1 . 已知正方形
和矩形
所在的平面互相垂直,
,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/403f03a4-f620-4a1c-8388-836385edea40.png?resizew=208)
(Ⅰ)若
为
的中点,求证:
平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)证明:存在点
,使得
平面
,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef70144bea23fc8154301b246bf3ef14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/403f03a4-f620-4a1c-8388-836385edea40.png?resizew=208)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0d2ea2af3f0ab189c4694eeb52ce43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae628604c47725bb01e22dff5dca8e5.png)
(Ⅲ)证明:存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27fb1ba55d814904c84d5581edf3a1b.png)
您最近一年使用:0次
2 . 如图,在五面体
中,四边形
是矩形,平面
平面
,
是正三角形,
,
,
.
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeedb5f361a1baff6338436fff6c471d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41d3f7d55fcbaebc4e2450ac63a3dc5.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9eff13d9afbbc79a05afbc0cbcfa3c.png)
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解题方法
3 . 如图,在五面体
中,四边形
是正方形,
是等边三角形,平面
平面
,
,
,
是
的中点.
平面
;
(2)求直线
与平面
所成角的大小;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c197d8b99f2eb7477947e53461b5d548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77d8c149eca1d8fbec01f82978b8860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5e0a296b2a9fd6c73320e29611be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199098479c92e87304b91871172d46e0.png)
您最近一年使用:0次
2024-01-17更新
|
347次组卷
|
3卷引用:北京市房山区2023-2024学年高二上学期期末考试数学试卷
4 . 如图,在四棱锥
中,
底面
,底面
是正方形,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/c895cf26-7e76-4e65-8ffb-04c09769a34c.png?resizew=154)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小;
(3)求点
到平面
的距离.
![](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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/c895cf26-7e76-4e65-8ffb-04c09769a34c.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
5 . 如图,在三棱柱
中,
平面
,
是
的中点,
,
.
(1)求证:
平面
;
(2)求二面角
的余弦值;
(3)判断直线
与平面
是否相交,如果相交,求出A到交点H的距离;如果不相交,求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a00465e9aeec98fc1c2bfd2e20c358a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/f51c2fe2-039d-4c14-b314-f0ac699b8786.png?resizew=135)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a446b91e73b181f9f4d56264dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5d02ab4d51f92d437057fd7ff9c1c1.png)
(3)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
您最近一年使用:0次
2023-11-10更新
|
306次组卷
|
3卷引用:北京市房山区2023-2024学年高二上学期期中考试数学试题
北京市房山区2023-2024学年高二上学期期中考试数学试题北京市第九中学2024届高三上学期12月月考数学试题(已下线)第二章 立体几何中的计算 专题二 空间距离 微点4 直线到平面的距离、两个平面间距离【基础版】
6 . 如图,在四棱锥
中,底面
是边长为1的正方形,
平面
,
为棱
的中点.
平面
;
(2)再从条件①、条件②、条件③中选择一个作为已知,
求:直线
与平面
所成角的正弦值,以及点
到平面
的距离.
条件①:
;
条件②:
平面
;
条件③:
.
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aebaf06bb1c96aecf49603c6a6bfcea.png)
(2)再从条件①、条件②、条件③中选择一个作为已知,
求:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aebaf06bb1c96aecf49603c6a6bfcea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aebaf06bb1c96aecf49603c6a6bfcea.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760d5434e6c8bf40ea411cb2009fd752.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ddcfd8985d6ef923063a301e2bc5ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990f9aca5b10d4850f0631288a9b1a97.png)
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7 . 如图,已知直三棱柱
中,
,
为
中点,
,再从条件①,条件②这两个条件中选择一个作为已知,完成以下问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/d75d8ac9-de11-4f4f-af96-5a08d9b13f33.png?resizew=125)
(1)证明:
;
(2)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/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/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/d75d8ac9-de11-4f4f-af96-5a08d9b13f33.png?resizew=125)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa8345302e8036af33d4598282144d7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b8f65872fbe939603c6e2acee74baa.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9959790095c938b094ddf5953d2b7d2b.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.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
解题方法
8 . 如图,四棱锥
的底面是矩形,
底面ABCD,
,M为BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/726658cd-4094-4fc6-bc8d-4ea871c3cc1f.png?resizew=153)
(1)求证:
平面PBD;
(2)求平面ABCD与平面APM所成角的余弦值;
(3)求D到平面APM的距离.
![](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/35883d6dd1d3d1454275b3b9574090ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/726658cd-4094-4fc6-bc8d-4ea871c3cc1f.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
(2)求平面ABCD与平面APM所成角的余弦值;
(3)求D到平面APM的距离.
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9 . 如图,在四棱锥
中,底面
为正方形,平面
平面
,点
在线段
上,
∥平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/251999d1-7d92-4668-8508-8b87948de17e.png?resizew=251)
(1)求证:
为
的中点;
(2)求平面
与平面
所成角的大小.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b05d9236a72555e4b0ceaa02ace108.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/251999d1-7d92-4668-8508-8b87948de17e.png?resizew=251)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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名校
10 . 如图,在直三棱柱ABC—A1B1C1中,
,AA1=4,AB⊥AC,BE⊥AB1交AA1于点E,D为CC1的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/1f0f804d-33c8-4029-aa77-97e6ca1f38c0.png?resizew=127)
(1)求证:BE⊥平面AB1C;
(2)求二面角C—AB1—D的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/1f0f804d-33c8-4029-aa77-97e6ca1f38c0.png?resizew=127)
(1)求证:BE⊥平面AB1C;
(2)求二面角C—AB1—D的余弦值.
您最近一年使用:0次
2022-08-15更新
|
1096次组卷
|
7卷引用:2022届北京市房山区良乡中学高三模拟考试数学试卷