解题方法
1 . 阅读下面题目及其解答过程.
如图,在直三棱柱
中,
,D,E分别为BC,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/d053b157-0829-465a-b6dc-3ea9c85cb713.png?resizew=138)
(1)求证:
平面
;
(2)求证:
.
解:(1)取
的中点F,连接EF,FC,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/0a94878a-2f4f-4376-980a-eaccd4e4ed9b.png?resizew=139)
在
中,E,F分别为
,
的中点,
所以
,
.
由题意知,四边形
为 ① .
因为D为BC的中点,所以
,
.
所以
,
.
所以四边形DCFE为平行四边形,
所以
.
又 ② ,
平面
,
所以,
平面
.
(2)因为
为直三棱柱,所以
平面ABC.
又
平面ABC,所以 ③ .
因为
,且
,所以 ④ .
又
平面
,所以
.
因为 ⑤ ,所以
.
以上题目的解答过程中,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,其中只有一个符合逻辑推理.请选出符合逻辑推理的选项,并填写在答题卡的指定位置(只需填写“A”或“B”).
如图,在直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/d053b157-0829-465a-b6dc-3ea9c85cb713.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
解:(1)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/0a94878a-2f4f-4376-980a-eaccd4e4ed9b.png?resizew=139)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac03bd962f6fbfecb16b558f3c374784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfbf154e19cbd0580d58ccc9bac077c.png)
由题意知,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
因为D为BC的中点,所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1ab54c55e934d0263f0aa33acb6116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0463b6e3d27b5cfc1df0e6c14fbef.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70099a8a0e7cff25485a63e8811a6aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeeadcae4a2964c73187962918724ae7.png)
所以四边形DCFE为平行四边形,
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dced11455b3e31a9090915f80a046fa3.png)
又 ② ,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e3ffd599e4fb57893b141bad96c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
所以,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83499936f532ddce9068dd1ff8eb2b01.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e3ffd599e4fb57893b141bad96c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f76925ed99b7172956319974258a9b.png)
因为 ⑤ ,所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
以上题目的解答过程中,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,其中只有一个符合逻辑推理.请选出符合逻辑推理的选项,并填写在答题卡的指定位置(只需填写“A”或“B”).
空格序号 | 选项 |
① | A.矩形 B.梯形 |
② | A.![]() ![]() ![]() ![]() |
③ | A.![]() ![]() |
④ | A.![]() ![]() ![]() ![]() |
⑤ | A.![]() ![]() |
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2 . 某公司出产了一款美观实用的筷子笼,如图,是由与圆柱底面成一定角度的截面截圆柱所得.如果从截面的最底端到最高端部分还原圆柱,如下图所示,AB,
分别为圆柱
底面直径,
,
为圆柱的母线,
,过
的平面
截圆柱且与底面所在平面交于直线
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/e8c50ced-4ea3-475f-92fa-a78be6572be7.png?resizew=511)
(1)证明:
;
(2)若底面有一动点M从A点出发在圆O上运动,过动点M的母线与截面
交于点N,设
,
,其中
.
①求
与
的函数关系;
②将圆柱
侧面沿母线
剪开并展平,请在所给的展开图中画出平面
截圆柱侧面的截痕,并建立适当的平面直角坐标系直接 写出其解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3671adea94a33848afff9b2edb6a902e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae781496bb5bc79b67abced9aa3cd0c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/e8c50ced-4ea3-475f-92fa-a78be6572be7.png?resizew=511)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa812513cb17ffa7901d1f5e3fb25c5.png)
(2)若底面有一动点M从A点出发在圆O上运动,过动点M的母线与截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d685845e1baa7e66d2502eebfcbb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914d142641c85ea5454b1eb05ac4204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d7581e52d1fa9eb225928fabd57fe9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②将圆柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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3 . 如图,从平面
外一点
,引射线
、
、
,在它们上面分别取点
、
、
,使得
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/84add72e-36fd-44dd-9ea4-470ff8224181.png?resizew=147)
(1)画出平面
并判断两个平面的位置关系;
(2)若点
到平面
的距离为2,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.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/e6c42149443e5eadab07087780ec7bec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/84add72e-36fd-44dd-9ea4-470ff8224181.png?resizew=147)
(1)画出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在三棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/68e3da10-b124-4ae1-96ab-6ef6e16e68d1.png?resizew=243)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/f5b1547a-91e7-45b6-9374-0e6c724a5534.png?resizew=276)
(1)根据图中所给主视方向,在下列方格纸(方格的单位长度为1)上已画出该三棱锥的主视图,请画出该三棱锥的左视图和俯视图;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ae8a050d7159d4296c2409e5bc0bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7898f562dffdf08263bfb0873e0691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/68e3da10-b124-4ae1-96ab-6ef6e16e68d1.png?resizew=243)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/f5b1547a-91e7-45b6-9374-0e6c724a5534.png?resizew=276)
(1)根据图中所给主视方向,在下列方格纸(方格的单位长度为1)上已画出该三棱锥的主视图,请画出该三棱锥的左视图和俯视图;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
您最近一年使用:0次
2021-07-24更新
|
98次组卷
|
2卷引用:江西师范大学附属中学2020-2021学年高二4月月考数学(文)试题