题目
题型:不详难度:来源:
解题思路:利用勾股定理易得AB=5利用
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051748-22180.png)
请你利用上述方法解答下面问题:
(1) 如图甲,已知Rt△ABC中,∠C=90°,CD⊥AB于D,BC=5,AC=12,求CD的长。
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051748-99877.png)
(2)如图乙,△ABC是边长为2的等边三角形,点D是BC边上的
任意一点,DE⊥AB于E点,DF⊥AC于F点,求DE+DF的值
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051748-87681.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051748-22180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-87070.png)
(2)等边三角形ABC的高线长是
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-45353.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-33546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-68272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-45353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-68272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-68272.png)
∵BC=" AB=" AC ∴DE+DF=
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-45353.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-20012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051749-20012.png)
(2)根据分析,过点A作AE⊥BC,垂足为E,再根据勾股定理得出AE,由S△ABC=S△ADB+S△ADC求出DE+DF即可.
核心考点
试题【利用“等积”计算或说理是一种很巧妙的方法, 就是一个面积从两个不同的角度表示。如图甲,已知Rt△ABC中,∠C=90°,CD⊥AB于D,BC=3,AC=4,求C】;主要考察你对相似图形性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051734-13114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051734-98417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051735-37217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051735-79139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051735-88815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051735-95966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051736-28229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051736-18129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051736-60362.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051736-13958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051736-39642.png)
(2)延长
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051737-91035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051737-10930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051737-45447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051737-66129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051737-89561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051738-21509.png)
(3)在⑵的条件下,若
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051738-37532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051738-72418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051739-62655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051739-37781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051739-15990.png)
试探索
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051739-57267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051740-79998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051740-14195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051740-29055.png)
A.108° | B.72° | C.54° | D.36° |
求证:CE=CF。
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051729-76805.png)
A.平行四边形 | B.等腰梯形 | C.矩形 | D.正方形 |
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103051720-89354.png)
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