名校
解题方法
1 . 如图正方体
的棱长为2,E是棱
的中点,过
的平面与棱
相交于点F.
(1)求证:F是
的中点;
(2)求点D到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/7a361594-95fa-43fe-b243-c60ec9d41799.png?resizew=161)
(1)求证:F是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
(2)求点D到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次
2023-11-24更新
|
892次组卷
|
4卷引用:重庆市巴蜀中学2023-2024学年高二上学期期中考试数学试卷
重庆市巴蜀中学2023-2024学年高二上学期期中考试数学试卷(已下线)考点11 空间距离 2024届高考数学考点总动员【练】四川省成都市棠湖外国语学校2023-2024学年高二上学期期末模拟质量检测数学试题北京市石景山区2023-2024学年高二上学期期末考试数学试卷
名校
解题方法
2 . 如图,在四棱锥
中,底面
是矩形,其中
,
,
底面
,
,
为
的中点,
为
的中点.
(1)证明:直线
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/68e9d843-fc85-4db1-837e-3af70dd6a431.png?resizew=144)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
您最近一年使用:0次
2023-10-18更新
|
821次组卷
|
2卷引用:四川省成都市金牛区成都七中万达学校2023-2024学年高三上学期期中文数试题
名校
解题方法
3 . 如图,斜三棱柱
中,D,
分别为AC,
上的点.
时,求证
平面
;
(2)若平面
平面
,求
的值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaadcb31e5284b68f1c99238cd6c843a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5b4c6d737d013ffb500f0eb7fd8611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424dd73a238dad799c9296e9ff829253.png)
您最近一年使用:0次
2023-06-20更新
|
708次组卷
|
5卷引用:浙江省杭州市六县九校联考2022-2023学年高一下学期4月期中数学试题
浙江省杭州市六县九校联考2022-2023学年高一下学期4月期中数学试题广东省广州市广雅中学2023-2024学年高一下学期期中数学试题(已下线)8.5.3 平面与平面平行(第2课时) 平面与平面平行的性质(分层作业)-【上好课】(已下线)专题19 平面与平面平行-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)
名校
4 . 如图,在四面体
中,
平面
是
的中点,
是
的中点,点
满足
.
(1)证明:
平面
;
(2)若
与平面
所成的角大小为
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999c8f0e34d080fbbc53f97e5317bbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91f0750166d53342ab1db4f85dee0f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/acb00f66-5b21-4743-843c-eed0ccffedfd.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-11-11更新
|
212次组卷
|
2卷引用:浙江省浙东北联盟(ZDB)2023-2024学年高二上学期期中数学试题
5 . 如图,在四棱锥
中,
底面
,
分别为
的中点.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求二面角
的余弦值.
![](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/657232c1d8b201d49c98659d218a9e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7631a5587cdcb6c1f2350955f8709d68.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/2/2258118c-3370-4abe-9c68-6d18c179941d.png?resizew=177)
(1)证明:
![](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/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f9bc6bf8ca426813d10b6db2e32d26.png)
您最近一年使用:0次
2023-08-31更新
|
429次组卷
|
2卷引用:四川省成都市彭州市2023-2024学年上学期高三期中考试数学(理科)试题
解题方法
6 . 如图,在正三棱柱
中,
是线段
上靠近点
的一个三等分点,
是
的中点.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/21/2281cca6-e4e0-42da-8a6c-49c5d9655e79.png?resizew=134)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565517c781e119de8d8e9c9f29e4e2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
2023-06-18更新
|
721次组卷
|
7卷引用:云南省楚雄州2022-2023学年高二下学期期中教育学业质量监测数学试题
云南省楚雄州2022-2023学年高二下学期期中教育学业质量监测数学试题(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)(已下线)1.4 空间向量应用(精讲)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)第06讲 1.4.2用空间向量研究距离、夹角问题(1)(已下线)1.4.2用空间向量研究距离、夹角问题(第1课时)湖南省株洲市炎陵县2023-2024学年高二上学期10月素质检测数学试题(已下线)专题06 用空间向量研究距离、夹角问题10种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
解题方法
7 . 如图为一个组合体,其底面
为正方形,
平面
,
,且
.
(1)证明:
平面
;
(2)证明:
平面
;
(3)求该组合体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73f874048f9e48ae35ee95bbf443bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3b89860bcc3e950f1b21575579d8bb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/9/9dc94746-58f1-43de-bf25-97ba64a153a3.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564376a88fa74090de9f7694226a6184.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)求该组合体的表面积.
您最近一年使用:0次
名校
8 . 如图所示,等边
所在平面与菱形
所在平面相垂直,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b85d7d422571c4cc3aa5e09505fd67.png)
平面
;
(2)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba4d0b54a0b2104e1c3a2061e4bffc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9087c01257b50f3bb8b6490d8804dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b85d7d422571c4cc3aa5e09505fd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2023-08-16更新
|
528次组卷
|
2卷引用:福建省厦门第一中学2022-2023学年高二下学期期中数学试题
名校
解题方法
9 . 如图,在棱长为2的正方体
中,P,Q分别是棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/adfe99d3-5f97-4225-b6bc-09af8ec54f10.png?resizew=147)
(1)若
为棱
上靠近
点的四等分点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
平面PQC;
(2)若平面PQC与直线
交于
点,求平面PRQC将正方体分割成的上、下两部分的体积之比.(不必说明画法与理由).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/adfe99d3-5f97-4225-b6bc-09af8ec54f10.png?resizew=147)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)若平面PQC与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
您最近一年使用:0次
名校
解题方法
10 . 三棱柱
的棱长都为2,D和E分别是
和
的中点.
平面
;
(2)若
,点B到平面
的距离为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a57dfb78e8579cc68dbfca90f80a1c5.png)
您最近一年使用:0次
2023-04-21更新
|
2344次组卷
|
6卷引用:浙江省杭州第二中学等四校联盟2022-2023学年高一下学期期中联考数学试题
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