1 . 如图,三角形
是边长为4的正三角形,
底面
,
,点
是
的中点,点
在
上,且
.
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497839104/STEM/ffe287c408e04d25895a9ac9b7693649.png)
(1)证明:平面
平面
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551e4cd76a93de89ea2750160fe74923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4014edd5ca7ddd954507ab87eb2638e5.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535a65c61f47d2b893706d4bc3499e20.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497839104/STEM/ffe287c408e04d25895a9ac9b7693649.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d85c98d07c0abe66dc7a529f0dcb14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
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2 . 如图,三角形△PDC所在的平面与长方形ABCD所在的平面垂直,PD=PC=4,AB=6,BC=3,点E是CD的中点,点F、G分别在线段AB、BC上,且AF=2FB,CG=2GB.
(1)证明:PE⊥FG;
(2)求二面角P﹣AD﹣C的正切值;
(3)求直线PA与直线FG所成角的余弦值.
您最近一年使用:0次
2016-12-03更新
|
4744次组卷
|
4卷引用:2015年全国普通高等学校招生统一考试理科数学(广东卷)
2015年全国普通高等学校招生统一考试理科数学(广东卷)四川省宜宾县第二中学校2017-2018学年高一下学期期末模拟数学试题(已下线)专题23 立体几何解答题(理科)-1专题30立体几何与空间向量解答题(第一部分)
12-13高二上·广东梅州·期末
3 . 如图正方体ABCD-
中,E、F、G分别是
、AB、BC的中点.
(1)证明:
⊥平面AEG;
(2)求
,![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/361ecb64299d4e038ee9985b012b7140.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/289a500d10474c9cb90e1f9405415070.png?resizew=62)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/dda4d0cee1974a3998bece70cd3586a1.png?resizew=29)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/0ff6e007c8664ee097974085ee16481e.png?resizew=32)
(2)求
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/1b65aa56036a434bb9100479b88dd19d.png?resizew=65)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/361ecb64299d4e038ee9985b012b7140.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/c44a38897617417690cee742c5d653c5.png?resizew=124)
您最近一年使用:0次
4 . 如图,在四棱锥
中,
平面
,底面
是菱形,
,
为
与
的交点,
为
上任意一点.
(1)证明:平面
平面
;
(2)若
平面
,并且二面角
的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86db010859f7a243badec02946a4e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36222db36e348661eb5f616820e4e60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccfd81d120348601cd611241d1a5dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af53bde2b93b4707c79d00010ac9ff06.png)
![](https://img.xkw.com/dksih/QBM/2018/3/25/1909534314594304/1912476343926784/STEM/d7f94517aeb34b6b99a53db8b1b90065.png?resizew=164)
您最近一年使用:0次
2016-12-03更新
|
17次组卷
|
4卷引用:2015届广东省汕头市潮南区高三高考模拟二理科数学试卷
5 . 已知梯形
所在平面垂直于平面
于
,
∥
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572977096335360/1572977102618624/STEM/9526aab3260a4afca442a492004ee0b1.png)
(1)求证:
;
(2)求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2bfa3d38d79fec4ad193aded145d364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba598b9c579ca748a0232727e19d8182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9eadc2feca23f49e36ade66f66512e1.png)
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572977096335360/1572977102618624/STEM/9526aab3260a4afca442a492004ee0b1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98db3820190babd3569a7e724bb0bc7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
您最近一年使用:0次
11-12高二上·广东·期中
名校
解题方法
6 . 如图,在三棱锥P﹣ABC中,E,F分别为AC,BC的中点.
(1)求证:EF∥平面PAB;
(2)若平面PAC⊥平面ABC,且PA=PC,∠ABC=90°,求证:平面PEF⊥平面PBC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/00199af2-9023-45c7-afc6-8b6f3d2bf55e.png?resizew=158)
(1)求证:EF∥平面PAB;
(2)若平面PAC⊥平面ABC,且PA=PC,∠ABC=90°,求证:平面PEF⊥平面PBC.
您最近一年使用:0次
2016-12-04更新
|
599次组卷
|
9卷引用:2011-2012学年度广东省东山中学高二第一学期期中理科数学试卷
(已下线)2011-2012学年度广东省东山中学高二第一学期期中理科数学试卷(已下线)2011-2012学年福建省福安一中高一下学期第一次月考数学试卷(已下线)2011-2012学年江西省会昌中学高一下学期第二次月考文科数学试卷2015-2016学年湖南省邵阳市邵东县高一上学期期末数学试卷(已下线)2018年11月25日 《每日一题》人教必修2-每周一测浙江省嘉兴市南湖区第一中学2019-2020学年高二上学期期中数学试题山东省泰安市2020-2021学年高一下学期期末数学试题山东省东营市广饶县第一中学三校区2022-2023学年高二9月月考数学试题山东省临沂市蒙阴县第一中学2022-2023学年高一下学期第二次月考数学试题
7 . 如图所示,四边形ABCD是菱形,O是AC与BD的交点,SA⊥平面ABCD
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526348410880/1572526353981440/STEM/93f3aaa998b54c09979319075893db33.png)
(Ⅰ)求证:平面SAC⊥平面SBD;
(Ⅱ)若∠DAB=120°,DS⊥BS,AB=2,求SO的长及点A到平面SBD的距离.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526348410880/1572526353981440/STEM/93f3aaa998b54c09979319075893db33.png)
(Ⅰ)求证:平面SAC⊥平面SBD;
(Ⅱ)若∠DAB=120°,DS⊥BS,AB=2,求SO的长及点A到平面SBD的距离.
您最近一年使用:0次
8 . 如图,在四棱锥
中,底面
是平行四边形,
,
.
平面
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/53538468f5d14d4cbbc6931298ddb7fa.png)
(1)求证:
平面
;
(2)求证:
.
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/04d2743b90bd4921950ca7a78032e3fc.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/2ca574a4391c4f0c858ac26d32435156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96063ea9fc9a250257cf3cd20a55cf89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/6bcf2f7d1a1d4e5c9de993cbd010fcc6.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/2ca574a4391c4f0c858ac26d32435156.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/2cbaadeabca444a29061c2c4ad75cdca.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/c6251dfa389f4ed180df7583e6462a0d.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/53538468f5d14d4cbbc6931298ddb7fa.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/8ba496e5e36d428d971bb8ff5affa940.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/b89625c897b64a8aa46cfa29460c33a0.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772499456/STEM/997a1e0136ce402fb2b02ccc4c8753d5.png)
您最近一年使用:0次
9 . 在如图的多面体中,EF⊥平面AEB,AE⊥EB,AD∥EF,EF∥BC,BC=2AD=4,EF=3,AE=BE=2,G是BC的中点.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287331328/STEM/a677a6ec39c6487db4f439213e599586.png)
(Ⅰ)求证:AB∥平面DEG;
(Ⅱ)求证:BD⊥EG.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287331328/STEM/a677a6ec39c6487db4f439213e599586.png)
(Ⅰ)求证:AB∥平面DEG;
(Ⅱ)求证:BD⊥EG.
您最近一年使用:0次
10 . 如图,已知
,
分别是正方形
边
、
的中点,
与
交于点
,
、
都垂直于平面
,且
,
,
是线段
上一动点.
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541628928/STEM/10ee63f2d5a241b5a5c86931a8515522.png)
(Ⅰ)求证:平面
平面
;
(Ⅱ)若
平面
,试求
的值;
(Ⅲ)当
是
中点时,求二面角
的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dafebaaf13781120dc57c277d0267c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a4950a6e4202efd609507964af238b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18091448701460b53e076331e7c575cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541628928/STEM/10ee63f2d5a241b5a5c86931a8515522.png)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba9008f244e609ad267e10b8861c8254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94cc30d46b4538a4c86064df7460356.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4cba9d2412e4a28f8740bddd5738d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad337a2ee42c1d43458859014c54b92.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa5cd4da0137515627593735100978e.png)
您最近一年使用:0次