名校
解题方法
1 . 如图,直角三角形ABC中,A=60°,沿斜边AC上的高BD将△ABD折起到△PBD的位置,点E在线段CD上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/189a2db1-3531-4755-a08c-5e7652ab7508.png?resizew=262)
(1)求证:PE⊥BD;
(2)过点D作DM⊥BC交BC于点M,点N为PB的中点,若
平面DMN,求
的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/189a2db1-3531-4755-a08c-5e7652ab7508.png?resizew=262)
(1)求证:PE⊥BD;
(2)过点D作DM⊥BC交BC于点M,点N为PB的中点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f79db7c270b6ff9fb0a538ee201cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7558aa5068ceb3d3a35bf56422418dea.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,
底面
,底面
是边长为1的菱形,
,
,
为
的中点,
为
的中点,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2021/12/18/2875341980663808/2912805677457408/STEM/ae324d00-37e8-4ba5-b126-1968ee4053cd.png?resizew=169)
(1)求证:
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.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/6afaa76e94414331574f42873e2b12c3.png)
![](https://img.xkw.com/dksih/QBM/2021/12/18/2875341980663808/2912805677457408/STEM/ae324d00-37e8-4ba5-b126-1968ee4053cd.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a407b262c22419f73396170ecdc849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
3 . 如图,四边形ABCD与BDEF均为菱形,且
,平面
平面BDEF,AC与BD交于点O.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/62c56c30-1143-4ea3-bde6-39d97a268ef8.png?resizew=158)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
平面FBC;
(2)求平面AFC与平面BFC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd3ed8807db1250667c70433e1b6f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/62c56c30-1143-4ea3-bde6-39d97a268ef8.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)求平面AFC与平面BFC夹角的余弦值.
您最近一年使用:0次
4 . 如图,在三棱柱
中,
,
,
分别为
,
,
的中点.
平面
;
(2)若平面
,求证:
为
的中点.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5655d18106ff98a1dc175a876facc40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedd56d72ca44daabb3a1afa3253d6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2022-09-14更新
|
2531次组卷
|
27卷引用:安徽省滁州市定远县育才学校2021-2022学年高一下学期第二次月考数学试题
安徽省滁州市定远县育才学校2021-2022学年高一下学期第二次月考数学试题【市级联考】江苏省苏州市常熟市2018-2019学年高二(上)期中数学试卷人教A版(2019) 必修第二册 突围者 第八章 第五节 课时3 平面与平面平行(已下线)考点22 空间几何平行问题(练习)-2021年高考数学复习一轮复习笔记山西省山西大学附中2019-2020学年高二上学期10月模块诊断数学试题江西省赣州市赣县区第三中学2020-2021学年高二(零班,奥数班)九月月考数学(文)试题(已下线)专题8.4 直线、平面平行的判定及性质(讲)-2021年新高考数学一轮复习讲练测广东省连平县忠信中学2020-2021学年高一下学期第二次段考数学试题河北省石家庄市元氏县第四中学2020-2021学年高一下学期期中数学试题(已下线)专题8.4 直线、平面平行的判定及性质(讲)- 2022年高考数学一轮复习讲练测(新教材新高考)人教A版(2019) 必修第二册 实战演练 第八章 课时练习28 平面与平面平行(已下线)押全国卷(文科)第19题 立体几何-备战2022年高考数学(文)临考题号押题(全国卷)苏教版(2019) 必修第二册 必杀技 第13章 立体几何初步 13.2 基本图形位置关系 13.2.4 平面与平面的位置关系 课时1 两平面平行(已下线)第47讲 直线与平面、平面与平面平行山东省潍坊高密市第三中学2022-2023学年高二上学期9月月考数学试题(已下线)空间直线、平面的平行(已下线)8.5 空间直线、平面的平行(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)第八章立体几何初步章末题型大总结(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)第26讲 空间直线、平面的平行的判定4种常见方法(已下线)专题20 空间几何解答题(文科)-3北京市良乡附中2022-2023学年高一6月月考数学试题江西省吉安市泰和中学2022-2023学年高一下学期7月月考数学试题江苏省苏州市苏州园三中2022-2023学年高一下学期5月月考数学试题(已下线)第十三章 立体几何初步(压轴题专练)-单元速记·巧练(苏教版2019必修第二册)(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)8.5.3 平面与平面平行【第一课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)8.5.3 平面与平面平行【第二练】“上好三节课,做好三套题“高中数学素养晋级之路
名校
5 . 如图,多面体ABCDEF中,DE⊥平面ABCD,底面ABCD是菱形,AB=2,∠BAD=60°,四边形BDEF是正方形.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854712830689280/2857331093274624/STEM/7aa19aee-ce29-46f3-b057-822b4ac118c0.png?resizew=258)
(1)求证;CF∥平面AED;
(2)求直线AF与平面ECF所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854712830689280/2857331093274624/STEM/7aa19aee-ce29-46f3-b057-822b4ac118c0.png?resizew=258)
(1)求证;CF∥平面AED;
(2)求直线AF与平面ECF所成角的正弦值.
您最近一年使用:0次
2021-11-23更新
|
314次组卷
|
4卷引用:安徽省宿州市砀山中学2021-2022学年高二上学期第一次质量检测数学试题
名校
6 . 如图,已知
为正三角形,D为AB的中点,E在AC上,且
,现沿DE将
折起,折起过程中点A仍然记作点A,使得平面
平面BCED,在折起后的图形中.
![](https://img.xkw.com/dksih/QBM/2021/9/13/2807128439554048/2815225309601792/STEM/80d94deb-2f09-4c04-872f-88daac4f7a21.png?resizew=472)
(1)在AC上是否存在点M,使得直线
平面ABD.若存在,求出点M的位置;若不存在,说明理由.
(2)求平面ABD与平面ACE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8f6c9335373be2e09046a1e51424f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://img.xkw.com/dksih/QBM/2021/9/13/2807128439554048/2815225309601792/STEM/80d94deb-2f09-4c04-872f-88daac4f7a21.png?resizew=472)
(1)在AC上是否存在点M,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfed58659a9cab4d1836c3d2effdc.png)
(2)求平面ABD与平面ACE所成锐二面角的余弦值.
您最近一年使用:0次
2021-09-24更新
|
526次组卷
|
2卷引用:安徽省宿州市砀山中学2021-2022学年高二上学期第一次质量检测数学试题
7 . 如图,
是圆柱的母线,边长为4的正
是该圆柱的下底面的内接三角形,
,
,
分别为
,
,
的中点,
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6f4f1c5f-a4f5-41c5-9d90-4de27f5f50ad.png?resizew=159)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602ee324ca5bc3cf9ef251a061b431ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6f4f1c5f-a4f5-41c5-9d90-4de27f5f50ad.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b859ca54ab085edf70c1179a7d103a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2021-08-13更新
|
155次组卷
|
2卷引用:安徽省六安市舒城中学、安庆市太湖中学2020-2021学年高二下学期期中联考理科数学试题
名校
解题方法
8 . 如图所示,几何体
中,
是正三角形,
,
均与面
垂直,且
,点
、
分别在棱
、
上,满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4aff93f7-04da-42a1-91d5-133bd6c8e11a.png?resizew=169)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1d97b95bccd80f06c3af864897da9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a798ddf34f0fed7cb1616228cc88936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65734b86acbb1df7057b72cbf6dcb4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4aff93f7-04da-42a1-91d5-133bd6c8e11a.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9c68879985182b4de065c552cb8e31.png)
您最近一年使用:0次
2021-07-15更新
|
390次组卷
|
2卷引用:安徽省滁州市定远县育才学校2021-2022学年高三下学期期中考试数学(文)试题
解题方法
9 . 如图,在正方体
中,M为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/1972fb34-f7ba-4c4b-9e6e-4832732872f9.png?resizew=146)
(1)试作出平面
与平面
的交线l,并说明理由;
(2)用平面
去截正方体,所得两部分几何体的体积分别为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/1972fb34-f7ba-4c4b-9e6e-4832732872f9.png?resizew=146)
(1)试作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e729d9e7acf6f180c311622c251fd30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)用平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e729d9e7acf6f180c311622c251fd30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef9b28d27417e49032fddbf8b4a64af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
您最近一年使用:0次
2021-07-10更新
|
537次组卷
|
3卷引用:安徽省皖八联盟2020-2021学年高一下学期统测数学试题
10 . 如图,矩形
垂直于直角梯形
,
,
,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/31/2732913818542080/2761292788105216/STEM/33d803df-9d25-4503-9bb6-67fce113b5a5.png?resizew=314)
(1)求证:
平面
;
(2)若
,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d72301ad8436f48383a747b8e067dae.png)
![](https://img.xkw.com/dksih/QBM/2021/5/31/2732913818542080/2761292788105216/STEM/33d803df-9d25-4503-9bb6-67fce113b5a5.png?resizew=314)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7e48723871f06a6aeae31a2a1ff79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
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