题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211456-22072.jpg)
答案
解析
试题分析:过N点作ND⊥PQ于D,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211457-48167.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211457-72996.png)
又∵AB=2,BC=1.6,PM=1.2,NM=0.8,
∴QD=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211457-81578.png)
∴PQ=QD+DP=QD+NM=1.5+0.8=2.3(米).
答:木竿PQ的长度为2.3米.
故答案是2.3.
核心考点
试题【在同一时刻两根木竿在太阳光下的影子如图所示,其中木竿AB=2米,它的影子BC=1.6米,木竿PQ的影子有一部分落在墙上,PM=1.2米,MN=0.8米,则木竿P】;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/20191102/20191102211449-71324.jpg)
探究发现:为了解决这个问题,我们可以先从一些简单的、特殊的情形入手:
(1)如图②:四边形ABCD中,点E、F是AD的3等分点,点G、H是BC的3等分点,连接EG、FH,那么S四边形EFHG与S四边形ABCD之间有什么关系呢?
如图③,连接EH、BE、DH,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-77774.jpg)
因为△EGH与△EBH高相等,底的比是1:2,
所以S△EGH=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
因为△EFH与△DEH高相等,底的比是1:2,
所以S△EFH=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
所以S△EGH+S△EFH=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
即S四边形EFHG=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
连接BD,
因为△DBE与△ABD高相等,底的比是2:3,
所以S△DBE=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-27570.png)
因为△BDH与△BCD高相等,底的比是2:3,
所以S△BDH=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-27570.png)
所以S△DBE +S△BDH=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-27570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-27570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-27570.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-27570.png)
即S四边形EBHD=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-86616.png)
所以S四边形EFHG=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211449-73651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-86616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211450-17759.png)
(1)如图④:四边形ABCD中,点E、F是AD的5等分点中最中间2个,点G、H是BC的5等分点中最中间2个,连接EG、FH,猜想:S四边形EFHG与S四边形ABCD之间有什么关系呢
验证你的猜想:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211451-75655.jpg)
(2)问题解决:如图①,在四边形ABCD中,点E、F是AD的n等分点中最中间2个,点G、H是BC的n等分点中最中间2个,连接EG、FH,(其中n为奇数)
那么S四边形EFHG与S四边形ABCD之间的关系为: (不必写出求解过程)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211441-77020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211441-30188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211429-27141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211430-29588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211430-29588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211430-46264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211430-47368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211431-18305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211431-16324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211431-61151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211431-61151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211431-19667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211432-75372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211432-54508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211431-16324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211432-35043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211432-35043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211433-14271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211433-33692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211433-77562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211433-29267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211434-52270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211434-99835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211434-17728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211434-85816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211434-78129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211435-57366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211435-45527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211435-64543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211435-37118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211436-26711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211436-82203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-11217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-84075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-65097.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-48254.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-29530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-90829.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-35947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-76516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211414-16814.png)
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