题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-95082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-93459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-63789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-33581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-95082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-74240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-46819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-95788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-31943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-33581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-93995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-35928.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-15326.png)
(2)△
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100559-95082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-95788.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-38273.png)
解析
(2)把所求阴影部分面积看作△FHP与△FMN的面积差,并且这两个三角形都与△ABC相似,根据∠A=90°,∠C=30°,BC=12cm,求出对应边的长,再根据相似三角形的面积比等于相似比的平方求面积即可.
解:设AC与DF和EF的交点分别为M,N,如下图所示:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100600-24338.png)
(1)∵∠A=90°,∠C=30°,BC=12cm,点P为斜面中点,
∴FD=6
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
根据旋转前后对应角相等可知:△FHP∽△FED,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-43978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-33960.png)
解得:PH=2
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
(2)∵∠C是公共角,∠CPN=∠A=90°,
∴△PNC∽△ABC得,
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100602-90498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100602-99288.png)
解得NP=2
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
FN=FP-NP=6-2
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
由△FMN∽△CPN,可知
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100602-36710.png)
根据相似三角形面积比等于相似比的平方,可知
S四边形MNPH=S△FHP-S△FMN=S△CNP-(1-
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100602-43665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100603-50597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100602-43665.png)
△ABC与△DEF重叠部分的面积为9cm2.
故答案为:2
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100601-79776.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-78069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-42093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-72343.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-36137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-23261.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-42624.gif)
(1)试说明:△
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-78069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-75055.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-61372.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-63943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100550-36137.gif)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100551-53773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100551-58335.gif)
A.2,3,4 | B.4,6,5 | C.14,13,12 | D.7,25,24 |
如图,直角三角形ABC中,点
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100539-75691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100539-44755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100540-71341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100540-65197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100540-62527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100533-72435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100534-90344.png)
A.2.7米 | B.1.8米 | C.0.9米 | D.6米 |
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103100530-89774.png)
A.9.5 | B.10.5 | C.11 | D.15.5 |
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