2010·江苏扬州·模拟预测
名校
解题方法
1 . 如图,在正三棱柱
中,点
在边
上,
.
平面
;
(2)如果点
是
的中点,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1ebdf74ee45f3736307d4a7e64717f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)如果点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d850305485a6d3ee30fe313dc8bb736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
您最近一年使用:0次
2020-10-25更新
|
942次组卷
|
12卷引用:广西防城港市防城中学2021-2022学年高二上学期期中考试数学试题
广西防城港市防城中学2021-2022学年高二上学期期中考试数学试题(已下线)2010年江苏省扬州市高三第四次模拟考试数学试题(已下线)2013-2014学年江苏连云港新海高级中学高一下学期期中考试数学试卷2016届江苏省清江中学高三考前一周双练冲刺四数学试卷【市级联考】河北省遵化市2018-2019学年高二上学期期中考试数学试题江苏省常州市高级中学2019-2020学年高三上学期期中数学(理)试题四川省成都七中2020-2021学年度高二上期10月阶段性考试理科数学试题四川省成都七中2020-2021学年度高二上学期10月阶段性考试文科数学试题湖北省恩施州巴东县第二高级中学2020-2021学年高二上学期期中数学试题(已下线)第十三章本章回顾苏教版(2019)必修第二册课本习题第13章复习题甘肃省2023年普通高中学业水平合格性考试数学模拟测试题
名校
解题方法
2 . 已知三棱柱
中,
平面
,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/319e0656-3c3b-4028-a144-22dabe13ee9d.png?resizew=162)
(1)证明:直线
平面
;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d11a5a756d8fdd7b294c4f5fd63467b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d3d5c6d668afddb0603556c9133996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/319e0656-3c3b-4028-a144-22dabe13ee9d.png?resizew=162)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504a36c231b8e80724d01649e7c0944f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
您最近一年使用:0次
2020-12-02更新
|
938次组卷
|
3卷引用:广西北海市2022-2023学年高二下学期期中数学试题
3 . 如图,在四棱锥
中,侧面
底面
,底面
为梯形![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b1a47b586cc69316a78902f1ac0728.png)
![](https://img.xkw.com/dksih/QBM/2020/1/12/2375417632333824/2375669895446528/STEM/0c1397b1-f1f6-4f33-9e92-276de01e495c.png)
(1)证明:
;
(2)若
为正三角形,求
点到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342170b9efb70024aa00bea5562cd83.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b1a47b586cc69316a78902f1ac0728.png)
![](https://img.xkw.com/dksih/QBM/2020/1/12/2375417632333824/2375669895446528/STEM/0c1397b1-f1f6-4f33-9e92-276de01e495c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fd5919817d72f4d912eaf11ac6b341.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2020-01-12更新
|
487次组卷
|
2卷引用:广西北流市实验中学2019-2020学年高二下学期期中考试数学(文)试题
4 . 如图,正方体
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
(1)求证:平面
;
(2)求直线与平面
所成角的正弦值.
您最近一年使用:0次
2018-12-15更新
|
522次组卷
|
2卷引用:【全国百强校】广西桂林市第十八中学2018-2019学年高二上学期期中考试数学(理)试题
名校
解题方法
5 . 正方形
与梯形
所在平面互相垂直,
,
,
,
,点
是
中点 .
![](https://img.xkw.com/dksih/QBM/2017/12/27/1847529124732928/1848252063375360/STEM/2fd9d9a9b5874cfdb2d05e2870614884.png?resizew=302)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://img.xkw.com/dksih/QBM/2017/12/27/1847529124732928/1848252063375360/STEM/2fd9d9a9b5874cfdb2d05e2870614884.png?resizew=302)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee48b4d6b9ee347b2ba6305f2fdc2bb0.png)
您最近一年使用:0次
2017-12-28更新
|
799次组卷
|
9卷引用:【校级联考】广西南宁市马山县金伦中学“4+ N”高中联合体2018-2019学年高二上学期期中考试数学(文)试题
【校级联考】广西南宁市马山县金伦中学“4+ N”高中联合体2018-2019学年高二上学期期中考试数学(文)试题2015届吉林省实验中学高三年级第二次模拟考试文科数学试卷山东省烟台市实验中学2018届高三上学期第三次诊断考试文科数学试题山东省济南外国语学校2018届高三1月月考数学(文)试题【全国百强校】安徽亳州市涡阳一中2018届高三最后一卷数学(文)试题西藏拉萨那曲第二高级中学2021届高三上学期第二次月考数学(文)试题西藏拉萨那曲第二高级中学2021届高三上学期第二次月考数学(理)试题甘肃省兰州市永登县第一中学2020-2021学年高三上学期期末数学(文)试题陕西省咸阳市高新一中2022-2023学年高三上学期第五次质量检测文科数学试题
6 . 如图,三棱柱
中,侧棱
平面
,
为等腰直角三角形,
,且
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/4c9b05b5-0302-4a65-b969-2e0cd3dd4b8d.png?resizew=188)
(1)求证:平面
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1857eadd6b23a87a1a5b4ffff584efd9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/4c9b05b5-0302-4a65-b969-2e0cd3dd4b8d.png?resizew=188)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fe9ec64aa4325c904184db96bbeb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2017-03-27更新
|
1900次组卷
|
2卷引用:广西南宁市第三中学2017-2018学年高二下学期期中考试数学(文)试题2
9-10高一下·新疆·阶段练习
名校
解题方法
7 . 如图,在正方体
中,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/9e38500f-1160-443c-80bd-94f053e5e2e3.png?resizew=177)
(1)求证:
平面
;
(2)求证:平面
平面
.
![](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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/9e38500f-1160-443c-80bd-94f053e5e2e3.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554923047631d16320c2ba39abeee99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d40fad0bf738887305d76fb6c23a22c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2016-11-30更新
|
1006次组卷
|
7卷引用:广西北流市实验中学2019-2020学年高一下学期期中考试数学试题
8 . 如图所示,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
平面
,且四边形
为矩形,四边形
为直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/12/24/1572391461404672/1572391465197568/STEM/a3082ae30bef4583a91f9a51b173f550.png)
(1)求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd63d5d1920dd2bae0e18386af8dd95.png)
平面
;
(2)求平面
与平面
所成锐二面角的余弦值;
(3)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/4237f6a1fc115bb790aa10704b7908c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac192cfba38bf0e2df0c2d490596aa65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00af8dfddaae7145aaefdb9af8f9721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f556bd2f45143b3ef33f411ecefe7555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c543f560d8a91d5d60c96feebff9ae50.png)
![](https://img.xkw.com/dksih/QBM/2015/12/24/1572391461404672/1572391465197568/STEM/a3082ae30bef4583a91f9a51b173f550.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd63d5d1920dd2bae0e18386af8dd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2011·江苏宿迁·二模
解题方法
9 . 如图,在棱长为2的正方体
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2011/3/17/1570046058397696/1570046063738880/STEM/442e0326-c9ce-49d7-bef7-2ca31929c477.png?resizew=180)
(1)求证:
平面
;
(2)求证:
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b866a756d422faec0f7eb229dfaabf.png)
![](https://img.xkw.com/dksih/QBM/2011/3/17/1570046058397696/1570046063738880/STEM/442e0326-c9ce-49d7-bef7-2ca31929c477.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d48dafb6b017b5739106c1b88be7ee.png)
您最近一年使用:0次
2016-11-30更新
|
978次组卷
|
6卷引用:2010-2011年广西桂林中学高二下学期期中考试数学
(已下线)2010-2011年广西桂林中学高二下学期期中考试数学(已下线)2011届江苏省宿豫中学高三第二次模拟考试数学试卷(已下线)2012届安徽省泗县双语中学高三摸底考试文科数学2015-2016学年贵州省凯里一中高二上滾动训练1数学试卷2015-2016学年河北省石家庄一中高二下期中文科数学试卷辽宁省实验中学、大连八中、大连二十四中、鞍山一中、东北育才学校2018届高三上学期期末考试数学(文)试题