题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212155-98297.png)
A.![]() | B.![]() | C.![]() | D.![]() |
答案
解析
试题分析:平行于三角形一边的直线截其他两边(或两边的延长线),所得的对应线段成比例,∵AB∥CD∥EF,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212156-47243.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212147-50312.jpg)
(1)若a=4厘米,t=1秒,则PM= _________ 厘米;
(2)若a=5厘米,求时间t,使△PNB∽△PAD,并求出它们的相似比;
(3)若在运动过程中,存在某时刻使梯形PMBN与梯形PQDA的面积相等,求a的取值范围;
(4)是否存在这样的矩形:在运动过程中,存在某时刻使梯形PMBN,梯形PQDA,梯形PQCN的面积都相等?若存在,求a的值;若不存在,请说明理由.
当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-83241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-40046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-72135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-51656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
探究证明:
如图所示,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-54048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-75752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-76313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-52651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-62978.png)
(1)分别用
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-41206.png)
(2)探求OC与CD表达式之间存在的关系(用含a,b的式子表示).
归纳结论:
根据上面的观察计算、探究证明,你能得出
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
实践应用:
要制作面积为4平方米的长方形镜框,直接利用探究得出的结论,求出镜框周长的最小值.
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212127-95313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212128-57291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212128-31321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212128-57553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212129-49274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212129-68517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212129-28641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-34535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-10703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-88579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-21562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-38893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-91635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-71841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-42734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212132-52592.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212132-87502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212119-70294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212119-31490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212119-95573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212120-20488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212114-37012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212114-64143.jpg)