如图,在正四棱台
中
分别为棱
,
的中点.证明:
四点共面;
(2)多面体
是三棱台.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46cd8de9db59ffe9e35401d5eb2a8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29e9b2ce4da8f9ce0795ae3f01e9e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
(2)多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125e43399d640dda4c00dc33ea0f696e.png)
更新时间:2024-05-08 17:43:59
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解答题-证明题
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【推荐1】(1)求证:三棱台
三条侧棱延长后相交于一点;
(2)三棱锥
中,D,E分别为PB,PC的中点,记三棱锥
的体积为
,
的体积为
,求
的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/93080a86-0696-45e9-95ef-d631cc55e168.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
(2)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f03e26e0050618bb006279fb75f4138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf19bc83893610b85997dcd220d95bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/93080a86-0696-45e9-95ef-d631cc55e168.png?resizew=170)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/c828fe80-1532-40ae-bf70-aaf6e3555d98.png?resizew=209)
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【推荐1】如图所示的一块木料中,
面
,
为面
内一点,现要用经过
和棱
的一个平面将木料锯开,该如何画线?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/77c337b5-10d6-4782-9a6f-7499c8df9f87.png?resizew=200)
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解题方法
【推荐2】正方体
中, M,N ,Q ,P 分别是AB ,BC ,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/fe44af6c-ee5e-4181-98d6-e8adc3644afb.png?resizew=153)
(1)证明:M,N ,Q ,P 四点共面.
(2) 证明:PQ,MN ,DC三线共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/fe44af6c-ee5e-4181-98d6-e8adc3644afb.png?resizew=153)
(1)证明:M,N ,Q ,P 四点共面.
(2) 证明:PQ,MN ,DC三线共点.
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【推荐1】在四面体
中,
,
分别是
,
的中点,
,
分别是边
,
上的点,且
.求证:
,
,
,
四点共面;
(2)直线
,
,
相交于一点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65817cfd7cbcea8e49033f93cb8e8cfe.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/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
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【推荐2】如图,在空间四边形ABCD中,E,F分别是AB和CB上的点,G,H分别是CD和AD上的点,且
,
.
求证:EH,BD,FG三条直线相交于同一点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a92f96a5660e4c97f9e27e1c82678f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4d4ba88e25b7277a15a6c3d81ce940.png)
求证:EH,BD,FG三条直线相交于同一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/95d8e6dd-245b-47b2-889b-3443e3effb1e.png?resizew=178)
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