题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215137-63475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-56887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215137-63475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-81490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-16165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-23816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-81490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215137-63475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-32489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-23816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-81490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215139-43176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215139-62479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215139-43176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-81490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215139-43745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215139-62479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215139-47646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-45640.jpg)
(1)判断△
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-33322.png)
(2)直接写出
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-16165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-72631.png)
(3)延长
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-82337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-89111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-17912.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-33322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-60169.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-66524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-96650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-40822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-72449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-69972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-14698.png)
(2)根据等腰三角形的性质结合函数图象上的点的坐标的特征求解即可;
(3)过
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-89111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215143-36932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215143-30292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215143-84539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-36981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-42486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-20860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-81709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-58686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-74335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-38597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-40176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-80500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-52413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-80500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-52413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-80500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-52413.png)
(1)△
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-33322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-62665.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-66524.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-23677.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-96650.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-40822.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-72449.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-69972.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215142-14698.png)
∴△
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-33322.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215138-16165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-72631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-60169.png)
(3)过
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215140-89111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215143-36932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215143-30292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215143-84539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-36981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-42486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-20860.png)
∵C为抛物线上异于顶点的任意一点,且BC=OC,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-81709.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215144-58686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-74335.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-38597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-40176.png)
①当点
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-80500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-52413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-14892.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215147-96411.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215147-61323.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215147-50533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215147-29733.png)
∴△
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215148-33955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215148-32870.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215148-18844.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215148-41868.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215148-83040.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-17912.png)
②当点
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-80500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-52413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215149-75369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215149-38519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215141-17912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215149-23862.png)
③当点
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215145-80500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215146-52413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215149-47819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215150-98492.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215150-28561.png)
点评:此类问题综合性强,难度较大,在中考中比较常见,一般作为压轴题,题目比较典型.
核心考点
试题【在平面直角坐标系xOy中,点的坐标是,过点作直线垂直轴,点是直线上异于点的一点,且.过点作直线的垂线,点在直线上,且在直线的下方,.设点的坐标为.(1)判断△的】;主要考察你对相似图形等知识点的理解。[详细]
举一反三
A.1∶2 | B.1∶![]() | C.1∶4 | D.2∶1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215129-84263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215129-90778.jpg)
求:(1)C点的坐标为 ;
(2)当t为何值时,△ANO与△DMR相似?
(3)①求△HCR面积S与t的函数关系式;
②并求以A、B、C、R为顶点的四边形是梯形时t的值及S的值.
画法初探
①如图②,在△ABC中,∠ACB>90°,画出△ABC的边AB上的相似点P(画图工具不限,保留画图痕迹或有必要的说明);
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215118-70401.png)
辩证思考
②是不是所有的三角形都存在它的边上的相似点?如果是,请说明理由;如果不是,请找出一个不存在边上相似点的三角形;
特例分析
③已知P为△ABC的边AB上的相似点,连接PC,若△ACP∽△ABC,则△ABC的形状是 ;
④如图③,在△ABC中,AB=AC,∠A=36°,P是边AB上的相似点,求的值.
(2)在矩形ABCD中,AB=a,BC=b(a≥b).P是AB上的点(P不与点A、点B重合),作PQ⊥CD,垂足为Q.如果矩形ADQP∽矩形ABCD,那么就称PQ为矩形ABCD的边AB、CD上的相似线.
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215118-85394.png)
①类比(1)中的“画法初探”,可以提出问题:对于如图④的矩形ABCD,在不限制画图工具的前提下,如何画出它的边AB、CD上的相似线PQ呢?
你的解答是: (只需描述PQ的画法,不需在图上画出PQ).
②请继续类比(1)中的“辩证思考”、“特例分析”两个栏目对矩形的相似线进行研究,要求每个栏目提出一个问题并解决.
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215114-96277.png)
①点M在运动过程中,当AM+DM的值最小时,BM= ;
②当 AM2+DM2的值最小时,BM= 。
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102215114-46529.png)
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