名校
解题方法
1 . 《九章算术》是我国古代数学名著,它在几何学中的研究比西方早
多年,在《九章算术》中,将底面为直角三角形且侧棱垂直于底面的三棱柱称为堑堵,将底面为矩形且一侧棱垂直于底面的四棱锥称为阳马,将四个面均为直角三角形的四面体称为鳖臑.如图在堑堵
中,
,
,
,
分别为棱
,
的中点,则下列说法正确的是______ .(只填序号)
①四面体
为鳖臑
②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
③若
,则
与
所成角的正弦值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
④三棱锥
的外接球的体积为定值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30821635432b069b6c2bf74fa09552f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dbd22b0cbb47c914c42a4355e3ca98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
①四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30821635432b069b6c2bf74fa09552f.png)
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