步精讲精练宝典(人教A版2019必修第二册)(已下线)专题06 立体几何初步解答题热点题型-《期末真题分类汇编》(江苏专用)广东省茂名市信宜市第二中学2023-2024学年高一下学期5月月考数学试题云南省玉溪市通海一中、江川一中、易门一中三校2023-2024学年高一下学期六月联考数学试卷
名校
3 . 如图,在梯形
中,
,
,
,
为等边三角形,平面
平面
,E为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/ca8deec9-fefe-4fc4-996f-bff155d5d0ab.png?resizew=189)
(1)证明:
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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c935feadc24f95b0b137d0b82ef9b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/ca8deec9-fefe-4fc4-996f-bff155d5d0ab.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ae72f5e5891249caa10c43224da89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2024-03-02更新
|
777次组卷
|
2卷引用:河北省承德市宽城满族自治县第一中学2023-2024学年高二下学期期初考试数学试卷
名校
解题方法
4 . 已知四棱台
中,底面
为正方形,
,
,
,
⊥底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/a8661119-3ec1-4e05-a917-0487b68452e6.png?resizew=152)
(1)证明:
.
(2)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0424446817f60c18f8e4e3cc202ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03bd2909f55de23a5a91034ee08adcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50943279ee6f0299b3725eecd77bafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/a8661119-3ec1-4e05-a917-0487b68452e6.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1de5964353beb55c5058b2a431eecaf.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
5 . 在如图所示的三棱锥
中,
分别是线段
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/ddb31d53-420c-421d-ad70-a7d3e7e889dd.png?resizew=134)
(1)证明:直线
平面
;
(2)若二面角
的大小为
,求直线
和平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358c6594ed1b0efc0415e8d64bbe8fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a77aa6c27acfffcc601d9ca7e6d4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f8c4ef0aee67b54282d9a6fa7714ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/ddb31d53-420c-421d-ad70-a7d3e7e889dd.png?resizew=134)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d3f5f4c4419913c1232b7aae03ade.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107b87854ea594f77a40b25becd36020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
您最近一年使用:0次
名校
6 . 如图,四棱锥
的底面
是平行四边形,
是边长为2的正三角形,平面
平面
为棱
的中点.
平面
.
(2)求直线
与平面
所成角的正弦值.
![](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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0ab48b6c32c1c594587bb86b39865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2024-02-29更新
|
1309次组卷
|
8卷引用:河北省保定市定州市第二中学2023-2024学年高二下学期开学考试数学试题
解题方法
7 . 如图1,在直角梯形
中,
,
,
,
,
,
分别为
,
的中点.将直角梯形
沿
,
,
折起,使得
,
,
重合于点
,得到如图2所示的三棱锥
.
(1)证明:
.
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454ef60ed4e4233a949345cb848d8483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1359ea39e0d3584a24b878a079e50a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e173b1a57fc78a1dc2405275611e668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e867e4fe4ee35b9098a39734c9737f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d803886ece8068dd12f174443bf01a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee51946da54ce4130fefa5e488589d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454ef60ed4e4233a949345cb848d8483.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/a659b85c-1eaf-4fbc-bedd-37f4ed9f2264.png?resizew=335)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbad7ad1465d1c4c177e3321e6ed12a.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
您最近一年使用:0次
8 . 如图,在正四棱台
中,
.
(1)证明:
;
(2)若正四棱台
的高为3,过
的平面α与
平行,求平面α与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d134433600df75f2a5d0f35deb2cac90.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/1/3350cb68-89ea-4aa5-99d8-f4d0fd67e8e0.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a0e00113872f921116b6c0c3177d0f.png)
(2)若正四棱台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2023-09-01更新
|
576次组卷
|
5卷引用:河北省保定市保定市部分高中2024届高三上学期开学数学试题
河北省保定市保定市部分高中2024届高三上学期开学数学试题内蒙古赤峰市2024届高三上学期开学考试理科数学试题内蒙古自治区赤峰市红山区2023-2024学年高三上学期开学考试理科数学试题湖南省株洲市第三中学2024届高三上学期8月月考数学试题(已下线)专题06 二面角4种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
解题方法
9 . 如图,在四边形
中,E为
上一点,若
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/cb3ede3d-a813-4b38-b465-59aa632c972d.png?resizew=171)
(1)求证:
;
(2)若
,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ab3bdca62b4ef50a82eee4f194ce33.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/cb3ede3d-a813-4b38-b465-59aa632c972d.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1a295da4be97f4601b2d06a7c077fd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5074059ab695965a2e478a5eeea6f81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022高一·全国·专题练习
名校
解题方法
10 . 如图,在三棱锥P-ABC中,PA⊥平面ABC,AB=AC=2,BC=2
,M,N分别为BC,AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/e98ad406-1e7e-4164-b39b-b6d9c6171235.png?resizew=149)
(1)求证:MN//平面PAC;
(2)求证:平面PBC⊥平面PAM;
(3)在AC上是否存在点E,使得ME⊥平面PAC,若存在,求出ME的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/e98ad406-1e7e-4164-b39b-b6d9c6171235.png?resizew=149)
(1)求证:MN//平面PAC;
(2)求证:平面PBC⊥平面PAM;
(3)在AC上是否存在点E,使得ME⊥平面PAC,若存在,求出ME的长;若不存在,请说明理由.
您最近一年使用:0次
2022-05-09更新
|
1000次组卷
|
7卷引用:河北省邯郸市大名县第一中学2021-2022学年高一下学期开学考试数学试题
河北省邯郸市大名县第一中学2021-2022学年高一下学期开学考试数学试题(已下线)第8章 立体几何初步 章末综合检测 -2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)广东省揭阳市普宁市华侨中学2021-2022学年高一下学期期中数学试题云南省会泽县实验高级中学校2021-2022学年高一5月月考数学试题第六章 立体几何初步测评-北师大版(2019)高中数学必修第二册第六章 立体几何初步测评 课后习题 2020-2021学年高一数学北师大版(2019)必修第二册4.4.2 平面与平面垂直的性质