名校
1 . 如图,在等腰梯形
中,
,四边形
为矩形,且
平面
,
.
(1)求证:
平面
;
(2)在线段
上是否存在点
,使得平面
与平面
所成锐二面角的平面角为
,且满足
.若不存在,请说明理由;若存在,求出
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182fca78237d12dc7236fb739b439e82.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/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/c66fea61-9472-4aa6-9417-c2701a556bc0.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)在线段
![](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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5743ebd4491ae361b1b50ae3976ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
您最近一年使用:0次
2023-09-19更新
|
912次组卷
|
4卷引用:河南省信阳高级中学2023届高三下学期3月测试(二)理科数学试题
河南省信阳高级中学2023届高三下学期3月测试(二)理科数学试题福建省泉州市晋江学校2023-2024学年高二上学期第一次阶段检测数学试题福建省福州第二中学2023-2024学年高二上学期第一次月考数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
名校
2 . 如图,在四棱锥
中,底面ABCD为平行四边形,
平面PAB,点O为PB的中点.
,
.
(1)求证:直线
平面ABCD;
(2)求直线PB与平面OAC夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6546d9c27cc1d9d5c5cbd2fc294f6b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae16b72924eb24c45f5dcfab07cc01b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/2390c75d-869b-4f69-9bcd-b4bb3ec5738e.png?resizew=132)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
(2)求直线PB与平面OAC夹角的正弦值.
您最近一年使用:0次
2023-09-06更新
|
321次组卷
|
5卷引用:河南省濮阳市范县第一中学2021-2022学年高二上学期第一次月考数学试题
名校
3 . 如图1,四边形
是边长为2的正方形,将
沿
折叠,使点
到达点
的位置(如图2),且
.
(1)求证:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80c2fe15c4561e583ceeedf1fa4d5c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/6ca11534-7438-4f29-aa17-68e47e1ad1aa.png?resizew=293)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7aa38ad18805583a59dfaaa53b294a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在直三棱柱
中,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7d65bb316f98c1748a2d14fd4d8a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4fcf607b0710d12aaabd17fd053d83.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/ced4d696-014b-4a44-b674-2629e6fdf575.png?resizew=135)
您最近一年使用:0次
名校
5 . 如图,在四棱锥
中,底面
为平行四边形,
为等边三角形,平面
平面
,
.
分别为
的中点,求证:
平面
;
(2)求证:
平面
;
(3)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/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2014b4b4ad8bceae6aae6c42750ba111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1679c3594dd9e0ef6827c00f0ccee296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4193fb98c610f41f9a6c89d046f13d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2023-07-14更新
|
1018次组卷
|
2卷引用:河南省信阳高级中学2023-2024学年高一下学期5月期中测试数学试题(二)
解题方法
6 . 如图,在多面体中,四边形
是正方形,
,
且
,二面角
是直二面角.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/5/58864f81-1d09-4d17-af67-4a9fa1f3aedd.png?resizew=133)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f61d8d0aaefc3ac491ad3659a2ba2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9a248d1d22e1c29cfbce96b32e2206.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93daae6ec80968c0630e229c1fa1b84.png)
您最近一年使用:0次
2023-08-03更新
|
686次组卷
|
5卷引用:河南省信阳市商城县上石桥高级中学2023-2024学年高二上学期9月月考数学试题
河南省信阳市商城县上石桥高级中学2023-2024学年高二上学期9月月考数学试题第6章 空间向量与立体几何 综合测试北师大版(2019) 选修第一册 章末检测卷(三) 空间向量与立体几何(已下线)专题04 空间中的点、直线、平面与空间向量5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)(已下线)通关练02 用空间向量的解决平行垂直问题10考点精练(50题) - 【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)
名校
7 . 如图,在四棱锥
中,底面
是正方形,侧面QAD是正三角形,侧面
底面
,M是QD的中点.
平面
;
(2)求侧面QBC与底面
所成二面角的余弦值;
(3)在棱QC上是否存在点N使平面
平面AMC成立?如果存在,求出
,如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11df029afb11e4233989b1338cb3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c550269f3199038726f55cbd281c13a.png)
(2)求侧面QBC与底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)在棱QC上是否存在点N使平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a2e866037fb17d7fb74b462ef2f34d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6525116388ec2bf0e2828bdc3cc5d3b9.png)
您最近一年使用:0次
2023-07-31更新
|
1478次组卷
|
10卷引用:河南省信阳市浉河区信阳高级中学2023-2024学年高一下学期6月月考数学试题
河南省信阳市浉河区信阳高级中学2023-2024学年高一下学期6月月考数学试题吉林省长春市实验中学2022-2023学年高一下学期期末数学试题(已下线)第10章 空间直线与平面(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)(已下线)第八章 立体几何初步(提升卷)-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)(已下线)高一下学期期末复习解答题压轴题二十四大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)高一下学期期末数学试卷(巩固篇)-举一反三系列(人教A版2019必修第二册)江苏省宿迁市泗阳县实验高级中学2023-2024学年高一下学期第二次调研测试(5月)数学试题安徽省安庆市第一中学2023-2024学年高一下学期5月同步测试数学试卷西安市交大附中2023—2024学年高一下学期第二次月考数学试题
名校
8 . 如图,在四棱锥
中,底面
为正方形,侧面
是正三角形,侧面
底面
,
是
的中点.
平面
;
(2)求侧面
与底面
所成二面角的余弦值.
![](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/852aabd89edffc1b94344ff3f1f31ccd.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-07-08更新
|
1704次组卷
|
8卷引用:河南省鹤壁市高中2022-2023学年高二下学期7月月考数学试题
解题方法
9 . 在平面四边形
中,
,
,点
为
的靠近
的三等分点,
,将
沿
折起,使得平面
平面
,已知点
在线段
上,且满足
,点
为
的中点.
平面
;
(2)若
为
的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab59d3710ddfb1388a43bb5731e1902a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d809626d493659af6f297326fa3f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c07b129ca17834b132540a253273006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268afbd3b3879074d8ee32f98ce9974c.png)
您最近一年使用:0次
名校
10 . 如图,在四棱锥
中,四边形
是菱形,
,
,
,点
是棱
的中点.
;
(2)求平面
与平面
所成角的余弦值.
![](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/32450995497b9e341be832e9efad3114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955e33abb9ac22ea8765272f1926f936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-10-13更新
|
846次组卷
|
8卷引用:河南省实验中学2023-2024学年高三上学期期中数学试题