如图四边形ABCD是矩形,
平面BCE,
,点F为线段BE的中点.
平面ABE;
(2)求证:
平面ACF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fb90434b6da93bdc6590f769ef118b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
22-23高一下·四川成都·期末 查看更多[5]
四川省成都市实验外国语学校2022-2023学年高一下学期期末数学试题湖南师范大学附属中学2022-2023学年高一下学期第二次大练习数学试题(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(2)江苏省徐州市沛县2022-2023学年高一下学期第二次学情调研数学试题(已下线)专题训练:线线、线面、面面平行与垂直证明大题-同步题型分类归纳讲与练(人教A版2019必修第二册)
更新时间:2023-06-11 16:56:47
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解答题-证明题
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解题方法
【推荐1】已知四棱柱
的所有棱长均为2,
平面
,E为
的中点,F为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/3/2864573563969536/2864614014296064/STEM/f414f44e-bc88-475d-a249-7052470b8982.png?resizew=274)
(1)求证:
//平面
;
(2)若直线
与平面
所成的角为
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2021/12/3/2864573563969536/2864614014296064/STEM/f414f44e-bc88-475d-a249-7052470b8982.png?resizew=274)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
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【推荐2】如图,在直三棱柱ADE-BCF中,平面ABFE和平面ABCD都是正方形且互相垂直,点M为AB的中点,点O为DF的中点.证明:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/7d10cd3f-da94-4209-8a6d-f5404345b601.png?resizew=154)
(1)OM∥平面BCF;
(2)平面MDF⊥平面EFCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/7d10cd3f-da94-4209-8a6d-f5404345b601.png?resizew=154)
(1)OM∥平面BCF;
(2)平面MDF⊥平面EFCD.
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【推荐1】如图,在正三棱柱
中,
分别为
的中点.
(1)证明:平面
平面
.
(2)若侧面
的中心为
为侧面
内的一个动点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
平面
,且
的轨迹长度为
,求三棱柱
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1394b37d41901748bc3c5643b58c812c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce21311bf50215101b605356358b9a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/17/bd5e334f-3f17-4af6-9764-92df8259b817.png?resizew=139)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3b56a19d400eb5ce0b5a8744c27d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef19f98e86ae7504671413780b3b1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af2fdf1944afebb51cb6a5e6c74aadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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【推荐2】如图所示,在正方体ABCD-A1B1C1D1中,M、N分别为A1C、BC1的中点.求证:
![](https://img.xkw.com/dksih/QBM/2021/4/13/2698985168470016/2807068634955776/STEM/9fee836c-841b-4430-8cfa-e5f0dd4b7d93.png?resizew=262)
(1)MN∥平面A1B1C1D1;
(2)A1C⊥平面BDC1.
![](https://img.xkw.com/dksih/QBM/2021/4/13/2698985168470016/2807068634955776/STEM/9fee836c-841b-4430-8cfa-e5f0dd4b7d93.png?resizew=262)
(1)MN∥平面A1B1C1D1;
(2)A1C⊥平面BDC1.
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