1 . 阳马,中国古代算数中的一种几何形体,是底面为长方形,两个三角面与底面垂直的四棱锥体.如图,四棱锥P-ABCD就是阳马结构,PD⊥平面ABCD,且
,
,
.
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c4336d602211dbca2f1c5fc511f45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae78e8bb0d1a42759b5464d23d63a601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e0b42cc7f2add2521ba2d876af2e4.png)
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2023-04-13更新
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1804次组卷
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5卷引用:第13章 立体几何初步(B卷·能力提升)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)
第13章 立体几何初步(B卷·能力提升)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)广西柳州高级中学、南宁市第三中学2023届高三联考数学(文)试题广东省肇庆市德庆县香山中学2022-2023学年高一下学期5月月考数学试题河南省许昌市鄢陵县职业教育中心(升学班)2022-2023学年高二下学期期中考试数学试题(已下线)第六章立体几何初步章末二十种常考题型归类(2)-【帮课堂】(北师大版2019必修第二册)
解题方法
2 . 如图,平面
平面
,点P是平面
、
外一点,从点P引三条不共面的射线PA、PB、PC,与平面
分别相交于点A、B、C,与平面
分别相交于
、
、
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1cd45f06dbe26e9e78769b4af511dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47e1cfa53212cf89d3ae38c0d9db19b.png)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962142273388544/2962989063979008/STEM/576461c4-d23c-4ccc-8904-e2ce04bbdf0e.png?resizew=171)
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解题方法
3 . 如图所示,已知多面体ABCDFE中,四边形ABCD为矩形,
,
,平面
平面ABCD,O,M分别为AB,FC的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879473344815104/2879709141008384/STEM/f8e810d2-b104-4f7a-bd34-b73496b8111f.png?resizew=210)
(1)求证:
;
(2)求证:
平面DAF;
(3)若过EF的平面交BC于点G,交AD于点H,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333ab24c4935210f4c232cd0c0fae358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c507610f462120218e2cd1894c957eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879473344815104/2879709141008384/STEM/f8e810d2-b104-4f7a-bd34-b73496b8111f.png?resizew=210)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd40e867f1d3377cf4fb9ae730d04cf7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1211fdbcc2a4a36e24b4e6c5c920bd.png)
(3)若过EF的平面交BC于点G,交AD于点H,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5188eea602f0d1a5a08da3fc421a076.png)
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