名校
解题方法
1 . 如图,
为矩形,
为梯形,平面
平面
,
,
,
.
(1)若M为
中点,求证:
平面
;
(2)求直线
与直线
所成角的大小;
(3)设平面
平面
,试判断l与平面
能否垂直?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5bf51c07144386bd23a422d9ceb140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6379891c7150af4188b5ab746d703bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d20fec32122b4a70b993976201c9ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7a201432af0a2f9d21c6803906f5c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/599366b6-410b-4aad-b455-1cc3281f16c7.png?resizew=161)
(1)若M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df21b7b7a47318ef2bb069450c39f1cd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c659d2ab07b9b66ed9a60cb604dd9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b951997af111a840cb333a082137402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解题方法
2 . 如图,直四棱柱
中,底面
是边长为
的正方形,点
在棱
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75040dea-6585-4344-9874-f463c59e6e88.png?resizew=180)
(1)求证:
;
(2)从条件①、条件②、条件③这三个条件中选择两个作为已知,使得
平面
,并给出证明.
条件①:
为
的中点;条件②:
平面
;条件③:
.
(3)在(2)的条件下,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5b6dfff10cb3dc3e06509db56d7b9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75040dea-6585-4344-9874-f463c59e6e88.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94a915aaf74001f8e3aba5168fae09e.png)
(2)从条件①、条件②、条件③这三个条件中选择两个作为已知,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94dea413b1f6c10afadc058c22d7e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565355ef0e4e11e714adce62efd9af5.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5b6dfff10cb3dc3e06509db56d7b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e9cc59aeac060a2450bf547efa69d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565355ef0e4e11e714adce62efd9af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a367a3355e56a76e4b0e8d9a30ada254.png)
(3)在(2)的条件下,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565355ef0e4e11e714adce62efd9af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c4e5059f9069e5434888dbf234c39e.png)
您最近一年使用:0次
2022-01-16更新
|
716次组卷
|
3卷引用:北京市朝阳区2021-2022学年高二上学期期末数学试题
名校
解题方法
3 . 如图,在三棱柱
中,侧面
是菱形,G是边
的中点.平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2020/10/20/2575283505111040/2578114044436480/STEM/bda0f61dc51048a48acc9ddc2cca33e9.png?resizew=215)
(1)求证:
;
(2)在线段
上是否存在点M,使得
平面
,若存在,请说明M点的具体位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2e00a3b5d4f1e10a52058f148060d.png)
![](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/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb64353c99068a7a1a8508a22f5b25b4.png)
![](https://img.xkw.com/dksih/QBM/2020/10/20/2575283505111040/2578114044436480/STEM/bda0f61dc51048a48acc9ddc2cca33e9.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a590a08b3823e01024de68e967cbf3f.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在三棱柱
中,
平面
,
,
在线段
上,
,
.
![](https://img.xkw.com/dksih/QBM/2018/2/7/1877300960157696/1878762482581504/STEM/79f5e4f79f464a11a1a4511872c511e9.png?resizew=170)
(1)求证:
;
(2)试探究:在
上是否存在点
,满足
平面
,若存在,请指出点
的位置,并给出证明;若不存在,说明理由.
![](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/615fc8790237a1b09af51d6bcad6b595.png)
![](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/3c1579e28325da0406c0e26e53145817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177f0adc6666014e717ef2381ea27fb7.png)
![](https://img.xkw.com/dksih/QBM/2018/2/7/1877300960157696/1878762482581504/STEM/79f5e4f79f464a11a1a4511872c511e9.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55171d348ce35d913d70b7fddacf168.png)
(2)试探究:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
2018-02-09更新
|
298次组卷
|
2卷引用:吉林省伊通满族自治县第三中学校等2017-2018学年高一上学期期末联考数学试题
名校
5 . 在四棱锥
中,
,
,
和
都是边长为2的等边三角形,设
在底面
的射影为
.
![](https://img.xkw.com/dksih/QBM/2017/3/6/1637836815663104/1637860221419520/STEM/9f3f9bef-f847-4992-9bc4-4e514e3a462c.png?resizew=184)
(1)求证:
是
中点;
(2)证明:
;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db08db31046bf98eb01abfbf356059ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c235aa3c3d273fdf205b1057eea7439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2017/3/6/1637836815663104/1637860221419520/STEM/9f3f9bef-f847-4992-9bc4-4e514e3a462c.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da48240e7fc3248f773ac1500c15ec14.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
2017-03-06更新
|
883次组卷
|
5卷引用:2017届广西柳州市、钦州市高三第一次模拟考试数学(理)试卷
6 . 一个长方体的平面展开图及该长方体的直观图的示意图如图所示.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
标记在长方体相应的顶点处(不需说明理由);
(2)在长方体中,判断直线
与平面
的位置关系,并证明你的结论;
(3)在长方体中,设
的中点为
,且
,
,求证:
平面
.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
(2)在长方体中,判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a8898c347a62c7de2bdca3f3c7e33.png)
(3)在长方体中,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c6c83ab4abc895ac36ab888a55be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53569e6ec795658b4fffcddeebe0f142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
您最近一年使用:0次
7 . 如图,梯形ABCD所在平面与以AB为直径的圆所在平面垂直,O为圆心,AB∥CD,∠BAD=90°,AB=2CD.若点P是⊙O上不同于A,B的任意一点.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572593359388672/1572593365196800/STEM/a4143852b681432a8bacea09c34e71f6.png)
(Ⅰ)求证:BP⊥平面APD;
(Ⅱ)设平面BPC与平面OPD的交线为直线l,判断直线BC与直线l的位置关系,并加以证明;
(Ⅲ)求几何体DOPA与几何体DCBPO的体积之比.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572593359388672/1572593365196800/STEM/a4143852b681432a8bacea09c34e71f6.png)
(Ⅰ)求证:BP⊥平面APD;
(Ⅱ)设平面BPC与平面OPD的交线为直线l,判断直线BC与直线l的位置关系,并加以证明;
(Ⅲ)求几何体DOPA与几何体DCBPO的体积之比.
您最近一年使用:0次
2016-12-04更新
|
406次组卷
|
2卷引用:2015-2016学年山东省济宁市高一上学期期末数学试卷
8 . 如图,AB是圆O的直径,点C是圆O上异于A,B的点,直线PC⊥平面ABC,E,F分别是PA, PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/c949747c-552f-453f-b427-89e51073a193.png?resizew=188)
(1)记平面BEF与平面ABC的交线为l,试判断直线l与平面PAC的位置关系,并加以证明.
(2)设(1)中的直线l与圆O的另一个交点为D,记直线DF与平面ABC所成的角为
,直线DF与直线BD所成的角为
,二面角
的大小为
,求证:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/c949747c-552f-453f-b427-89e51073a193.png?resizew=188)
(1)记平面BEF与平面ABC的交线为l,试判断直线l与平面PAC的位置关系,并加以证明.
(2)设(1)中的直线l与圆O的另一个交点为D,记直线DF与平面ABC所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d682fd0344452998187cb6d48de3dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd506c8ce8db557d4808388b780f9d6.png)
您最近一年使用:0次
名校
9 . 如图所示,在多面体
中,
是边长为2的等边三角形,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/2016/10/18/1573075820511232/1573075826180096/STEM/e95b2324e6d74ccf9fd5eada8aa33a89.png)
(1)若平面
平面
,证明:
;
(2)求证:
;
(3)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbd8413124e31d3eb17dfcc86d36d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb153f719cd276e88cbcabb46a2f8e9.png)
![](https://img.xkw.com/dksih/QBM/2016/10/18/1573075820511232/1573075826180096/STEM/e95b2324e6d74ccf9fd5eada8aa33a89.png)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8896be7a7f0b770c26c6ba510bec7f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d93e8f028872b039dc221d6aa118c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c8cf9c6833b585aa0310713817db40.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecf1ad8d9ce0afefc4fc0d454c01222.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a6c82b56df458f8173cbc931ab2f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31641780a982c3fcb5d9895dd6b72484.png)
您最近一年使用:0次
2016-12-04更新
|
340次组卷
|
2卷引用:2017届河南百校联盟高三9月质监乙卷数学(文)试卷
10 . 如图,已知正方形
和矩形
所在平面互相垂直,
,
,
是线段
的中点.用向量方法证明与解答:
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572430991204352/1572430997536768/STEM/d9a50fd20aa44e658af6b05c3c4041ad.png)
(1)求证:
∥平面
;
(2)试判断在线段
上是否存在一点
,使得直线
与
所成角为
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572430991204352/1572430997536768/STEM/d9a50fd20aa44e658af6b05c3c4041ad.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)试判断在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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