名校
解题方法
1 . 如图,在正方体
中,
为
的中点.
‖平面
;
(2)
上是否存在一点
,使得平面
‖平面
?若存在,请确定点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c241f900cb6ed341c137a3d71216a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,已知
平面ACD,
平面ACD,三角形ACD是正三角形,且
,F是CD的中点.
平面CDE;
(2)求直线EF与平面CBE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb59a3752da728cfa77557dd14d0f737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06781fd124cad40fa5fd120b074157f.png)
(2)求直线EF与平面CBE所成角的正弦值.
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1028次组卷
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4卷引用:河南省济源市第四中学2023-2024学年高二上学期12月考数学试卷
河南省济源市第四中学2023-2024学年高二上学期12月考数学试卷(已下线)第1套 全真模拟卷 (基础)【高一期末复习全真模拟】(已下线)专题08 立体几何大题常考题型归类-期末考点大串讲(人教B版2019必修第四册)河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
名校
3 . 如图,已知四边形
为矩形,
,
,E为
的中点,将
沿
进行翻折,使点D与点P重合,且
.
;
(2)设
,
的延长线交于点N,则线段
上是否存在点Q,使得平面
与平面
所成角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58bbc02479917ad761a24eaae0dbfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985905ab3559ed7ec54e745a493629af.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24daf297c1d4e669a05623e8dde92de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,已知四棱台
的上、下底面分别是边长为2和4的正方形,平面
平面ABCD,
,点P是棱
的中点,点Q在棱BC上.
,证明:
平面
;
(2)若二面角
的正切值为5,求BQ的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b90595662af9a1936e1e703462cb69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fea37dbf4145c3b311bcec0fc25ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e866091156cbd7beea724fbbdb25082.png)
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真题
5 . 如图,在以A,B,C,D,E,F为顶点的五面体中,四边形ABCD与四边形ADEF均为等腰梯形,
,
,
,
为
的中点.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7587fdb043dc96ed724386286c9941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2231488d2261886446f5764fa559ba9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc150deaf709d073034cd8d56817f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e736704191faaf440edf6e57c98fc56d.png)
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4卷引用:2024年高考全国甲卷数学(理)真题
真题
解题方法
6 . 如图,
,
,
,
,
为
的中点.
平面
;
(2)求点
到
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62144e91faeae6b634f7dc0a28d0f79a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d65be32159e3b778677cddb989b28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae16f0e7561e767d9c23f7b6b247df94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941eba4dbc1094107e1eeb02c8d8cd56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0285afe567ca0b32f0ccafc30167cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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3380次组卷
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6卷引用:2024年高考全国甲卷数学(文)真题
2024年高考全国甲卷数学(文)真题专题07立体几何与空间向量专题32立体几何与空间向量解答题(第二部分)(已下线)2024年高考全国甲卷数学(文)真题变式题16-23(已下线)五年全国文科专题15立体几何与空间向量解答题(已下线)三年全国文科专题08立体几何与空间向量
名校
7 . 如图,在直三棱柱
中,
,
,
,
.
时,求证:
平面
;
(2)设二面角
的大小为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42da806a6bd2472459f6c4ad1dab7b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b360c98bd3fd209525fd8fece4246590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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3卷引用:立体几何与空间向量-综合测试卷B卷
名校
解题方法
8 . 如图,在正方体
中,
是
的中点,
分别是
的中点. ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
平面
;
(2)若正方体棱长为1,过
三点作正方体的截面,画出截面与正方体的交线,并求出截面的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c7b255eaafe00d925cf7284b573c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)若正方体棱长为1,过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a643637f6ac4c594c1665be42b6184.png)
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名校
解题方法
9 . 如图,在等腰梯形
中,
,
,
,
平面
,
平面
,
,点P在线段
上运动.
;
(2)是否存在点P,使得
平面
?若存在,试求点P的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a38fcce7dd0dee12192a18eee9f9cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b014302812d64fb8cb558ac6ace3c903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8455347237248c7701100642c5b119.png)
(2)是否存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
10 . 如图,在正方体
中,
,点E在棱
上,且
.
的体积;
(2)在线段
上是否存在点F,使得
平面
,若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4b2b4c0c6650ae7e8fa57465848553.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a98287a302228ece1fa53c5c66c590f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1125973328ed42da7a53b457d587e3.png)
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