1 . 已知在三棱锥
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/078c5af6-d62c-43a2-bccf-bf5a7015ca9c.png?resizew=138)
(1)求证:
;
(2)若
,
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1af71094b0522a0df6c7fae1580e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dbe55407b556be48d67cde5c5dc94f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/078c5af6-d62c-43a2-bccf-bf5a7015ca9c.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96127e45e2dd2494fccb1c0905951f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f0f9487303d04e6914b29ae805a0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4bddf1ea3c5d37f2233a4821909e9.png)
您最近一年使用:0次
2 . 如左图,平面五边形
中,
,
,将△
沿
折起,得到如右图的四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/d7db16bd-f00e-4e5e-820d-ccb641492a13.png?resizew=358)
(1)证明:
;
(2)若平面
平面
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7b0d00cbe53f9bbdb464a1c8c5e59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e413f89893a9b2e24d2a9d1c00e00f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/d7db16bd-f00e-4e5e-820d-ccb641492a13.png?resizew=358)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebfe6fda511e39f72ba2519f4da31c9.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c4cc37d6ba218107c9c5d820740fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
真题
名校
3 . 如图2,四边形
为矩形,
平面
,
,
,作如图3折叠,折痕
.其中点
、
分别在线段
、
上,沿
折叠后点
在线段
上的点记为
,并且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/2f16de95-a474-4b1a-800f-7d9265067e48.png?resizew=364)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b5a0816e54cef8e861e3a5dcb801b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06772d7ccc921f77319c503c23326be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab7f21bfaf137ca321483d7403ddde7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/2f16de95-a474-4b1a-800f-7d9265067e48.png?resizew=364)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1eba64530b30116eda7fe30bc081f9.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5452197f58d5f1b8e377d0f79069fbc.png)
您最近一年使用:0次
2019-01-30更新
|
2339次组卷
|
9卷引用:2014年全国普通高等学校招生统一考试文科数学(广东卷)
2014年全国普通高等学校招生统一考试文科数学(广东卷)广东省佛山市顺德区第一中学2019-2020学年高二上学期期中数学试题四川省成都市龙泉第二中学2017届高三5月高考模拟考试(一)数学(理)试题(已下线)专题22 空间几何体及其表面积与体积-十年(2011-2020)高考真题数学分项四川省新津中学2020-2021学年高三9月月考数学(文)试题甘肃省兰州大学附属中学2021-2022学年高三上学期第五次月考数学(文科)试题江西省临川一中暨临川一博中学2021-2022学年高二下学期第二次月考数学(文)试题陕西省咸阳市秦都区2021-2022学年高一上学期期末数学试题(已下线)专题23 立体几何解答题(文科)-2
12-13高三·广东·阶段练习
4 . 如图,在底面为平行四边形的四棱柱
中,![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/459499c9977d42909410f364a4eb72a8.png)
底面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/9107e00a58c44b05a907ab5879f418ad.png)
(Ⅰ)求证:平面
平面
;
(Ⅱ)若
,求四棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/59f15fec45f24b359a0221da7b20c67a.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/459499c9977d42909410f364a4eb72a8.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/a18bbc3b47244a25a2c03e0d6e665926.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/5c07416e66e741779181e3f5c9a8372b.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/e249dd563ef34fb581b4af5dd52c70fe.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/fc4cb58e7a4b44b4838a9fcda45d4ea0.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/9903e9b85f164b278df2bc1f13938266.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/9107e00a58c44b05a907ab5879f418ad.png)
(Ⅰ)求证:平面
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/93c6159590a04549860e97c952dcc4e9.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/2c943e5126834979a4822db0248c06e6.png)
(Ⅱ)若
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/e5d57afadc30465d809a894a70ae2908.png)
![](https://img.xkw.com/dksih/QBM/2013/12/31/1571450665197568/1571450670792704/STEM/643f107316ab4752a0dd75f1458899a5.png)
您最近一年使用:0次
5 . 如图,四棱锥
中,
平面
,
为等腰直角三角形,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/a91adba8-1e4a-486d-ad20-8ccf513d2e5c.png?resizew=222)
(1)求证:
;
(2)若
,求四棱锥
的体积.
![](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/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2694c32ca1e120e988012b7ecd74f625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b5d2943803894bc5d204e75e2d172b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633bf2de732ae51fc06ef3d559915da0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/a91adba8-1e4a-486d-ad20-8ccf513d2e5c.png?resizew=222)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0910601e7d760188d10beee6a48f2ac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746f70c9993f04a5037c53daf3d1af00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
6 . 如图所示,已知ABCD是直角梯形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6b28c949-b57a-4359-925b-e65c7bdce20b.png?resizew=174)
(1)证明:
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15fba58c1ecfb2e650da339b7f30d99a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6b28c949-b57a-4359-925b-e65c7bdce20b.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c231fb9aeaf4b73c2d835bb4c3d42b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b183492677d0457b8701c53d9fa1414.png)
您最近一年使用:0次
2019-06-05更新
|
435次组卷
|
3卷引用:广东省揭阳市产业园2019-2020学年高一上学期期末数学试题
7 . 如图甲,⊙
的直径
,圆上两点
在直径
的两侧,使
,
.沿直径
折起,使两个半圆所在的平面互相垂直(如图乙),
为
的中点,
为
的中点.
为
上的动点,根据图乙解答下列各题:
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178130649088/1572178136727552/STEM/a10e8e1796914503b4a7bbc2a37982c3.png)
(1)求点
到平面
的距离;
(2)求证:不论点
在何位置,都有
⊥
;
(3)在
弧上是否存在一点
,使得
∥平面
?若存在,试确定点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bddb90e3606387c047807ee4cec379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefb8568cff65e8ae19e27a2b769017f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178130649088/1572178136727552/STEM/a10e8e1796914503b4a7bbc2a37982c3.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:不论点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
8 . 如图,三角形
所在的平面与长方形
所在的平面垂直,
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572138642317312/1572138647937024/STEM/ab59150e-3610-402e-b4be-805aa116adda.png?resizew=171)
(1)证明:
平面
;
(2)证明:
;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae363146bb57d55b1fe84f08115dba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4a1dc86ec008a976874c72f84c45c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5142708254cf9157e1d1d568c63b0c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1afbbcd87f63f6b2c050e265fd992a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d797446c13984c47ae58a297419575.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572138642317312/1572138647937024/STEM/ab59150e-3610-402e-b4be-805aa116adda.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e7c3e31d02f3c4b84ee8a3abdc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855a7a1241c673bb8ffa9d66c0f22d0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e39a9d86d76caff7ba7111208eae5e.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855a7a1241c673bb8ffa9d66c0f22d0.png)
您最近一年使用:0次
2019-01-30更新
|
2658次组卷
|
8卷引用:2015年全国普通高等学校招生统一考试文科数学(广东卷)
2015年全国普通高等学校招生统一考试文科数学(广东卷)【全国百强校】北京市人大附中2018届高三5月考前热身练习(三模)数学文科试题北京市人大附中2018届高三下学期三模考试数学(文科)试题(已下线)第01章 章末检测-2018-2019版数学创新设计课堂讲义同步系列(苏教版必修2)四川省峨眉第二中学校2021-2022学年高二下学期5月月考文科数学试题(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)(已下线)专题23 立体几何解答题(文科)-3专题32立体几何与空间向量解答题(第二部分)
9 . 如图所示,平面多边形
中,AE=ED,AB=BD,且
,现沿直线
,将
折起,得到四棱锥
.
![](https://img.xkw.com/dksih/QBM/2018/2/28/1891898824294400/1910512682786816/STEM/62a6b5431f2b44f39341d9d5836f0f9e.png?resizew=294)
(1)求证:
;
(2)若
,求PD与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6723f8b9d907981aa735cd96386bee36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b52d49aadd2f44212e855e72ae59f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae119c3aebd074e7d172542378dbe78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://img.xkw.com/dksih/QBM/2018/2/28/1891898824294400/1910512682786816/STEM/62a6b5431f2b44f39341d9d5836f0f9e.png?resizew=294)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edc1be5141e54264eb9ade93bb8bb33.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d47209676e3c9a779eb4ba1527e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da035673ef0edcfae6b72fb5e5ba34a.png)
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2018-03-26更新
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501次组卷
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2卷引用:广东省揭阳市2018届高三学业水平考试数学理试题
10 . 如图,在底面是正方形的四棱锥
面ABCD,BD交AC于点E,F是PC中点,G为AC上一点.
(1)求证:
;
(2)确定点G在线段AC上的位置,使FG//平面PBD,并说明理由;
(3)当二面角
的大小为
时,求PC与底面ABCD所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a1c291f44afb96922096b93cb9d24e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c799d3d37ed64c9c74c0d3d932cd3f3f.png)
(2)确定点G在线段AC上的位置,使FG//平面PBD,并说明理由;
(3)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://img.xkw.com/dksih/QBM/2018/3/9/1898492046327808/1906173459415040/STEM/5e7ee2759f67420e841fb496f11c09ef.png?resizew=215)
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2018-03-20更新
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907次组卷
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15卷引用:2013届广东省惠阳一中实验学校高三9月月考理科数学试卷
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