2011·黑龙江·一模
名校
1 . 已知三棱柱
,底面三角形
为正三角形,侧棱
底面
,
,
为
的中点,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/692acc42-566f-429c-8e34-bcf10e932166.png?resizew=129)
(1)求证:直线
平面
;
(2)求平面
和平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/aed5e5d514bba98dbd038d0857a34ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/692acc42-566f-429c-8e34-bcf10e932166.png?resizew=129)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2016-12-04更新
|
669次组卷
|
6卷引用:2011届黑龙江省哈三中高三第一次模拟考试数学理卷
2 . 已知四棱锥P-ABCD的三视图如下图所示,E是侧棱PC上的动点.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572957322633216/1572957328752640/STEM/e88ce08aa26048b1979f0fbf6f8af970.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572957322633216/1572957328752640/STEM/2b50450df6ae4efda1da893d91d9db02.png)
(1)求证:BD⊥AE
(2)若点E为PC的中点,求二面角D-AE-B的大小.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572957322633216/1572957328752640/STEM/e88ce08aa26048b1979f0fbf6f8af970.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572957322633216/1572957328752640/STEM/2b50450df6ae4efda1da893d91d9db02.png)
(1)求证:BD⊥AE
(2)若点E为PC的中点,求二面角D-AE-B的大小.
您最近一年使用:0次
2016-12-04更新
|
1573次组卷
|
7卷引用:黑龙江省大庆实验中学2020届高三综合训练(四)数学(理)试题
解题方法
3 . 如图,三棱柱
侧棱垂直于底面,
,
,
为
的中点.
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd108abaf2b7fc1d0239b28afcf4ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e5dc81fbafbe58bff0842f7776d80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46f9f7d220d3b871911a376104f0d6e.png)
您最近一年使用:0次
2011·北京朝阳·一模
名校
4 . 如图,在四棱锥
中,底面
为直角梯形,且
,
,侧面
底面
. 若
.
(1)求证:
平面
;
(2)侧棱
上是否存在点
,使得
平面
?若存在,指出点
的位置并证明,若不存在,请说明理由;
(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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efa6508d6820f972de28c360aea7504.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/460516ee9c61f1bdd231759be0033e80.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e867e5c7ef4da37d8985ce82022060e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/2e2a8b06-0a67-4422-b704-0ce085dc1db7.png?resizew=200)
您最近一年使用:0次
2016-12-02更新
|
850次组卷
|
8卷引用:2013-2014学年黑龙江省哈尔滨四中高二下学期期末考试理科数学试卷
(已下线)2013-2014学年黑龙江省哈尔滨四中高二下学期期末考试理科数学试卷(已下线)2011届北京市朝阳区高三第一次综合练习数学理卷(已下线)2012-2013学年广东省广州六中高二上学期期末考试理科数学试卷(已下线)2013届中国人民大学附属中学高考冲刺二理科数学试卷北京市人大附中2018届高三高考数学(理科)零模试题湖南省衡阳市第一中学2020-2021学年高三上学期第五次月考数学试题(已下线)江苏省苏州市吴江区2019-2020学年高二下学期期中联考数学试题天津市蓟州区第一中学2021届高三下学期模拟检测二数学试题
11-12高二上·黑龙江牡丹江·期中
名校
解题方法
5 . 如图,在直四棱柱
中,底面ABCD为等腰梯形,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e7ce6718d15919e328ec3cd046bfcb.png)
分别是棱
的中点
(1)证明:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a667900b37d61c8e5b86d2dca625283.png)
平面
;
(2)求:二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cf99a0d5833beacc3a0ee39d39458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e7ce6718d15919e328ec3cd046bfcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b8b4aa1f3d0867b7d63e2cec4299c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1132f0aa9e5409535b20094e041c4a.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a667900b37d61c8e5b86d2dca625283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a456b9e47c1dc1ca65494bf60518994b.png)
(2)求:二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/730631d92dd95dfd52b5e7184e8974c0.png)
![](https://img.xkw.com/dksih/QBM/2011/12/29/1570669040443392/1570669045948416/STEM/750d0e13-527b-4222-987a-73b9dabfe3a0.png?resizew=161)
您最近一年使用:0次
6 . 如图,正方体
中,
分别为
与
的中点.
![](https://img.xkw.com/dksih/QBM/2011/12/5/1570556496969728/1570556501909504/STEM/dd12af7389f34b9bba362c62fcacb1d1.png?resizew=152)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2011/12/5/1570556496969728/1570556501909504/STEM/dd12af7389f34b9bba362c62fcacb1d1.png?resizew=152)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1167959ebbc724159e6181759b58658b.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd0a3b418f3b1ae176d2e9c5b4987de.png)
您最近一年使用:0次
7 . .在三棱锥
中,
,且
,如图 .
![](https://img.xkw.com/dksih/QBM/2011/7/28/1570276489248768/1570276494794752/STEM/705ba31d726f412f9b99ff00daca3dfa.png?resizew=185)
(1)求侧面
与底面
所成二面角的大小.
(2)求三棱锥的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc755e20d7e1d4efacf2a73d704ac24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf971e5e66e66d1e8841e200933578a8.png)
![](https://img.xkw.com/dksih/QBM/2011/7/28/1570276489248768/1570276494794752/STEM/705ba31d726f412f9b99ff00daca3dfa.png?resizew=185)
(1)求侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求三棱锥的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a52d7952cee9eabaefe13cad9220fe7.png)
您最近一年使用:0次
8 . 在直四棱柱
中,已知底面四边形
是边长为3的菱形,且
,
,点E在线段
上,点F在线段
上,且
.
(1)求证:直线
平面
;
(2)求二面角
的余弦值.
![](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/262e062dcdd2039084a356862b123e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962ddfa6a45e5588279c2a93f142924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e905e7cf3fb2152a68c89dcdf19567b6.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16835e3f230ba3f543b6804e445e283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f03875520d0d13da79567aab63ce273.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92261f1a78bb370fdea3f919494d0444.png)
![](https://img.xkw.com/dksih/QBM/2011/5/16/1570199914635264/1570199919886336/STEM/c2d8f7b011f54d0ba9e257e7173413c5.png?resizew=194)
您最近一年使用:0次
9 . 在四棱锥
,
平面
,
,
,
,
.
(1)求证:平面
平面
;
(2)当点
到平面
的距离为
时,求二面角
的余弦值;
(3)当
为何值时,点
在平面
内的射影
恰好是
的重心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99293d0e9aadc20e62a74acf864f042a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a719cb3370fe6ddc7d2437dfaa9b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513f52a3eb125158c4294aeff05fcb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa9a88f1e317011b44e845003aeb281.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9557b784a82680a8c2d300060e9a2b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d39f37441ee55dbc8f1a6ca199a66b.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7609a1407f1e965fc9f1235552dcf9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b48694e35e9de0ece4ff9d5bfd6c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8282f7fe4c82900a207e7267bf43b300.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3142b1af4ce67d3e55417b4c0de257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5233ab4347d3783c9416476c8aba9039.png)
![](https://img.xkw.com/dksih/QBM/2011/4/14/1570118536364032/1570118541893632/STEM/0cdb2aca26c64cbb89fec4a860b88e33.png?resizew=185)
您最近一年使用:0次