名校
1 . 如图,在三棱柱
中,平面
平面
.
分别为
的中点,证明:
平面
;
(2)当直线
与平面
所成角的正弦值为
时,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1581e407394e9a82188a0ddc67e81e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bab3b60f5d766fb43f542c8ca78101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
您最近一年使用:0次
2024-01-18更新
|
1625次组卷
|
7卷引用:2024年北京高考数学真题平行卷(提升)
(已下线)2024年北京高考数学真题平行卷(提升)广东省肇庆市2024届高三第二次教学质量检测数学试题(已下线)微考点5-1 新高考新试卷结构立体几何解答题中的斜体建坐标系问题(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 立体几何非常规建系问题 微点4 立体几何非常规建系问题综合训练【培优版】河北省部分示范性高中2024届高三下学期一模数学试题(已下线)数学(全国卷理科03)广东省江门市新会第一中学2024届高三下学期高考热身考试数学试题
名校
2 . 如图,在三棱柱
中,侧面
为正方形,
,
,
为
的中点.
平面
;
(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/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.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/554923047631d16320c2ba39abeee99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b5068a142c39664e25539d27be030b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e9f163cab6799928b68cb9b80337f7.png)
您最近一年使用:0次
2024-04-08更新
|
1629次组卷
|
4卷引用:北京市西城区2024届高三下学期4月统一测试数学试卷
北京市西城区2024届高三下学期4月统一测试数学试卷(已下线)6.3 空间中的平行关系与垂直关系(高考真题素材之十年高考)湖南省株洲市炎陵县2023-2024学年高二下学期4月素质质量检测数学试卷四川成都实验外国语学校2023-2024学年高二下学期期中考试数学试题
名校
3 . 如图, 在三棱柱
中,
为等边三角形,四边形
是边长为2的正方形, D为AB中点, 且 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50b193e9a6e49d78f89a479fd04f97a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/219733bf-a7ed-4c58-b52e-08bc2dd0019f.png?resizew=171)
(1)求证: CD⊥平面
;
(2)已知点 P 在线段
上,且直线AP 与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770abdd10660689c605577f9cb6d9db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50b193e9a6e49d78f89a479fd04f97a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/219733bf-a7ed-4c58-b52e-08bc2dd0019f.png?resizew=171)
(1)求证: CD⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)已知点 P 在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ca3bdb7a6f14db41bbc013000c510a.png)
您最近一年使用:0次
4 . 在三棱柱
中,
,平面
平面
,
分别为棱
的中点,如图:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/cce4fc8f-3773-44a9-a5a8-8ca21ea6d283.png?resizew=181)
(1)求证:
平面
;
(2)若
,
①求
与平面
所成角的正弦值;
②求线段
在平面
内的投影
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a1d8b135a43429bba122bb000ca83e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e34cc1159ab9198480cd0b585620d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9369aed2d8309af46ac3eaffb9cce537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d172b97111c32fa11369a6c59719c8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/cce4fc8f-3773-44a9-a5a8-8ca21ea6d283.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e5e2ba78a5b1dd0f39bb65d2a0a0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bfd8e9f2f08a5807a23677988b240b.png)
②求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bfd8e9f2f08a5807a23677988b240b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae626b30192bba5c433d399bba65411.png)
您最近一年使用:0次
2023-12-21更新
|
289次组卷
|
2卷引用:北京市西城区北师大附属实验中学2024届高三上学期12月月考数学试题
解题方法
5 . 直三棱柱
中,点M、N分别为BC、
中点.
(1)求证:
平面
;
(2)已知
,
,
.
(i)求直线
与平面
所成角的大小;
(ii)求点C到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/c4dabed4-2a37-49ef-a540-1fc781d9bf95.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df209c58c4cc146ef62100e6d3b068d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(ii)求点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
解题方法
6 . 如图,在四棱锥
中,底面ABCD为平行四边形,平面
平面ABCD,
,
,点M为棱PC中点,平面ABM与棱PD交于点N.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/943d64f7-4c44-4159-8227-e067f026977d.png?resizew=183)
(1)求证:N是棱PD的中点;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求:
(i)二面角
的余弦值;
(ii)在棱PA上是否存在点Q,使得
平面BDM?若存在,求出
的值;若不存在,说明理由.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d9f95acb654472e6a0b00554e5f7c4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/943d64f7-4c44-4159-8227-e067f026977d.png?resizew=183)
(1)求证:N是棱PD的中点;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求:
(i)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64785e4401e1d79632e360fd3626ed62.png)
(ii)在棱PA上是否存在点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5197adf1af97b29adc08417400807c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc953f0be1dafec1b4d1836cbafbf59.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
注:如果选择条件①和条件②分别解答,按第一个解答计分.
您最近一年使用:0次
7 . 如图,在四棱锥
中,
平面
,
,
,
.
(1)求证:
平面
;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求平面
与平面
所成锐二面角的大小.
条件①:
;
条件②:
平面
.
注:如果选择的条件不符合要求,第(2)问得0分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
![](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/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1720da6d65e7fa854d98322d3864240.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/fea268da-aa15-4504-9425-7062dcb8b407.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)再从条件①、条件②这两个条件中选择一个作为已知,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06201e4f55b78d8b30afb257d5a1b16b.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
注:如果选择的条件不符合要求,第(2)问得0分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
您最近一年使用:0次
2024-03-28更新
|
876次组卷
|
3卷引用:北京市石景山区2024届高三下学期3月统一练习数学试卷
名校
8 . 如图,在五面体ABCDEF中,四边形ABCD是矩形,
.
(1)求证:
:
(2)从下面三个条件中选择一个作为已知,使五面体ABCDEF存在.求直线AE与平面BCF所成角的正弦值.
条件①:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件②:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件③:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dac702fe64edf1bc265da4b98cf2a0.png)
注:如果选择的条件不符合要求,得0分;如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04dee62ab0a09454e3906fbd0d3f14a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/af0a558d-cb99-475b-9565-df5ed4ffd77f.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333ab24c4935210f4c232cd0c0fae358.png)
(2)从下面三个条件中选择一个作为已知,使五面体ABCDEF存在.求直线AE与平面BCF所成角的正弦值.
条件①:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a68a008a22d5a8cea5fe8dcf31e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件②:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dac702fe64edf1bc265da4b98cf2a0.png)
注:如果选择的条件不符合要求,得0分;如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
9 . 在三棱柱
中,平面
平面
为正三角形,
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/b0070e84-b6a7-42df-8de9-c7d9c3df5e1e.png?resizew=140)
(1)求证:
平面
;
(2)若
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cfd6b6a7e911d10d1a4bed9ca5e749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db36b4497b911bc047253b832ae01c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/b0070e84-b6a7-42df-8de9-c7d9c3df5e1e.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6b480f7e4def1568a2d8bbfdde7842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8930e01f0a2c9d1915571e47a06e0b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
您最近一年使用:0次
名校
10 . 如图,在圆锥
中,
是圆
的直径,且
是边长为4的等边三角形,
为圆弧
的两个三等分点,
是
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e49817548cb45b3d1e58570644c6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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