1 . 下列类比推理正确的序号为( )
①“边长为
的正三角形内任一点到三边距离之和是定值
”类比空间,“棱长为
的正四面体内任一点到四个面的距离之和是定值
”;
②在平面上,若两个正三角形的边长比为
,则他们的面积比为
.类似的,在空间中,若两个正四面体的棱长比为
,则他们的体积比为
;
③已知椭圆具有性质:若
,
是椭圆上
关于原点对称的两个点,点
是椭圆上任意一点,则当
,
的斜率都存在,
,类似的,点
若在双曲线
上,则
.
④长宽分别为
,
的矩形的外接圆的面积为
,类比空间中,长宽高分别为
,
,
的长方体的外接球的面积为
.
①“边长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd988e1c7fcd3cc8526722fede422bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e849d89b9b5ccfc6cda523a364f5642.png)
②在平面上,若两个正三角形的边长比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c934d84feba963335cc7edf01610e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765fed228492b11196a8b2bc776a7645.png)
③已知椭圆具有性质:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be86d360cf391d521c4c31b1f9ce79b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23f4936c8e2ff75d6f395615e8a599b.png)
④长宽分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d6d3d174c67ab2a4b92df4834ad3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e4b7727b2960b51a06fbe3ee522e33.png)
A.①③ | B.②④ | C.①④ | D.②③ |
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