名校
1 . 如图,在四棱锥
中,
,
平面
,底面
为正方形,
,
分别为
,
的中点.
(1)求证:
平面
;
(2)求直线
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/1365206d14224e0b2d40a7bd8b7965ac.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/578e3534-c0e1-4c0f-8a35-d416eab64d16.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
您最近一年使用:0次
2023-10-17更新
|
389次组卷
|
12卷引用:西藏拉萨市2020届高三第二次模拟考试数学(理)试题
西藏拉萨市2020届高三第二次模拟考试数学(理)试题2020届北京市高考适应性测试数学试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)专题20 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)北京师范大学亚太实验学校2021届高三上学期期中数学试题黑龙江省哈尔滨市第九中学校2020-2021学年高二上学期期中考试数学(理)试题北京市第四十三中学2021届高三1月月考数学试题天津市河西区梧桐中学2020-2021学年高二上学期第一次学情调研数学试题福建省尤溪县第五中学2021-2022学年高二上学期第一次月考数学试题北京市朝阳区北京工业大学附属中学2023-2024学年高二上学期10月月考数学试题云南省砚山县第三高级中学2021-2022学年高二上学期期末考试数学试题云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(B卷)
2 . 如图,正方体
的棱长为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/3fca0077-a488-4b95-82c9-fc72287e753f.png?resizew=174)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/3fca0077-a488-4b95-82c9-fc72287e753f.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb96d9ea39bf7974143973559058dbec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
2023-12-17更新
|
181次组卷
|
2卷引用:西藏自治区拉萨市2024届高三一模数学(理)试题
3 . 如图,在直三棱柱
中,
,
,
分别为
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/2023/5/8/3233425156571136/3233909931556864/STEM/d151e1559e0741709f726664e877cdc8.png?resizew=137)
(1)求证:
平面
;
(2)若
,求直线
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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2023/5/8/3233425156571136/3233909931556864/STEM/d151e1559e0741709f726664e877cdc8.png?resizew=137)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f475878dd1b32b0486cbf7b5ffbedd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb74eeb04f2f2f68095db616f14c971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
您最近一年使用:0次
2023-05-09更新
|
1801次组卷
|
3卷引用:西藏林芝市第二高级中学2023届高三第四次模拟考试数学(理)试题
解题方法
4 . 如图,在直三棱柱
中,
,
,
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/6c9e2af0-b34d-497c-a0b4-4df42193b9cb.png?resizew=150)
(1)求证:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de9b94a20b9d6ea37cfe135d790801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78f0b646ccbe31c8d4df21054f82003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a78f1bee29c69699ae6c7dd553c73c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/6c9e2af0-b34d-497c-a0b4-4df42193b9cb.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a0a3bb566b5d2404e4bb823abddfa9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f0d992b0879916037fa5f61d6bea67.png)
您最近一年使用:0次
名校
5 . 如图,在四棱台中,底面四边形
为菱形,
,
,
平面
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a382ccd078374f1efebb26a43599e596.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912d03b664bbf5896427da55c5d4e0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c7d7907053678842c08e1f91f33cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147567c35a9527de9e56192583da0891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9139251b27b393fcb37577828bbf53bf.png)
您最近一年使用:0次
2023-02-22更新
|
609次组卷
|
5卷引用:西藏林芝市2023届高三二模数学(理)试题
名校
解题方法
6 . 如图所示,直三棱柱
的底面是边长为
的正三角形,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/03faad06-5232-46c4-8874-7fa1e9b8257e.png?resizew=130)
(1)求证:平面
平面
.
(2)若
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/03faad06-5232-46c4-8874-7fa1e9b8257e.png?resizew=130)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0575c501b47fc040112da75262809344.png)
您最近一年使用:0次
7 . 已知在三棱锥
中,平面
平面
,
为等边三角形,
,
,且
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712441864536064/2716145844789248/STEM/1ec3e547-28bb-415f-9518-3ddf16035875.png?resizew=241)
(1)求证:
平面
;
(2)若
为
的中点,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfac9ab1dc776c9ec076ab2a132fcd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712441864536064/2716145844789248/STEM/1ec3e547-28bb-415f-9518-3ddf16035875.png?resizew=241)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b4e753ef119608188c46a50ec597e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)若
![](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/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb5255e2159617505e0c87d01437a57.png)
您最近一年使用:0次
解题方法
8 . 如图,在三棱柱
中,
平面
,
分别为
的中点,
点为靠近
的三等分点,
,
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712441583607808/2715833561137152/STEM/29ca31e7-fdfb-4c41-a094-d99e8ffb6078.png?resizew=216)
(1)求证:
平面
;
(2)求二面角
的余弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c152744e7eb9d9f86eaf937ed96a737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efa2b0018617bd579875185dafca39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d5815dc775d5a5810fff0b016a8d5.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712441583607808/2715833561137152/STEM/29ca31e7-fdfb-4c41-a094-d99e8ffb6078.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1f7689bff6644bfdeb9e36feb163.png)
您最近一年使用:0次
名校
9 . 如图,平面
平面
,
,
,
,
为
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/2021/5/10/2717991448190976/2785209666428928/STEM/c190524978304d729d1ad4802b4849f9.png?resizew=158)
(1)证明:
平面
;
(2)若平面
与平面
所成锐二面角为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39c74cc0a6bb988738787b9e0fcb5e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://img.xkw.com/dksih/QBM/2021/5/10/2717991448190976/2785209666428928/STEM/c190524978304d729d1ad4802b4849f9.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2021-08-13更新
|
1473次组卷
|
10卷引用:西藏林芝市第一中学2021届高三上学期模拟考试数学(理)试题
西藏林芝市第一中学2021届高三上学期模拟考试数学(理)试题广东省湛江市2021届高三一模数学试题广东省北大附中深圳南山分校2021届高三下学期3月一模数学试题(已下线)专题1.7 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线)精做04 立体几何-备战2021年高考数学(理)大题精做广东省高州市第一中学2021届高三下学期3月月考数学试题安徽省芜湖市第一中学2021-2022学年高二上学期第一次月末诊断测试数学试题湖北省武汉市育才高级中学2021-2022学年高二上学期第一次月考数学试题(已下线)专题19 空间向量与立体几何(解答题)-备战2022年高考数学(理)母题题源解密(全国甲卷)(已下线)解密10 空间向量与立体几何(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(浙江专用)
名校
10 . 如图,四棱锥
中,
底面
,
,
,
,且
,
,
分别为
,
的中点.
,求证:
平面
;
(2)若四棱锥
的体积为2,求二面角
的余弦值.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9723a6e093c297b001436e8932b1820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d5a42a8509e15a0dca186f06be73dc.png)
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