题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-30137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-18765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-73819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-30137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-18765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-73819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073418-40013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-57927.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-70313.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-53123.gif)
请运用类比思想,对于空间中的四面体V—BCD,存在什么类似的结论?并用体积法证明.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-64294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-94958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-84109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-51378.gif)
解析
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-64294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-26656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-15424.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-89188.gif)
在四面体O—BCD与V—BCD中:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-64294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-94958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-84109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-51378.gif)
同理有:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-26656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073421-39288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-15424.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073421-90328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-89188.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073421-66850.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073419-64294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-26656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-15424.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073420-89188.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073421-62788.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073422-70189.gif)
核心考点
试题【 已知O是△ABC内任意一点,连结AO、BO、CO并延长交对边于A′,B′,C′,则++=1,这是一道平面几何题,其证明常采用“面积法”.++=++==1,请运】;主要考察你对合情推理与演译推理等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073411-38000.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073411-11026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073411-75655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073411-81494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073411-75655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073400-95514.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073400-63546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073400-92982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073401-51854.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073401-35978.gif)
(2)猜想数列
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073400-63546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073351-51702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073351-31851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073351-30657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073351-48798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073343-22924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073344-10342.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073344-62885.gif)
(1)写出此数列的前5项;(2)归纳猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073343-22924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073336-24439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073336-68689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073336-15982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073337-83933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106073337-65912.gif)
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