名校
解题方法
1 . 如图,已知在正三棱柱
中,
,且点
分别为棱
的中点.
作三棱柱截面交
于点
,求线段
长度;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef4495309b23e5218be6f611d04c38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8e45b50c77bf6a2cde628ea3455ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35850dbc661ded6456b70767cc6cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2024-05-03更新
|
898次组卷
|
2卷引用:北京市北京师范大学第二附属中学2023-2024学年高二下学期第二次月考数学试题
名校
2 . 如图,在直三棱柱
中,
,D为
中点.
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,求直线
与平面
所成角的正弦值.
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/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1604adab63e6350177d8130123dca0f9.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)再从条件①、条件②这两个条件中选择一个作为已知,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55171d348ce35d913d70b7fddacf168.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a736e9e92c1350409c07d8bb424ceb.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
名校
解题方法
3 . 如图,在四棱锥
中,底面ABCD是边长为2的正方形,
,
,E为BC的中点,F为PD的中点.
平面PAB;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求直线AD与平面AEF所成角的正弦值.
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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073a88b42836fb88433679932b48ad03.png)
(2)再从条件①、条件②这两个条件中选择一个作为已知,求直线AD与平面AEF所成角的正弦值.
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1720da6d65e7fa854d98322d3864240.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
名校
4 . 四棱锥
中,底面
为平行四边形,平面
平面
,
,E为棱
的中点,过点B,C,E的平面交棱
于点F.
(1)求证:F为
中点;
(2)若
,再从条件①,条件②,条件③中选择一个作为已知,使四棱锥唯一确定,求二面角
的余弦值.
条件①:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
条件②:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100881607bf473a178dad4e4705e0bc0.png)
条件③:
与平面
所成角的正切值为2
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/ac79f86d-d814-4a96-a54c-03e02edc824f.png?resizew=156)
(1)求证:F为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52fc8f990adbe930de1ebe715d8c84b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3908c561b3d7cf640ed68acc1af40e5.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100881607bf473a178dad4e4705e0bc0.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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
5 . 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
解题方法
6 . 如图,从长、宽、高分别为a,b,c的长方体中截去部分几何体后,所得几何体为三棱锥
.下列四个结论中,所有正确结论的个数是( ).
①三棱锥的体积为
;
②三棱锥的每个面都是锐角三角形;
③三棱锥中,二面角
不会是直二面角;
④三棱锥中,三个侧面与底面所成的二面角分别记为
,
,
,则
.
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
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7 . 如图,直三棱柱
中,D为
的中点,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/9a2afd97-4888-4b2a-9ff8-01615f853bff.png?resizew=149)
(1)求证:
平面
;
(2)若二面角
的大小为
时,求线段BC的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/9a2afd97-4888-4b2a-9ff8-01615f853bff.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,因为
平面
,底面
为菱形,
,
分别为
,
的中点.
平面
;
(2)若
,
,再从条件①、条件②这两个条件中选择一个作为已知.求二面角
的大小.
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/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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b8df87ef099eae61bb07018f2ab335.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3672e603d06c9186edd20cfc662d8dc.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
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9 . 如图,在四棱锥
中,
,
是棱
上靠近点
的三等分点.
平面
;
(2)设平面
与平面
的交线为
,若平面
平面
,
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6fac6c785c339fba14205ca26eb6a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6c23afda5016ebbae7a9a5611c1039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6546d9c27cc1d9d5c5cbd2fc294f6b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
您最近一年使用:0次
2024-01-04更新
|
490次组卷
|
3卷引用:北京市海淀区首都师范大学附属中学2023-2024学年高三上学期阶段练习(1月)数学试题
名校
10 . 如图,在四棱锥
中,底面
为直角梯形,其中
,
,
,
,
平面
,且
,点
在棱
上,点
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/236c2a32-a601-4fd1-8953-21356591f05f.png?resizew=160)
(1)证明:若
,直线
平面
;
(2)求二面角
的余弦值;
(3)是否存在点
,使
与平面
所成角的正弦值为
?若存在求出
值;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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.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/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/236c2a32-a601-4fd1-8953-21356591f05f.png?resizew=160)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85ce5e111acf7162b8e1b5a3f6b220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1000f47a7a77a81c2d0bf1b1f8599f.png)
(3)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d567bdeba9b8e17d0911f594e141eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47548785e478bc5b9591341a881e3127.png)
您最近一年使用:0次