解题方法
1 . 用光线照射物体,在某个平面上得到的影子叫做物体的投影,照射光线叫做投影线,投影所在的平面叫做投影面.由平行光线形成的投影叫做平行投影,由点光源发出的光线形成的投影叫做中心投影.投影线垂直于投影面产生的平行投影叫做正投影,投影线不垂直于投影而产生的平行投影叫做斜投影.物体投影的形状、大小与它相对于投影面的位置和角度有关.如图所示,已知平行四边形
在平面
内的平行投影是四边形
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/71cf6fa5-9cb4-4d8d-a907-fa7ccdcd6d3d.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9fc4f21f-3f78-4976-887c-0642c3365737.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/462c058d-eb41-4d4a-ac0e-89fb806fef7a.png?resizew=314)
(1)若平行四边形
平行于投影面(如图
),求证:四边形
是平行四边形;
(2)在图
中作出平面
与平面
的交线(保留作图痕迹,不需要写出过程);
(3)如图
,已知四边形
和平行四边形
的面积分别为
,平面
与平面
的交线是直线
,且这个平行投影是正投影.设二面角
的平面角为
(
为锐角),猜想并写出角
的余弦值(用
表示),再给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/71cf6fa5-9cb4-4d8d-a907-fa7ccdcd6d3d.png?resizew=314)
图
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9fc4f21f-3f78-4976-887c-0642c3365737.png?resizew=314)
图
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/462c058d-eb41-4d4a-ac0e-89fb806fef7a.png?resizew=314)
图
(1)若平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
(2)在图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/7021666155884a8aa345ed8eec3d2a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
您最近一年使用:0次
名校
解题方法
2 . 如图1,在等腰梯形
中,
,
,
,
,E、F分别为腰
、
的中点.将四边形
沿
折起,使平面
平面
,如图2,H,M别线段
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/9066276c-44d7-477f-a965-e155543e93ed.png?resizew=413)
(1)求证:
平面
;
(2)请在图2所给的点中找出两个点,使得这两点所在直线与平面
垂直,并给出证明:
(3)若N为线段
中点,在直线
上是否存在点Q,使得
面
?如果存在,求出线段
的长度,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744c636a21ef089c9239eeafff4b83ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/9066276c-44d7-477f-a965-e155543e93ed.png?resizew=413)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a984e08781547575be9680e8c61bb21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d4b05a1402beb3f13d4ce7d22089b9.png)
(2)请在图2所给的点中找出两个点,使得这两点所在直线与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769f81c1b5a405e2e7eb78f199f9e6e.png)
(3)若N为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d42170c7d4249f6b390823606c18c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a158113467436c24c6db00f058cf91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769f81c1b5a405e2e7eb78f199f9e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
您最近一年使用:0次
2020-11-02更新
|
1357次组卷
|
4卷引用:北京市密云区2019-2020学年高一下学期数学期末试题
3 . 如图1,已知菱形
的对角线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178a2a5f277bab230e7e65ee5b8b53a1.png)
交于点
,点
为
的中点.将三角形
沿线段
折起到三角形
的位置,如图2所示.
(1)求证:
平面
;
(2)证明:平面
平面
;
(3)在线段
上是否分别存在点
,使得平面
平面
?若存在,请指出点
的位置,并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178a2a5f277bab230e7e65ee5b8b53a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/31/0c8ed141-e18a-444a-84f5-bac476792bec.png?resizew=363)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1457d2e76a5b86de1abf121c51eb9d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42bda8898cce4936691bb5ec6579c07c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbc9387f41c6f138c40de12588eb86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
您最近一年使用:0次
2018-05-04更新
|
1675次组卷
|
5卷引用:【全国市级联考】北京市海淀区2018届高三第二学期期末练习(二模)数学(文)试题
【全国市级联考】北京市海淀区2018届高三第二学期期末练习(二模)数学(文)试题(已下线)2018年10月11日 《每日一题》一轮复习理数-空间线面位置关系(2)(已下线)2018年10月17日 《每日一题》一轮复习(文数)-空间线面位置关系(2)苏教版(2019) 必修第二册 过关斩将 第13章 13.2 综合拔高练(已下线)第18讲 基本图形位置关系
4 . 如图,在三棱柱中,侧面
是矩形,
,
,
,且
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/6/fc5812d0-79a6-477a-bea9-a91a591417f8.png?resizew=149)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140088b0cb73812aa9d523c44559298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)设D是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
您最近一年使用:0次
2017-02-08更新
|
1511次组卷
|
4卷引用:【全国百强校】北京师范大学附属中学2019届高三(下)四月份月考数学(文科)试题(五)
2011·北京西城·一模
5 . 如图,
是边长为
的正方形,
平面
,
,
,
与平面
所成角为
.
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/c2dd45c4ba1646c69e090be9382caaf5.png)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)设点
是线段
上一个动点,试确定点
的位置,使得
平面
,并证明你的结论.
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/fe701b53575443c292db4d872e40ef05.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/2a3e33d681e842f8b71707d3b573487c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05638d82225327da27e5f916d2d4e747.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/fe701b53575443c292db4d872e40ef05.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/4ff673aaecc44d63acbd5c98d6eac0a3.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/527f9ac3d51e4280b1e8f14331835f42.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/b0a0b01103ed4e7b9373b12fcb75fef5.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/fe701b53575443c292db4d872e40ef05.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/7ae9bad96345493fb94386207d35553e.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/c2dd45c4ba1646c69e090be9382caaf5.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599b63c003aeb99d777e87182db8f019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(Ⅱ)求二面角
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/8162eff6ad1c42db89028790e9e2fb4f.png)
(Ⅲ)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
解题方法
6 . 已知四棱锥
的底面为直角梯形,
,
,
,平面
平面
,
是
的中点.
(1)求证:
平面
;
(2)求证:
平面
;
(3)设棱
与平面
交于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71622531dfa894f21b2da123d020d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/2f07fa32-2d6f-4d32-bba7-631bc7b108d3.png?resizew=252)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa14afe6f0aad22e8e869c39a60be657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)设棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50cafe199913787a939fe9e100924023.png)
您最近一年使用:0次
2023-07-10更新
|
1168次组卷
|
3卷引用:北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题
北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题【北京专用】专题14立体几何与空间向量(第三部分)-高一下学期名校期末好题汇编(已下线)专题06 空间中点线面的位置关系6种常考题型归类(2) -期期末真题分类汇编(北京专用)
名校
解题方法
7 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,
为棱
的中点.
(1)证明:
∥平面
;
(2)若
,
,
(i)求二面角
的余弦值;
(ii)在线段
上是否存在点
,使得点
到平面
的距离是
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67284a0d23bbc582d6d1fb0e72d912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b624742fe28db114e0554c6c87bff05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/f851b1d9-e23c-4572-aa2b-8143178ac69f.png?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ee7262d0b5cbbade014e07e7373501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
(i)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b270c5d399f46eb9048aeebf7a1fe174.png)
(ii)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c76e558109d9b8dd700c1a7f9cc73ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bae31b0483451fa72e8ede6d280b43.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,四棱锥
的底面为菱形,
,
,
底面
,
,
分别是线段
,
的中点,
是线段
上的一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/995042db-ddac-4478-a675-e326cde38a77.png?resizew=142)
(1)若
平面
,求证:
为
的中点;
(2)若
是直线
与平面
的交点,试确定
的值;
(3)若直线
与平面
所成角的正弦值为
,求三棱锥
体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b5d2943803894bc5d204e75e2d172b.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/995042db-ddac-4478-a675-e326cde38a77.png?resizew=142)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dace90bcafd1fbf25f272b05c3875f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b544c9dfc27b50fcde4b12d694c12ad4.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bbc7e0de28c652ae10a8db5b4e2687.png)
您最近一年使用:0次
名校
9 . 如图,在三棱柱
中,四边形
是边长为4的菱形,
,点D为棱AC上动点(不与A,C重合),平面
与棱
交于点E.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/d24c04ce-db04-4e92-8d11-2c9457388807.png?resizew=216)
(1)求证:
;
(2)若
,从条件①、条件②、条件③这三个条件中选择两个条件作为已知,求直线AB与平面
所成角的正弦值.条件①:平面
平面
;条件②:
;条件③:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf3bff56a7f4ab6c0008e90823025d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445cfd832967db6bbaa0a2ea311b4f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f31a48422525cb066a51b5b6a6673e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a81eb09967a29554c7476e02eae551c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b10b969819d397711310c8dbb399ebc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/d24c04ce-db04-4e92-8d11-2c9457388807.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271bf95761d1cc26b4106214f4166af5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f085f65b6f426a24b1653dbfec7d70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6ca194414a76b40f936e097c504e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0b2a4616dbc8c104bbb1cf9ec211d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445cfd832967db6bbaa0a2ea311b4f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4625ece44b3a06dc5968e71e1870e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc7e2ffe38421dbaf2b7658cafc6dbe.png)
您最近一年使用:0次
2022-10-20更新
|
2788次组卷
|
15卷引用:北京市西城区2022届高三二模数学试题
北京市西城区2022届高三二模数学试题北京市昌平区第二中学2022-2023学年高二上学期10月月考数学试题北京市第五十七中学2022-2023学年高二上学期10月月考数学试题北京市东城区2023届高三一模数学试题查漏补缺练习试题(2)(已下线)2022年新高考北京数学高考真题变式题9-12题空间向量与立体几何中的高考新题型(已下线)2022年新高考北京数学高考真题变式题16-18题全国大联考2023届高三第四次联考数学试卷(已下线)专题8-2 立体几何中的角和距离问题(含探索性问题)-3(已下线)北京市西城区2022届高三二模数学试题变式题16-21(已下线)模块十一 立体几何-2重庆市第八中学校2022届高三下学期高考考前模拟数学试题(已下线)模块六 专题8 易错题目重组卷(重庆卷)陕西省延安市宜川县中学2023届高三一模理科数学试题(已下线)专题4 大题分类练(空间向量与立体几何)拔高能力练 高二期末
名校
解题方法
10 . 如图,已知直三棱柱
,
,
,
,点
为
的中点.
平面
;
(2)求直线
与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
2022-11-08更新
|
1089次组卷
|
5卷引用:北京市丰台区2022-2023学年高二上学期期中练习数学(A卷)试题
北京市丰台区2022-2023学年高二上学期期中练习数学(A卷)试题河北省唐山市第二中学2022-2023学年高一下学期期末数学试题(已下线)专题1 立体几何与解三角形(已下线)重难点专题15 空间中的五种距离问题-【帮课堂】(苏教版2019必修第二册)(已下线)第11章:立体几何初步章末重点题型复习(2)-【帮课堂】(人教B版2019必修第四册)