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1 . 在棱长为a的正方体ABCD-A1B1C1D1中,M,N分别是棱A1B1,B1C1的中点,P是棱AD上一点,AP=
,过P,M,N的平面与棱CD交于Q,则PQ=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f249b606a13fd3ed5ef15d09235dac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/45f5bb70-0844-4bc5-a621-55f9e9e2d975.png?resizew=172)
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2017-12-03更新
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212次组卷
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5卷引用:上海市华东师范大学第二附属中学2021-2022学年高二上学期10月月考数学试题
(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期10月月考数学试题人教B版(2019) 必修第四册 逆袭之路 第十一章 立体几何初步 11.3.2 直线与平面平行人教A版高中数学必修二2.2.2平面与平面平行的判定2第二章 第二节 2.2直线、平面平行的判定及其性质(已下线)8.5.3 第2课时 平面与平面平行的性质(课时作业)-2021-2022学年高一数学同步精品课件+课时作业(人教A版2019必修第二册)
2 . 在正四棱柱
中,
是底面
的中心,底面边长为2,正四棱柱的体积为16
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/aa2c7f1e-6282-4704-b3b5-c067af8a54e7.png?resizew=166)
(1)求证:直线
平行于平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求
与平面
所成的角的大小
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/aa2c7f1e-6282-4704-b3b5-c067af8a54e7.png?resizew=166)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee51552e3c12bc27cf8ab1777bf191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
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3 . 如图,在直三棱柱
中,
,
,
是
的中点.
(Ⅰ)求证:
∥平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)试问线段
上是否存在点
,使
与
成
角?若存在,确定
点位置,若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570763143053312/1570763148238848/STEM/2ecd578588114996b854c12ed67af56f.png?resizew=96)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3054bfbd706c492cba96b09d5780e2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2f39d3fcb1664705228e683c2cc3b1.png)
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570763143053312/1570763148238848/STEM/e03eb1b7526846c78df8f690799a72d6.png?resizew=18)
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570763143053312/1570763148238848/STEM/d9e33085b2184814818ba1030f67b39c.png?resizew=27)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f25c5543b39190dc2499aa66f939659.png)
(Ⅲ)试问线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570763143053312/1570763148238848/STEM/5b25ba2ad1f34d989c68ce4c89b0cfea.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260200d547998bcac50a4a491382e7f4.png)
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570763143053312/1570763148238848/STEM/5b25ba2ad1f34d989c68ce4c89b0cfea.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570763143053312/1570763148238848/STEM/6157ae3972094edd8b89e1d59759fb88.png?resizew=192)
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4 . 如图,正三棱柱ABC—A1B1C1的各棱长都相等,M、E分别是
和AB1的中点,点F在BC上且满足BF∶FC=1∶3.
![](https://img.xkw.com/dksih/QBM/2014/2/12/1571506197364736/1571506202992640/STEM/475a6d4ea09f482b855903de5f1546be.png)
(1)求证:BB1∥平面EFM;
(2)求四面体
的体积.
![](https://img.xkw.com/dksih/QBM/2014/2/12/1571506197364736/1571506202992640/STEM/b111eea127594f67a9b11a257cb66e77.png)
![](https://img.xkw.com/dksih/QBM/2014/2/12/1571506197364736/1571506202992640/STEM/475a6d4ea09f482b855903de5f1546be.png)
(1)求证:BB1∥平面EFM;
(2)求四面体
![](https://img.xkw.com/dksih/QBM/2014/2/12/1571506197364736/1571506202992640/STEM/954fd03a260541258fba4271d9cf18d3.png)
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5 . 如图,四棱锥
的底面为正方形,
底面
分别是线段
的中点,
是线段
上的一点.
平面
;
(2)若直线
与平面
所成角的正弦值为
,试确定点
的位置.
![](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/8b80954cf89e31d1e5d89252f1094e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930e85bc9f73e86cfb6ce9b076433f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d4548c32861ade058b139a5b2ec801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6 . 如图是某直三棱柱(侧棱与底面垂直)被削去上底后的直观图与三视图的侧视图、俯视图,在直观图中,M是BD的中点,侧视图是直角梯形,俯视图是等腰直角三角形,有关数据如图所示.
(I)求出该几何体的体积;
(II)求证:EM∥平面ABC;
(III)试问在棱DC上是否存在点N,使NM⊥平面
?若存在,确定点N的位置; 若不存在,请说明理由.
(I)求出该几何体的体积;
(II)求证:EM∥平面ABC;
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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