2010·广东汕头·一模
名校
解题方法
1 . 如图,四棱锥
的底面是边长为1的正方形,侧棱
底面
,且
,E是侧棱
上的动点.
的体积;
(2)如果E是
的中点,求证:
平面
;
(3)是否不论点E在侧棱
的任何位置,都有
?证明你的结论.
![](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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)如果E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)是否不论点E在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
您最近一年使用:0次
2024-01-04更新
|
624次组卷
|
5卷引用:汕头市2009-2010学年度第二学期高三级数学综合测练题(理四)
(已下线)汕头市2009-2010学年度第二学期高三级数学综合测练题(理四)2017届北京市海淀区高三3月适应性考试(零模)文科数学试卷广东省2024年1月高中合格性学业水平考试模拟测试数学试题(三)陕西省西安市西安中学2023-2024学年高二学考仿真考试数学试题(已下线)第13讲 8.6.2直线与平面垂直的性质定理 (第2课时)-【帮课堂】(人教A版2019必修第二册)
解题方法
2 . 阅读下面题目及其证明过程,在
处填写适当的内容.
已知三棱柱
,
平面
,
,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/daabe3a8-f5d5-4b94-9577-eeb61c3f5b0f.png?resizew=135)
(1)求证:
∥平面
;
(2)求证:
⊥
.
解答:(1)证明: 在
中,
因为
分别为
的中点,
所以 ① .
因为
平面
,
平面
,
所以
∥平面
.
(2)证明:因为
平面
,
平面
,
所以 ② .
因为
,
所以
.
又因为
,
所以 ③ .
因为
平面
,
所以
.
上述证明过程中,第(1)问的证明思路是先证“线线平行”,再证“线面平行”; 第(2)问的证明思路是先证 ④ ,再证 ⑤ ,最后证“线线垂直”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d5d02301554aad6cc89452c83f0862.png)
已知三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d77afb7d8280995886ff690e7a6c9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/daabe3a8-f5d5-4b94-9577-eeb61c3f5b0f.png?resizew=135)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
解答:(1)证明: 在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9e1e0d29bc4bdf0c6d38ca4db43343.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d77afb7d8280995886ff690e7a6c9a.png)
所以 ① .
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871502ee0c5d1414cfe81e8409b62d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f196748dc6a0d0bd9e9e4dd30ac4ed0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)证明:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以 ② .
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
又因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d970e34169fb0de8a3f10e4c6ae40d.png)
所以 ③ .
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6cb3896ef1afc6a56a5aa0243022e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
上述证明过程中,第(1)问的证明思路是先证“线线平行”,再证“线面平行”; 第(2)问的证明思路是先证 ④ ,再证 ⑤ ,最后证“线线垂直”.
您最近一年使用:0次
解题方法
3 . 阅读下面题目及其证明过程,并回答问题.
如图,在三棱锥
中,
底面
,
,
,
分别是棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/10/2590155875131392/2590586443956224/STEM/59e96d8fb6364a7a9a0c2415e5ced222.png?resizew=229)
(1)求证:
平面
;
(2)求证:
.
解答:(1)证明:在
中,
因为
,
分别是
,
的中点,
所以
.
因为
平面
,
平面
,
所以
平面
.
(2)证明:在三棱锥
中,
因为
底面
,
平面
,
所以______.
因为
,且
,
所以______.
因为
平面
,
所以______.
由(1)知
,
所以
.
问题1:在(1)的证明过程中,证明的思路是先证______,再证______.
问题2:在(2)的证明过程中,设置了三个空格.请从下面给出的四个选项中,为每一个空格选择一个正确的选项,以补全证明过程.
①
;②
;③
平面
;④
.
如图,在三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2020/11/10/2590155875131392/2590586443956224/STEM/59e96d8fb6364a7a9a0c2415e5ced222.png?resizew=229)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
解答:(1)证明:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
因为
![](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/48f3c9abbd78e9a6840ee5f30381daac.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6c1984e2068203465b10ea4ead7916.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871502ee0c5d1414cfe81e8409b62d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9fe3c7e943c3beb7f4bbf345822064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)证明:在三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8690d88536618e3f993dae41a3de66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以______.
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34baf7aadc048e75e776b80eea5b62b5.png)
所以______.
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9fe3c7e943c3beb7f4bbf345822064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
所以______.
由(1)知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6c1984e2068203465b10ea4ead7916.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
问题1:在(1)的证明过程中,证明的思路是先证______,再证______.
问题2:在(2)的证明过程中,设置了三个空格.请从下面给出的四个选项中,为每一个空格选择一个正确的选项,以补全证明过程.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d9ef979b9f27a28cbda6923e888ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da48240e7fc3248f773ac1500c15ec14.png)
您最近一年使用:0次
4 . 已知过原点的三条直线与抛物线
:
依次交于
,
,
三点,同样这三条直线与抛物线
:
依次交于
,
,
三点.
(1)试判断直线
与
的位置关系,并证明;
(2)试判断
与
的面积比是否为定值,若是求出此定值,若不是请说明理由;
(3)若
与
都与抛物线
:
相切,求证
也和
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34876d748f30fa4fc2eb6a686b5ff5.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828dc8dc7259c510b6d63abf40f60e90.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
您最近一年使用:0次
5 . 如图,在直四棱柱
中,库面四边形
的对角线
,
互相平分,
为
的中点.
(1)求证:
平面
;
(2)若______,则平面
平面
.试在三个条件“①四边形
是平行四边形;②四边形
是矩形;③四边形
是菱形”中选取一个,补充在上面问题的横线上,使得结论成立,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/c80af623-5fef-41e1-98e0-00fd62c7b8de.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)若______,则平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2020-09-21更新
|
1033次组卷
|
4卷引用:福建省普通高中2019-2020学年高二1月学业水平合格性考试数学试题
福建省普通高中2019-2020学年高二1月学业水平合格性考试数学试题福建省泉州市安溪第八中学2021届高三学业合格模拟检测(一)数学试题人教A版(2019) 必修第二册 实战演练 第八章 验收检测(已下线)第8章 立体几何初步(单元提升卷)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)
6 . 阅读下面题目及其解答过程,并补全解答过程.
以上解答过程中,设置了①~⑤五个空格,如下的表格中为每个空格给出了两个选项,其中只有一个正确,请选出你认为正确的,并填写在答题卡的指定位置.
已知函数![]() (Ⅰ)当 ![]() ![]() (Ⅱ)求证:函数 ![]() ![]() 解答:(Ⅰ)当 ![]() ![]() 因为 ![]() 所以当 ![]() ![]() 因为函数 ![]() ![]() 所以 ![]() ![]() 所以 ![]() 所以 ![]() 所以函数 ![]() (Ⅱ)证明:任取 ![]() ![]() 因为 ![]() 所以 ![]() 所以⑤. 所以 ![]() 所以函数 ![]() ![]() |
空格序号 | 选项 | |
① | A.![]() | B.![]() |
② | A.![]() | B.![]() |
③ | A.![]() | B.![]() |
④ | A.![]() | B.![]() |
⑤ | A.![]() | B. ![]() |
您最近一年使用:0次
7 . 对于给定的抛物线
,使得实数p、q满足
.
(1)若
,求证:抛物线
与x轴有交点.
(2)证明:抛物线
的最大值大于等于抛物线
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d972cf8c74b5218298b60908716a8d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c059fce1db054ebb94902a84d25fcd43.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e864b9d4b6a0aa76416348778b26d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2630d6cf14b3e8c82ee7080799901b8d.png)
(2)证明:抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bee92cd110cd46e04633e18c17c4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188f03bd3b6ee375cbc88926cfbcd774.png)
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解题方法
8 . 已知
是常数,在数列
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94ae936f82425aadd82bfbc76079d2a.png)
(1)若
,求
的值;
(2)若
=4,证明:数列
是等比数列,并求数列
的通项公式;
(3)在(2)的条件下,设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94ae936f82425aadd82bfbc76079d2a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)在(2)的条件下,设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1302abaebc9df026c2a83291063e83b4.png)
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9 . 如图,在三棱锥
中,
平面ABC,点D,E,F分别为PC,AB,AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/f1c930c8-c484-49cb-aa40-23ab41bc30a0.png?resizew=182)
(Ⅰ)求证:
平面DEF;
(Ⅱ)求证:
.
阅读下面给出的解答过程及思路分析.
解答:(Ⅰ)证明:在
中,因为E,F分别为AB,AC的中点,所以①.
因为
平面DEF,
平面DEF,所以
平面DEF.
(Ⅱ)证明:因为
平面ABC,
平面ABC,所以②.
因为D,F分别为PC,AC的中点,所以
.所以
.
思路分析:第(Ⅰ)问是先证③,再证“线面平行”;
第(Ⅱ)问是先证④,再证⑤,最后证“线线垂直”.
以上证明过程及思路分析中,设置了①~⑤五个空格,如下的表格中为每个空格给出了三个选项,其中只有一个正确,请选出你认为正确的选项,并填写在答题卡的指定位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/f1c930c8-c484-49cb-aa40-23ab41bc30a0.png?resizew=182)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d276d0010fd458383ea3dd61415e1aa.png)
阅读下面给出的解答过程及思路分析.
解答:(Ⅰ)证明:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fa6d320a49764f0fbd3df95bde452a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b102c0fb7a1e3911e22535579ffa84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
(Ⅱ)证明:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8690d88536618e3f993dae41a3de66a.png)
因为D,F分别为PC,AC的中点,所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb5dc3315629bf14991d5c4feb3a1ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d276d0010fd458383ea3dd61415e1aa.png)
思路分析:第(Ⅰ)问是先证③,再证“线面平行”;
第(Ⅱ)问是先证④,再证⑤,最后证“线线垂直”.
以上证明过程及思路分析中,设置了①~⑤五个空格,如下的表格中为每个空格给出了三个选项,其中只有一个正确,请选出你认为正确的选项,并填写在答题卡的指定位置.
空格 | 选项 | ||
① | A.![]() | B.![]() | C.![]() |
② | A.![]() | B.![]() | C.![]() |
③ | A.线线垂直 | B.线面垂直 | C.线线平行 |
④ | A.线线垂直 | B.线面垂直 | C.线线平行 |
⑤ | A.线面平行 | B.线线平行 | C.线面垂直 |
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10 . 阅读下面题目及其证明过程,在横线处应填写的正确结论是
如图,在三棱锥
中,平面
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60964e720188e325eb18c9528b1fa95.png)
证明:因为平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30f1a3b00e2ce8dacc26bc70bd908b8.png)
,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以______.
因为
平面
.
所以![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60964e720188e325eb18c9528b1fa95.png)
如图,在三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60964e720188e325eb18c9528b1fa95.png)
证明:因为平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3916b70bbe029987dc22850fb4f104e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30f1a3b00e2ce8dacc26bc70bd908b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8690d88536618e3f993dae41a3de66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以______.
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9f8e741b213a3b98a491e58bc82f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60964e720188e325eb18c9528b1fa95.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2018-12-14更新
|
729次组卷
|
4卷引用:2018年北京市普通高中学业水平考试数学试卷
2018年北京市普通高中学业水平考试数学试卷【市级联考】贵州省贵阳市2017-2018学年高一(下)期末模拟数学试题(已下线)【新教材精创】11.4.2平面与平面垂直(第2课时)练习(1)(已下线)6.5.2 平面与平面垂直-同步精品课堂(北师大版2019必修第二册)