解题方法
1 . 如图,在四棱锥P—ABCD中,底面ABCD是正方形,侧面PAD⊥底面ABCD,且PA=PD=AD=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/01c74de8-04cc-45bf-a8de-309a9a6b53d3.png?resizew=195)
(1)若点E为线段PD的中点,求证:AE⊥平面PDC;
(2)若
,则线段AB上是否存在一点F,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面PBC,若存在,请确定点F的位置,并求三棱锥F
PBC的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/01c74de8-04cc-45bf-a8de-309a9a6b53d3.png?resizew=195)
(1)若点E为线段PD的中点,求证:AE⊥平面PDC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f3d7c9faeea54db96aeb1f0073c3f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
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2022-07-12更新
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3卷引用:广西百色市2022-2023学年高一下学期数学期末考试模拟试题
解题方法
2 . 如图,在三棱锥
中,平面
平面BCD,
,O为BD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/13/cbf5e0f6-9f5f-416a-92a2-58134df91450.png?resizew=184)
(1)证明:
平面BCD;
(2)若
是边长为1的等边三角形,点E在棱AD上,
,且二面角
的大小为
,求三棱锥
的体积.
![](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/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/13/cbf5e0f6-9f5f-416a-92a2-58134df91450.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d76c5ac5c9f0a2ec064487c02c476e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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名校
解题方法
3 . 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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481次组卷
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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
解题方法
4 . 三棱锥
的顶点都在球O的球面上,且
,
,若三棱锥
的体积最大值为
,则球O的表面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6610676353016a9f7235d306b731c1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be245bc5bbc4dc4e668f2cf5321c7043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a44d321ae2abfc4e566933a92637d1.png)
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5 . 如图,在棱长为1的正方体
中,E,F分别为
,CD的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/8c6f184b-2ba0-46e2-8f93-3f8d9110503d.png?resizew=203)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/8c6f184b-2ba0-46e2-8f93-3f8d9110503d.png?resizew=203)
A.直线![]() ![]() |
B.二面角![]() ![]() |
C.经过三点A,E,F截正方体的截面是等腰梯形 |
D.点![]() ![]() ![]() |
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解题方法
6 . 已知m,n是两条不重合的直线,
,
,
是三个不重合的平面,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
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解题方法
7 . 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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2022-06-30更新
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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
8 . 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
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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
9 . 在空间,下列命题正确的是( )
A.平行于同一平面的两条直线平行 | B.平行于同一直线的两个平面平行 |
C.垂直于同一平面的两条直线平行 | D.垂直于同一平面的两个平面平行 |
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2022-06-13更新
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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 . 如图,平面四边形
中,
是等边三角形,
且
是
的中点.沿
将
翻折,折成三棱锥
,翻折过程中下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303653896192/STEM/3445b240-0268-42df-a6a4-92ec57df03e6.png?resizew=403)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8915e8e775538d41debf1933102c6b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ed50d0d07c007195a0263a57adbf3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303653896192/STEM/3445b240-0268-42df-a6a4-92ec57df03e6.png?resizew=403)
A.存在某个位置,使得![]() ![]() |
B.棱![]() ![]() ![]() ![]() ![]() |
C.当三棱锥![]() ![]() |
D.当二面角![]() ![]() ![]() |
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2022-06-04更新
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2809次组卷
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6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