如图,在四棱台
中,
底面
,M是
中点,四边形
为正方形,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2616713e2801e00bdcf4c9883f973b.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712436809400320/2716542322786304/STEM/af257467-2d63-45fc-828a-5680baac009d.png?resizew=295)
(Ⅰ)求证:直线
平面
;
(Ⅱ)求D点到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2616713e2801e00bdcf4c9883f973b.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712436809400320/2716542322786304/STEM/af257467-2d63-45fc-828a-5680baac009d.png?resizew=295)
(Ⅰ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2164a9dd77a54b1999a0f5ab0ecf09df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4a1f5a0cdcabfcb417d26f69b337de.png)
(Ⅱ)求D点到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4a1f5a0cdcabfcb417d26f69b337de.png)
更新时间:2021-05-08 11:22:24
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【推荐1】已知圆锥的体积为
,底面半径
与
互相垂直,且
;
是母线
的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/27/2601870764351488/2605516177252352/STEM/9c2fc2e5-070a-4360-bfee-762ec8712f71.png?resizew=235)
(1)求圆锥的表面积
(2)求异面直线
与
所成角的大小(结果用反三角函数表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f16e77b039842ae40a4b04c527655a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://img.xkw.com/dksih/QBM/2020/11/27/2601870764351488/2605516177252352/STEM/9c2fc2e5-070a-4360-bfee-762ec8712f71.png?resizew=235)
(1)求圆锥的表面积
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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【推荐2】如图,在三棱锥
中,平面
平面
,
为等边三角形,
且
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/b042ddb9-1035-4081-a182-3d97a09f60e5.png?resizew=164)
(1)求证:
平面
;
(2)求直线
和平面
所成角的正切值;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8704811c9c5dba854310ae0de2ba6b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7eaac66c8a1d94860390668ffecfaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bc7774144c164f7ebaeca54fa657e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/b042ddb9-1035-4081-a182-3d97a09f60e5.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d39135a2f8472d66ea00eda3b13ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526e2fe627bb4ddebe708c07d0a22fc.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526e2fe627bb4ddebe708c07d0a22fc.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3015d59da3d7abcb7814eecc375aa2d8.png)
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【推荐1】如图,在正方体
中,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/5c6f84f2-bb4e-42ec-9e40-ff5906242041.png?resizew=158)
(1)求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/5c6f84f2-bb4e-42ec-9e40-ff5906242041.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f1035b0c9b7127aa49b76707c8844.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370ad2e20e4d6eed9c2101209731a1f7.png)
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【推荐2】如图,已知正方体![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a11ad3ead3d14279df351b3ca55af3b.png)
![](https://img.xkw.com/dksih/QBM/2020/10/25/2578586259939328/2579425435672576/STEM/71d5eb2883ff480da12a1aaa7a55b74a.png?resizew=204)
(1)求异面直线
与
所成的角;
(2)证明:
平面ABCD;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a11ad3ead3d14279df351b3ca55af3b.png)
![](https://img.xkw.com/dksih/QBM/2020/10/25/2578586259939328/2579425435672576/STEM/71d5eb2883ff480da12a1aaa7a55b74a.png?resizew=204)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efd3ad8ddccdc251c85533353d2633f.png)
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【推荐1】如图,在矩形ABCD中,AB=2AD,E为AB的中点,N为BC的中点,沿DE将△ADE折起.若平面ADE⊥平面BCDE,求证:AB=AC.
![](https://img.xkw.com/dksih/QBM/2020/8/22/2533492318158848/2542350802624512/STEM/f2fccea46f4e40aa9c88f0c309cf962a.png?resizew=217)
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【推荐2】菱形
的边长为2,
,P为平面
外一点,若
平面
,
,求P到
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](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/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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