长方体
中,
,
.点
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/a5b069ed-227e-4938-9540-a82305a05945.png?resizew=158)
(1)求证:
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f4df0a32a910db7d39695ffd86665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/a5b069ed-227e-4938-9540-a82305a05945.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f11f1840eb8b17e7b07c3fe7e987a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
23-24高二上·广东江门·期中 查看更多[3]
广东省江门市台山市华侨中学2023-2024学年高二上学期期中数学试题(已下线)第6章 空间向量与立体几何 章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)(已下线)3.4.1 判断空间直线、平面的位置关系(六大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
更新时间:2023-12-01 22:14:37
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解答题-证明题
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【推荐1】如图,四棱锥
中,
平面
,底面
是正方形,且
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/dae97294-dae5-488b-9b46-f7916b53d34b.png?resizew=168)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eebf6d56f8385a3f0b8bf92fce137bb.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/99926bf272cd757f0985c69b390ebcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/dae97294-dae5-488b-9b46-f7916b53d34b.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab8a10e675354fa0c6e7da3d06b999d.png)
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【推荐2】如图,在四面体
中,
,
分别是线段
,
的中点,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/253139bc-3d0b-4508-b21f-ae6fc83ea8fd.png?resizew=156)
(1)证明:EF⊥平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3681efc3c5f6ea6bf6a2e072eac3fd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6691f794110163cc99c81a11a720912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a05e0ab55e325fb3b85fc8ca9c27c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bd96607d65cb403490f7dc32e1150e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/253139bc-3d0b-4508-b21f-ae6fc83ea8fd.png?resizew=156)
(1)证明:EF⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0f73cf7ab0c2a8a0099cb2873c81f4.png)
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【推荐3】已知正方体
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/c5ceebea-29c3-4668-aa0e-0c6550db3d26.png?resizew=170)
(1)求异面直线
与
所成角的大小;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/c5ceebea-29c3-4668-aa0e-0c6550db3d26.png?resizew=170)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9756b7c2a9f0cb5a1b025ad4821abdcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14463d09a4b1755f877c466e31d39259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b3b1cac8011583d3f5fe5d6eaa4a17.png)
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解题方法
【推荐1】如图三棱柱
中,
和
是等边三角形.
,
分别为棱
,
的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/93b5f0b2-f62d-40bb-9fa4-b2f16a7b1d53.png?resizew=167)
(Ⅰ)若三棱柱
的体积为3,求
;
(Ⅱ)在线段
上是否存在点
,使得
平面
,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166ccfa0ac0388903f3f5960c7fa3660.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/93b5f0b2-f62d-40bb-9fa4-b2f16a7b1d53.png?resizew=167)
(Ⅰ)若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(Ⅱ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2fef2c0e49ecae8688ca60802310e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
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【推荐2】设直线l同时垂直于平面
内两条相交的直线a,b.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749a36b37211099584b1e475b327a2b7.png)
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