名校
解题方法
1 . 如图1,等腰
满足
,
,
于
.如图2,将
绕着直线SA旋转时,在BA旋转而成的平面
内总有点
满足
,
,(点
,点
分别在直线BD两侧).
长;
(2)求证:
平面
;
(3)记三棱锥
的体积为
,三棱锥
的体积为
,当四棱锥
的体积最大时,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79482c6de6bbd05affc78f9c625e52f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2affc8264f2e40743bb12dd7ea57177b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe85217cea14241255ec21200b25b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe0bb7d51e559e73aa16a954fe7fa33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79482c6de6bbd05affc78f9c625e52f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c279c8033acb94c3f91be2e05b0a6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)记三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d535bfd65eb04a29d64425d54b2acf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dd9f16a5c7a66e62e52fd66f4449ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c773ac7c3a6575fb7d432c93fe5f2a32.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在直三棱柱
中,
,
,M,N,P分别为
,AC,BC的中点.
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d954212889c8aae3cbb84de7cb362a.png)
您最近一年使用:0次
2024-03-23更新
|
2546次组卷
|
5卷引用:黑龙江省哈尔滨市第三十二中学校2023-2024学年高一下学期5月期中考试数学试题
黑龙江省哈尔滨市第三十二中学校2023-2024学年高一下学期5月期中考试数学试题陕西省西安市临潼区2024届高三第二次模拟检测数学(文科)试题(已下线)专题05 空间直线﹑平面的平行-《知识解读·题型专练》(人教A版2019必修第二册)海南省海口市琼山华侨中学2023-2024学年高一下学期期中考试数学试卷(已下线)第六章立体几何初步章末二十种常考题型归类(2)-【帮课堂】(北师大版2019必修第二册)
3 . 如图所示,
平面ABC,
平面ABC,
,
,
,F为BC的中点.
(1)求证:
平面BDE;
(2)求凸多面体ABCED的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5359ad5437bb4605bea0dc58da9b94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0761165f1176f3a5fe4f7b052832316d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/3/32ae021c-b747-4a26-8d18-363ea0c5fa31.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
(2)求凸多面体ABCED的体积.
您最近一年使用:0次
2023-10-13更新
|
348次组卷
|
2卷引用:黑龙江省哈尔滨市第九中学校2023-2024学年高三上学期10月月考数学试题
4 . 如图,在直三棱柱
中,
,
,D,E分别是棱
,AC的中点.
是否为棱柱并说明理由;
(2)求多面体
的体积;
(3)求证:平面
平面AB1D.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c330e73dbbf9e2c0f2fb755461e3c898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79500e7c4884160f9a5ff65e9ef3aae8.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79500e7c4884160f9a5ff65e9ef3aae8.png)
(3)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3174c9335b600eea4173815da15de049.png)
您最近一年使用:0次
2023-05-14更新
|
1794次组卷
|
11卷引用:黑龙江省哈尔滨市2022-2023学年高一下学期期末数学试题
黑龙江省哈尔滨市2022-2023学年高一下学期期末数学试题河南省新高中创新联盟TOP二十名校2022-2023学年高一下学期5月调研考试数学试题安徽省皖北县中联盟2022-2023学年高一下学期5月联考数学试题新疆石河子第一中学2022-2023学年高一下学期5月月考数学试题河北省沧州市盐山中学、海兴中学、南皮中学等2022-2023学年高一下学期6月月考数学试题四川省成都市树德中学光华校区2022-2023学年高一下学期数学测试(六)辽宁省大连市第八中学2022-2023学年高一下学期6月月考数学试题吉林省四平市实验中学2022-2023学年高一下学期期末数学试题江苏省无锡市江阴市两校联考2023-2024学年高一下学期4月期中考试数学试题江苏高一专题01立体几何广东省清远市南阳中学2023-2024学年高一下学期第二次月考(期中)数学试题
名校
解题方法
5 . 如图,三棱柱ABC﹣A1B1C1中,AA1⊥平面ABC,D、E分别为A1B1、AA1的中点,点F在棱AB上,且AF=
AB.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/25/5fdfa695-72de-44de-9f1a-f1b6dca36bb9.png?resizew=158)
(1)求证:EF∥平面BDC1;
(2)在棱AC上是否存在一个点G,使得平面EFG将三棱柱分割成的两部分体积之比为1:15,若存在,指出点G的位置;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/25/5fdfa695-72de-44de-9f1a-f1b6dca36bb9.png?resizew=158)
(1)求证:EF∥平面BDC1;
(2)在棱AC上是否存在一个点G,使得平面EFG将三棱柱分割成的两部分体积之比为1:15,若存在,指出点G的位置;若不存在,说明理由.
您最近一年使用:0次
2023-01-06更新
|
762次组卷
|
8卷引用:黑龙江省哈尔滨市第六中学校2022-2023学年高一下学期期中数学试题
黑龙江省哈尔滨市第六中学校2022-2023学年高一下学期期中数学试题2016届安徽省淮南市高三下学期二模文科数学试卷2016-2017学年湖北襄阳五中高二上学期开学考数学文试卷辽宁省沈阳市东北育才学校2014-2015学年高一上学期第二次段考数学试题(已下线)8.5 空间直线、平面的平行(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)立体几何专题:空间几何体体积的5种题型(已下线)专题08 空间直线与平面的平行问题(2) - 期中期末考点大串讲广东省广雅中学花都校区2022-2023学年高一下学期期中数学试题
解题方法
6 . 如图,在直四棱柱
中,底面
是平行四边形,
,
,M为
的中点.
(1)证明:
∥平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeb1554fc1cec56b983a08e9dc52c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571821f5f2d335a4293ef6eed97cbd12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/29/b181616b-160b-4943-b881-25621ebc7874.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041434f0c90fb3cdd685b8eb1c2b4b26.png)
您最近一年使用:0次
7 . 如图,PCBM是直角梯形,
,
,
,
,又
,
,
,且直线AM与直线PC所成的角为60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/7570a4f4-1491-4131-8a14-b1c240b1e7d3.png?resizew=244)
(1)求证:平面PAC⊥平面ABC;
(2)求异面直线PA与MB所成角的余弦值;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8432a44f6c6b37f4961dc63521fa7f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3624d307a5482ff913eb8d608d827077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dca0fddd44a2a325754baf9452fe90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/7570a4f4-1491-4131-8a14-b1c240b1e7d3.png?resizew=244)
(1)求证:平面PAC⊥平面ABC;
(2)求异面直线PA与MB所成角的余弦值;
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142ea3931dc45cfe66b66ef17d3cefcd.png)
您最近一年使用:0次
名校
解题方法
8 . 如图所示,正三棱柱
,
,
,
分别为
,
的中点.
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f41d364b55d88688cd1f571ed231228.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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/4a279866-b1fe-4150-b9f8-7012f17af1ed.png?resizew=136)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2ac20af67f3e0891be3102d70557ba.png)
您最近一年使用:0次
2023-06-08更新
|
887次组卷
|
2卷引用:黑龙江省哈尔滨市双城区兆麟中学2022-2023学年高一下学期期中数学试题
名校
解题方法
9 . 如图,四棱锥
中,底面ABCD为矩形,
平面ABCD,E为PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/6/8d6a07f3-6bad-4094-9111-6d1fccf1d182.png?resizew=196)
(1)证明:
//平面AEC
(2)设三棱锥
的体积是
,
,求平面DAE与AEC的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/6/8d6a07f3-6bad-4094-9111-6d1fccf1d182.png?resizew=196)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)设三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565e518d475a50358fedff2f0bb8dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ec13ca7115ccd73a9d793758f1c170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412048bf1422752f89049f5521095a8.png)
您最近一年使用:0次
2023-08-05更新
|
1483次组卷
|
5卷引用:黑龙江省哈尔滨市南岗区哈尔滨市第七十三中学校2023届高三上学期期中数学试题
名校
10 . 如图,等腰梯形
中,
,
,现以
为折痕把
折起,使点
到达点
的位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/21/76537170-8a47-4876-8412-4f51684ace9b.png?resizew=341)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
平面
;
(2)若
为
上一点,且三棱锥
的体积是三棱锥
体积的2倍,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442866160751e8ad0b35f7b4f8fd2f50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/21/76537170-8a47-4876-8412-4f51684ace9b.png?resizew=341)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](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/a40043464067061b41399b4ec0bb29c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bad875ab4b5b8c707d452db4cabaa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
您最近一年使用:0次
2022-12-18更新
|
791次组卷
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6卷引用:黑龙江哈尔滨工业大学附属中学校 2021-2022学年高二下学期期末理科数学试题
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