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1 . 在我国古代数学名著《九章算术》中,将底面为直角三角形,且侧棱垂直于底面的棱柱称为堑堵.已知在堑堵
中,
,
,
,则
与平面
所成角的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c7d01c3618d579121d95d41a63c565.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617a5dd99e43fa539f28a1234293f8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e434076ebf76bf0d1518a63cb0f92d5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 《九章算术》中将底面为长方形且有一条侧棱与底面垂直的四棱锥称之为阳马,将四个面都为直角三角形的四面体称之为鳖臑.在如下图所示的阳马P-ABCD中,侧棱
底面ABCD,且
,则当点E在下列四个位置:PA中点、PB中点、PC中点、PD中点时分别形成的四面体E-BCD中,鳖臑有
![](https://img.xkw.com/dksih/QBM/2020/3/11/2417270334832640/2418053776637952/STEM/2c87f5eb-b9ce-4712-9470-dcb89c6e5885.png?resizew=238)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c772949a7425943d058f513629c9a983.png)
![](https://img.xkw.com/dksih/QBM/2020/3/11/2417270334832640/2418053776637952/STEM/2c87f5eb-b9ce-4712-9470-dcb89c6e5885.png?resizew=238)
A.1个 | B.2个 | C.3个 | D.4个 |
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3 . 在
九章算术
中,将底面为长方形且有一条侧棱与底面垂直的四棱锥称之为阳马
如图,已知四棱锥
为阳马,且
,
底面
若E是线段AB上的点
含端点
,设SE与AD所成的角为
,SE与底面ABCD所成的角为
,二面角
的平面角为
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/a53c00d4-82fe-4179-8cfa-8723cf2acfaf.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d940f671bda7e5682583f996599e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d6117d3266ecb6784bcc6f7c77fd63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f08faa7f1550cb3732de12b2be5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb32dae6823f572ffa028d684733c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aad1b6aad765172a3a2ea2c96006836.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b314fdbf3f9ecbf94185687f642338a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/a53c00d4-82fe-4179-8cfa-8723cf2acfaf.png?resizew=175)
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【市级联考】浙江省宁波市2018学年高二第一学期期末考试数学试题浙江省绍兴市诸暨市诸暨中学2019-2020学年高二上学期10月月考数学试题(已下线)专题1 鳖臑阳马 巧用性质 讲(已下线)第四章 立体几何解题通法 专题五 平移变换法 微点2 平移变换法(二)【培优版】
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4 . 我国古代数学名著《九章算术》中有这样一些数学用语,“堑堵”意指底面为直角三角形,且侧棱垂直于底面的三棱柱,而“阳马”指底面为矩形且有一侧棱垂直于底面的四棱锥.现有一如图所示的“堑堵”
,
,若
,当“阳马”
体积最大时,则“堑堵”
的表面积为
![](https://img.xkw.com/dksih/QBM/2017/8/21/1757064628109312/1757729433903104/STEM/bd3873802f2f491b9b50c426f3498cf0.png?resizew=184)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0c82028e1259f300facd32775a15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/2017/8/21/1757064628109312/1757729433903104/STEM/bd3873802f2f491b9b50c426f3498cf0.png?resizew=184)
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5 . 《九章算术》中,将四个面都为直角三角形的四面体称之为鳖臑,如图2,在鳖臑PABC中,PA ⊥平面ABC,AB⊥BC,且AP=AC=1,过A点分别作AE⊥ PB于E、AF⊥PC于F,连接EF当△AEF的面积最大时,tan∠BPC的值是( )
![](https://img.xkw.com/dksih/QBM/2015/11/6/1572281287688192/1572281293520896/STEM/b92d749106e6477dba7639037c41b240.png?resizew=138)
![](https://img.xkw.com/dksih/QBM/2015/11/6/1572281287688192/1572281293520896/STEM/b92d749106e6477dba7639037c41b240.png?resizew=138)
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