名校
解题方法
1 . 如图,在四棱锥
中,
底面
,底面
是正方形,且
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2020/4/12/2439992711577600/2440183013744640/STEM/db282ee53d094c32b3c7a26237510bd5.png?resizew=189)
求证:直线
平面
;
求直线
与平面
的夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.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/45cafe187bef7a5aa6792e649933fffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://img.xkw.com/dksih/QBM/2020/4/12/2439992711577600/2440183013744640/STEM/db282ee53d094c32b3c7a26237510bd5.png?resizew=189)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e04a28a7f47d499eaf7451d5a6c3872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
您最近一年使用:0次
2020-04-13更新
|
588次组卷
|
7卷引用:北京市八一中学2018~2019学年高二3月月考数学试题
2 . 如图所示,菱形ABCD与正三角形BCE的边长均为2,它们所在的平面互相垂直,DF⊥平面ABCD且DF
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/358649d8-3298-4a34-b04c-76f21be33b7c.png?resizew=124)
(1)求证:EF//平面ABCD;
(2)若∠ABC=∠BCE,求二面角A﹣BF﹣E的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e589def3e7fe21b601bc6d5144073202.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/358649d8-3298-4a34-b04c-76f21be33b7c.png?resizew=124)
(1)求证:EF//平面ABCD;
(2)若∠ABC=∠BCE,求二面角A﹣BF﹣E的余弦值.
您最近一年使用:0次
2020-03-26更新
|
713次组卷
|
5卷引用:北京市首都师范大学附属中学2020-2021学年高二上学期第一次月考数学试题
名校
解题方法
3 . 如图所示,在四棱锥
中,底面四边形
为正方形,已知
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/12b2f808-0347-417c-ab08-4b11783c2eaf.png?resizew=133)
(1)证明:
;
(2)求
与平面
所成角的正弦值;
(3)在棱
上是否存在一点
,使得平面
平面
?若存在,求
的值并证明,若不存在,说明理由.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/12b2f808-0347-417c-ab08-4b11783c2eaf.png?resizew=133)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c54d01623f09f23103f03ba1135fc6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add47889f6b4911133999a898d3666d3.png)
您最近一年使用:0次
2020-02-15更新
|
834次组卷
|
2卷引用:2020届北京市西城区师范大学附属实验中学高三摸底数学试题
名校
解题方法
4 . 如图,在四棱锥
中,
平面
,四边形
为矩形,
是
的中点,
是
的中点,点
在线段
上且
.
![](https://img.xkw.com/dksih/QBM/2020/3/12/2417993854902272/2418841944547328/STEM/8182ea4baf2843028055858b3a19c23f.png?resizew=324)
(1)证明
平面
;
(2)当
为多大时,在线段
上存在点
使得
平面
且
与平面
所成角为
同时成立?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf4832894665baedfda42021f5430a4.png)
![](https://img.xkw.com/dksih/QBM/2020/3/12/2417993854902272/2418841944547328/STEM/8182ea4baf2843028055858b3a19c23f.png?resizew=324)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d46cbffebff091d8435b4f17c8710d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bebb16c0ffc99a945619ae0986cadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
您最近一年使用:0次
5 . 在四棱锥P—ABCD中,
PAB为正三角形,四边形ABCD为矩形,平面PAB⊥平面ABCD.AB=2AD,M,N分别为PB,PC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/3d75fdae-a202-4bb4-adaa-8bfdce7e24e0.png?resizew=172)
(1)求证:MN//平面PAD;
(2)求二面角B—AM—C的大小;
(3)在BC上是否存在点E,使得EN⊥平面AMV?若存在,求
的值:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d808f07f15c42f4be119b7ed4c0c35c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/3d75fdae-a202-4bb4-adaa-8bfdce7e24e0.png?resizew=172)
(1)求证:MN//平面PAD;
(2)求二面角B—AM—C的大小;
(3)在BC上是否存在点E,使得EN⊥平面AMV?若存在,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc1b6c333a4d80c2bfac4eb8d00dd0a.png)
您最近一年使用:0次
6 . 如图,三棱柱
中,侧面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
底面
,
,且
,O为
中点.
(Ⅰ)证明:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4237f6a1fc115bb790aa10704b7908c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31510125b0db45b7edef1ef444d71bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af254745c1c19bd20e83344bee674ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855303b220da1fb141252b61189a0a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
![](https://img.xkw.com/dksih/QBM/2012/5/22/1570863067906048/1570863073509376/STEM/5c54ab7768cc4b08a100b480be503402.png)
您最近一年使用:0次
2018-09-09更新
|
1278次组卷
|
6卷引用:2012届北京市第六十六中学高三上学期补考数学试卷
名校
7 . 如图,由直三棱柱
和四棱锥
构成的几何体中,
,平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(I)求证:
;
(II)若M为
中点,求证:
平面
;
(III)在线段BC上(含端点)是否存在点P,使直线DP与平面
所成的角为
?若存在,求
得值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b3e8bee41beb61f3c4afdc554cb455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba90c0290ae59b9e4f150a48eed8de4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98cf9cb5b6b6de8dd40dce5628d77a1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(I)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a773326771e4d98979061f9949ee0af0.png)
(II)若M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1477ae90a240deba97f8dadf4d7c41aa.png)
(III)在线段BC上(含端点)是否存在点P,使直线DP与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1477ae90a240deba97f8dadf4d7c41aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fb46419d4c5868342f6615adcd36d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/5/f028d440-a7d1-4f85-8e59-f48b2e94ba81.png?resizew=148)
您最近一年使用:0次
2018-05-19更新
|
3598次组卷
|
12卷引用:2017届北京市海淀区高三下学期期中考试数学理试卷
2017届北京市海淀区高三下学期期中考试数学理试卷北京市第五十七中学2021-2022学年高二10月月考数学试题北京第五十七中学2020-2021学年高二上学期期末试题北京市东城区第一七一中学2024届高三上学期12月月考数学试题河北省衡水中学2016-2017学年高一下学期期末考试数学(理)试题【全国市级联考】天津市河北区2018年高三二模数学(理)试题湖南省怀化市2018-2019学年高三下学期期末博览联考数学(理)试题山西省山西大学附属中学2018-2019学年高二上学期期中数学(理)试题(已下线)理科数学-2020年高考押题预测卷01(新课标Ⅰ卷)《2020年高考押题预测卷》2020届天津市第一百中学高考模拟数学试题江苏省苏州市新草桥中学2020-2021学年高三上学期10月月考数学试题湖北省武汉市蔡甸区汉阳一中2020-2021学年高二上学期9月月考数学试题
解题方法
8 . 如图,正三棱柱ABC-A1B1C1的底面边长是2,侧棱长是
,D是AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/950424d0-602f-4ae3-9e14-853fd47a0d8c.png?resizew=287)
(1).求证:B1C∥平面A1BD;
(2).求二面角A1-BD-A平面角的大小;
(3).在线段AA1上是否存在一点E,使得平面B1C1E⊥平面A1BD,若存在,求出AE的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/950424d0-602f-4ae3-9e14-853fd47a0d8c.png?resizew=287)
(1).求证:B1C∥平面A1BD;
(2).求二面角A1-BD-A平面角的大小;
(3).在线段AA1上是否存在一点E,使得平面B1C1E⊥平面A1BD,若存在,求出AE的长;若不存在,说明理由.
您最近一年使用:0次
名校
9 . 如图,平面
平面
,四边形
和
是全等的等腰梯形,其中
,且
,点
为
的中点,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/83e26f2d-55bf-430d-ba81-1afe0ee799a7.png?resizew=220)
(1)请在图中所给的点中找出两个点,使得这两个点所在直线与平面
垂直,并给出证明 ;
(2)求二面角
的余弦值;
(3)在线段
上是否存在点
,使得
?如果存在,求出
的长度,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d53aeabf77688e80280d23d766b4c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8be22425679fbdc28350119f68c274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba6f4177822927b5875b92cd5f2038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8be22425679fbdc28350119f68c274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab51fc49d74110a334e2bd6b6148797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ee278ec8164c0ca89b79d707a72732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/83e26f2d-55bf-430d-ba81-1afe0ee799a7.png?resizew=220)
(1)请在图中所给的点中找出两个点,使得这两个点所在直线与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb093f3dfd9b79be8fd6be9f202e27dd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1105dc7a3bae6e74641fa653cfae0aa8.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7e9d0055901f6a4b2e22503e314072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
您最近一年使用:0次
2018-01-20更新
|
707次组卷
|
2卷引用:北京市海淀区2017-2018学年高二上学期期末考试理科数学试题2