解题方法
1 . 如图,四棱锥
中,
平面ABCD,底面ABCD是直角梯形,
,
,
,
,
,点E在棱PC上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/775d8a54-18b2-4ac5-98e2-26dc125f4f65.png?resizew=170)
(1)证明:平面
平面PAB;
(2)已知点E是棱PC上靠近点P的三等分点,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/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/775d8a54-18b2-4ac5-98e2-26dc125f4f65.png?resizew=170)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.png)
(2)已知点E是棱PC上靠近点P的三等分点,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeab80976db9b4689b9446cda06196a.png)
您最近一年使用:0次
2023-01-15更新
|
568次组卷
|
2卷引用:云南省昭通市永善县知临中学2023届高三下学期3月月考数学试题
解题方法
2 . 如图所示,在直角梯形
中,
,
,
分别是
,
上的点,
,且
(如图甲),将四边形
沿
折起,连接
,
,
(如图乙).
(1)判断四边形
是否是平面四边形,并写出判断理由;
(2)当
时,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb18f3937480ab5ad6cf0d65a357c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03adecaa4d13a1cce20d422c4f1ee869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/b6388949-d623-4918-90fc-1558d8461886.png?resizew=356)
(1)判断四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1be2a5bfe8bab50cb68fe52d0f92ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
3 . 如图,
为圆
的直径,点
在圆
上,且
为等腰梯形,矩形
和圆
所在的平面互相垂直,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/7/4f34f281-e539-40ec-87e0-bc0db3fc82da.png?resizew=153)
(1)求证:平面
平面
;
(2)当
的长为何值时,二面角
的大小为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fb67185648985ee00f25b3332d7690.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/7/4f34f281-e539-40ec-87e0-bc0db3fc82da.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630675e0bd82419bc787b557181303d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603c7e98deecdba0cf3773757a9b8304.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d733daf111889f16d5404b731d40fd12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
您最近一年使用:0次
2023-02-04更新
|
982次组卷
|
3卷引用:云南省昭通市巧家县第一中学2023届高三数学省测模拟试题
解题方法
4 . 一个几何体的三视图如图所示,则该几何体表面两两垂直的平面共有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/7b63229f-64e0-4c5d-8729-0a19847720f7.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/7b63229f-64e0-4c5d-8729-0a19847720f7.png?resizew=136)
A.5对 | B.4对 | C.3对 | D.6对 |
您最近一年使用:0次
5 . 如图,在底面为正三角形且侧棱垂直于底面的三棱柱
中,
,
分别是
,
的中点.求证:
(1)平面
‖平面
;
(2)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
(1)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223b0eb54c1e71f75e58e64a19d169f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161a4660d3a35f0de6af3d9068cf7bea.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497fcba48527feaff406cbddea38ceb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/2d0c37bd-0fb6-4c0a-9883-ba8074cd030c.png?resizew=147)
您最近一年使用:0次
2021-08-09更新
|
312次组卷
|
5卷引用:云南省昭通市绥江县第一中学2020-2021学年高二上学期第一次月考数学试题
云南省昭通市绥江县第一中学2020-2021学年高二上学期第一次月考数学试题云南省弥勒市第一中学2020-2021学年高一下学期第三次月考数学试题云南省巍山彝族回族自治县第二中学2020-2021学年高一下学期第三次月考数学试题(已下线)专题8.5 直线、平面垂直的判定及性质(练)- 2022年高考数学一轮复习讲练测(新教材新高考)云南省曲靖天人高级中学2022-2023学年高一下学期期中考试数学试题
名校
解题方法
6 . 已知在六面体PABCDE中,PA⊥平面ABCD,ED⊥平面ABCD,且PA=2ED,底面ABCD为菱形,且∠ABC=60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/ec7404f9-d7a0-4031-bbd2-a9c08e9bac87.png?resizew=213)
(1)求证:平面PAC⊥平面PBD;
(2)若直线PC与平面ABCD所成角为45°,试问:在线段PE上是否存在点M,使二面角P﹣AC﹣M为60°?若存在,确定点M的位置;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/ec7404f9-d7a0-4031-bbd2-a9c08e9bac87.png?resizew=213)
(1)求证:平面PAC⊥平面PBD;
(2)若直线PC与平面ABCD所成角为45°,试问:在线段PE上是否存在点M,使二面角P﹣AC﹣M为60°?若存在,确定点M的位置;若不存在,请说明理由.
您最近一年使用:0次
2021-08-07更新
|
460次组卷
|
5卷引用:云南省云天化中学2022届高三摸底测试数学(理)试题
云南省云天化中学2022届高三摸底测试数学(理)试题云南省水富县云天化中学2020-2021学年高二下学期期末数学(理)试题2021年高考理科数学预测押题密卷Ⅰ卷(已下线)押第19题 立体几何-备战2021年高考数学(理)临考题号押题(全国卷2)(已下线)专题02 立体几何中存在性问题的向量解法-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)
名校
解题方法
7 . 如图1,在
中,
,
,
别为边BM,MC的中点,将
沿AD折起到
的位置,使
,如图2,连结PB,PC.
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646623838511104/2646806049964032/STEM/2c34396b-fab4-45ca-be8b-6c6ecc6cd7f1.png)
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646623838511104/2646806049964032/STEM/4c9c24b0-7a51-4a4a-ae52-3211780f01a7.png)
(1)求证:平面
平面ABCD;
(2)线段PC上是否存在一点E,使二面角
的余弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad3e2b2689dfe97ec82d473ab6cf469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f8ec91ebf38b062920cbebce3e8be7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acea3c19d0ff7d15fd0b1c9f38410db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cbf03524f866cc66d019a01e7c4284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f17680a23635f823b7dc446e4f3b0a.png)
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646623838511104/2646806049964032/STEM/2c34396b-fab4-45ca-be8b-6c6ecc6cd7f1.png)
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646623838511104/2646806049964032/STEM/4c9c24b0-7a51-4a4a-ae52-3211780f01a7.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
(2)线段PC上是否存在一点E,使二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf126ef95080e8caa2b862122ab5d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4c04c86cd24080e84cef166c9ce556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add47889f6b4911133999a898d3666d3.png)
您最近一年使用:0次
2021-01-29更新
|
591次组卷
|
5卷引用:云南省昭通市昭通一中教研联盟2023-2024学年高二上学期10月期中质量检测数学试题(B卷)
8 . 如图,三棱锥
,
均为底面边长为
、侧棱长为
的正棱锥,且四边形
是边长为
的菱形(点
在平面
的同侧),
交于点
.
![](https://img.xkw.com/dksih/QBM/2020/12/15/2614849631830016/2619044939759616/STEM/8fb7ca49-92d8-407c-92aa-2383d1ba9568.png)
(1)证明:平面
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ccef06bd7c89746239123517347c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2020/12/15/2614849631830016/2619044939759616/STEM/8fb7ca49-92d8-407c-92aa-2383d1ba9568.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61259bb537ac8eb81986f45d60555733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee188333e1fa99417aede565c6a4a136.png)
您最近一年使用:0次
2020-12-21更新
|
761次组卷
|
2卷引用:云南省云天化中学2022届高三摸底测试数学(文)试题
9 . 如图,在三棱柱
中,
,
平面
,
,
.
(1)证明:平面
平面
;
(2)求三棱锥
的体积.
![](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/9e16f65c3a318220c2f5baac171bbb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/4479a1df-3c26-4665-9631-8a5fa483250f.png?resizew=186)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767c061dd96dfaaa7fa1acdbee764ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdaa8065bea92fe61bce56090d8cb235.png)
您最近一年使用:0次
2020-10-10更新
|
476次组卷
|
2卷引用:云南省昭通市绥江县第一中学2020-2021学年高二上学期期末考试数学试题
名校
10 . 如图,四棱锥S-ABCD的底面是边长为1的正方形,则棱SB垂直于底面.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/f84654c9-fa4d-4565-8735-080acb459d4f.png?resizew=146)
(1)求证:平面SBD⊥平面SAC;
(2)若SA与平面SCD所成角的正弦值为
,求SB的长.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/f84654c9-fa4d-4565-8735-080acb459d4f.png?resizew=146)
(1)求证:平面SBD⊥平面SAC;
(2)若SA与平面SCD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
您最近一年使用:0次
2019-12-16更新
|
187次组卷
|
2卷引用:云南省昭通市昭阳区第一中学2019-2020学年高一下学期第一次月考数学试题