已知四棱锥
的正视图为等腰直角三角形,俯视图中正方形的边长为3.
![](https://img.xkw.com/dksih/QBM/2020/9/13/2549125092319232/2550535845994496/STEM/cdb55ede16f843689c81df9c7789ece8.png?resizew=373)
(1)求四棱锥
的体积;
(2)若平面
与平面
的交线为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2020/9/13/2549125092319232/2550535845994496/STEM/cdb55ede16f843689c81df9c7789ece8.png?resizew=373)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56adc934c9ad3cb261c5cbdc346b9631.png)
更新时间:2020-09-15 22:21:22
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相似题推荐
解答题-证明题
|
较易
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解题方法
【推荐1】如图,在四棱锥
中,底面
为矩形,
平面
,
为线段
上一点,
平面
.
(1)证明:
为
的中点;
(2)若直线
与平面
所成的角为
,且
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/12/0cbcb15a-90fb-4e6d-93b6-c68462adabd0.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8800cfd7c230485a1fd9ea6063b8e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565e518d475a50358fedff2f0bb8dec.png)
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【推荐2】直三棱柱
中,
,
,
,F为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395180670017536/2395272055611392/STEM/de5c8bd6-dd5b-49a6-acf9-139bb7363dee.png)
(1)求证:
;
(2)点M在线段
上运动,求三棱锥
的体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bd6d0c5f24bfb21fe0aed406aed90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cad7b03f934718b18ce34cdf0b85863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e7fe3b5d6a05075983af954d65c71c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395180670017536/2395272055611392/STEM/de5c8bd6-dd5b-49a6-acf9-139bb7363dee.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8350081c6259800279b6e090a2e3c5de.png)
(2)点M在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b875b54ca7370441a08f9e89963436b.png)
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解题方法
【推荐1】如图,四棱锥
,
,
,
,平面
平面
,平面
平面
.若点
为线段
中点,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ea4bd288944d3ba3d6a319de869dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1b292baa30ffc34df3a47d57b60c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca0832e094d5c05ec13c38ae556b3f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c0566d4ccf791d639c7823398941d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828cd6ec91191ba72e0eb6bb84aab88b.png)
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【推荐2】木工小罗在处理如图所示的一块木料时,发现该木料表面
内有一裂纹
,已知
平行于平面AC.他打算经过点M和棱
将木料锯开,却不知如何画线,你能帮助他解决这个问题吗?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e737bc35da650eda3825d29799b5f86f.png)
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