名校
解题方法
1 . 如图,四棱锥
的底面ABCD是矩形,
平面ABCD,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/ff3f7a21-e910-48a5-9e99-5cd118c72885.png?resizew=139)
(1)求证:
平面
;
(2)求二面角
余弦值的大小;
![](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/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/ff3f7a21-e910-48a5-9e99-5cd118c72885.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d9f756419912dd298a0d6857130c80.png)
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2023-10-18更新
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687次组卷
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6卷引用:广西平果市铝城中学2023-2024学年高二上学期期末模拟数学试题(一)
名校
解题方法
2 . 在四棱锥
中,底面
为梯形,
,
,
,
,
,
⊥平面
.
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9742a7f64ff91be02601331f4ef2bb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b3539fcb35e07fcf3339eb04e7748d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab4007a35a23105744177d982caf747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6823a329628699619a39cde927510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db37b5ce697dab3189a15881d00fcd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/a71e5192-9737-4ee3-9971-35af857f8eed.png?resizew=147)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
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2023-10-15更新
|
900次组卷
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4卷引用:广西平果市铝城中学2023-2024学年高二上学期期末模拟数学试题(二)
名校
3 . 如图,直三棱柱
的所有棱长都是2,
分别是
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/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98842968c75427c940b34de391a3a778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d06f8edd1a1f18ca2dae700c6a29ab4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/23/2b6a3e38-044b-4132-8316-b256242a0019.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
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2023-10-03更新
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2卷引用:广西壮族自治区百色市德保县德保高中2023-2024学年高二上学期11月期中考试数学试题
名校
解题方法
4 . 已知四面体
的四个面均为直角三角形,其中
平面
,
,且
.若该四面体的体积为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
A.![]() ![]() | B.平面![]() ![]() |
C.![]() | D.四面体![]() ![]() |
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名校
5 . 四边形
为菱形,
平面
,
,
,
.
(1)设
中点为
,证明:
平面
;
(2)求平面
与平面
的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c88ac0eb1df661709d1316a3786cf49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5182849d8527befb00f5b803ad26f564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4280be91682e5d8a0d0704190319bb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/15/fbc9fecb-8dc8-48c7-9840-245dc2b95caa.png?resizew=187)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf187bc2ede965870b90757b495f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddf878892070bc3f2e5ac3379fa5836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1d7219cd40346442b33dba84deb5c.png)
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2023-09-15更新
|
1949次组卷
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8卷引用:广西壮族自治区百色市贵百联考2024届高三上学期9月月考数学试题
6 . 在四棱锥
中,底面
是矩形,若
,
.
(1)证明:平面
平面
;
(2)若
分别是
的中点,动点P在线段EF上移动,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff05040c164bc24caae03c76d0969de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03befc271004ef5243160fa41ab25964.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/20/ce250c2b-2ed0-437f-a10d-18a4cfee1fae.png?resizew=170)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11df029afb11e4233989b1338cb3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b041f67681af16a47cea903e43525d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
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2023-06-18更新
|
536次组卷
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2卷引用:广西百色市2022-2023学年高一下学期数学期末复习预测试题
名校
7 . 如图1,
是等边三角形,
是直角三角形,BD⊥BC,
,将
沿BD折起,使得平面ABD⊥平面BCD,如图2.
![](https://img.xkw.com/dksih/QBM/2022/7/18/3025338667294720/3026840079572992/STEM/9c703a8f6c244473a8fd0c9a45c67b12.png?resizew=357)
(1)证明:BC⊥平面ABD;
(2)求平面ABC与平面BCD所成的二面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8e6ffc3766967d5bca6eaf3f462949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://img.xkw.com/dksih/QBM/2022/7/18/3025338667294720/3026840079572992/STEM/9c703a8f6c244473a8fd0c9a45c67b12.png?resizew=357)
(1)证明:BC⊥平面ABD;
(2)求平面ABC与平面BCD所成的二面角的正切值.
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2022-07-20更新
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645次组卷
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4卷引用:广西平果市第二中学2021-2022学年高一下学期期中考试数学试题
广西平果市第二中学2021-2022学年高一下学期期中考试数学试题内蒙古自治区阿拉善盟第一中学2021-2022学年高一下学期期末考试数学试题(已下线)7.4 几何法求空间角(精练)(已下线)8.6.3平面与平面垂直(第1课时平面与平面垂直的判定定理)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
名校
解题方法
8 . 已知
,
是两条不重合的直线,
,
是两个不重合的平面,则下面四个结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() ![]() |
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4卷引用:广西平果市第二中学2021-2022学年高一下学期期中考试数学试题
广西平果市第二中学2021-2022学年高一下学期期中考试数学试题广西柳州市2021-2022学年高一下学期期末联考数学试题(已下线)13.2.3 直线和平面的位置关系(2)甘肃省临洮中学2022-2023学年高一下学期第二次月考数学试题
解题方法
9 . 如图,四棱锥
中,底面ABCD是边长为2的菱形,且
,
,
,M为AD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/3869779f-51ed-4af1-86ad-240eb00dfd0d.png?resizew=212)
(1)证明:
平面PBM;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1b1cf43d7dbb0725e92913cef8c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfb8d8c26dd656f60119ad25b9fff2d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/3869779f-51ed-4af1-86ad-240eb00dfd0d.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2022-06-17更新
|
711次组卷
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3卷引用:广西百色民族高级中学2021-2022学年高一下学期期末数学模拟题3
名校
解题方法
10 . 已知
矩形ABCD所在的平面,且
,M、N分别为AB、PC的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/11/2a20239f-268a-4c7b-8f7c-af20333520bc.png?resizew=224)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面ADP;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f6967901d6c855864df01e7bf7a15c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/11/2a20239f-268a-4c7b-8f7c-af20333520bc.png?resizew=224)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828247a3338571cb0d4ba2a5bf88929c.png)
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2022-07-10更新
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7卷引用:广西百色市2021-2022学年高一下学期期末教学质量调研测试数学试题
广西百色市2021-2022学年高一下学期期末教学质量调研测试数学试题广东省揭阳第一中学2020-2021学年高一下学期期末数学试题重庆市荣昌中学校2020-2021学年高二上学期十月月考数学试题(已下线)专题8.3 空间点、直线、平面之间的位置关系(练)- 2022年高考数学一轮复习讲练测(新教材新高考)内蒙古赤峰市赤峰第四中学2022-2023学年高一下学期5月月考数学试题甘肃省白银市会宁县第四中学2022-2023学年高一下学期第一次月考数学试题广东省鹤山市第一中学2023-2024学年高二上学期第一阶段考数学试题