题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215917-56269.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215918-55992.png)
(2)求这个矩形EFGH的周长.
答案
解析
试题分析:(1)根据矩形的性质可得EF∥GH,即可证得△AHG∽△ABC,从而得到结论;
(2)由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215918-59055.png)
(1)∵四边形EFGH为矩形
∴EF∥GH
∴∠AHG=∠ABC
又∵∠HAG=∠BAC
∴△AHG∽△ABC
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215918-59055.png)
(2)由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215918-59055.png)
AM=AD-DM=AD-HE=30-x
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215918-67083.png)
解得x=12,2x="24"
所以矩形EFGH的周长为2×(12+24)=72cm.
点评:相似三角形的应用是初中数学的重点,贯穿于整个初中数学的学习,是中考常见题,一般难度不大,需熟练掌握.
核心考点
试题【如图,△ABC是一张锐角三角形的硬纸片,AD是边BC上的高,BC=40cm,AD=30cm.从这张硬纸片上剪下一个长HG是宽HE的2倍的矩形EFGH,使它的一边】;主要考察你对相似图形等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215906-86893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215906-63119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215907-42920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215907-68515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215907-57230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215908-85406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215908-68340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215909-24538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215909-30134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215909-24538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215909-38224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215909-78415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215909-39251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215910-23375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215910-38348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215910-20875.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-11985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-47139.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-89501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-30014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215912-98272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-30014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-11985.png)
(3)如图②,连接
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215912-93500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215912-74552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215913-96500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215913-40525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-11985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215913-40525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215911-11985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215855-10902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215856-84518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215856-89801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215856-54932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215856-98501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215857-50639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215857-28800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215857-50167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215857-50271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215858-33878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215858-71210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215858-71210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215858-74169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215859-15928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215859-61901.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-29233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-44236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-95721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-44236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-29233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-81092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-95721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-44236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-44847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-44236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-86976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-82159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-44236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-37391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-18600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-61054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-95721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-73977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-94998.png)
(1)求观测点
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-95721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215848-29233.png)
(2)该轮船航线的速度(结果精确到
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-34697.png)
参考数据:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-43009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-65955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215849-54118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215850-49990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215850-10269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215850-33028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215850-18749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215837-27553.png)
A.∠BAD=∠CAE | B.∠B=∠D | C.![]() | D.![]() |
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