1 . 已知一个四棱锥的三视图如下,该四棱锥的四个侧面中,直角三角形的个数为____________ .
![](https://img.xkw.com/dksih/QBM/2023/4/6/3210686638145536/3292606112202752/STEM/d6dffac078064c77988d3cda8305c165.png?resizew=228)
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解题方法
2 . 设直线与三条坐标轴的夹角分别为
,与三个坐标平面的夹角分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d0a2241095464f835e3ce4574f66c.png)
_________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2361805faef1a259a987e224eb938635.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef72093f571da03c6580a5e5fa9b0d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d0a2241095464f835e3ce4574f66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2361805faef1a259a987e224eb938635.png)
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解题方法
3 . 在直三棱柱
中,
,D、E、F分别为棱
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/13d77b45-67fb-41ea-9936-2df546a427f1.png?resizew=124)
(1)求证:
平面
;
(2)求证:
;
(3)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3788d69acba900ae9e013ef0a23bb347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d6885901907652b1653be2cef5f665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/13d77b45-67fb-41ea-9936-2df546a427f1.png?resizew=124)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7a3dc3f3a02f4400e22dec2f2fee23.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5034b24ff73d35c3f34e5c45daa0624d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05925f665156215b1e031ea6c190616a.png)
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