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本文以一道中考试题为例,探讨动点背景下线段最值问题的常用方法,供参考.题目(2016年三明中考题)如图1,等边△ABC中,AB=4,P是BC边上的动点,点P关于AB、AC的对称点分别是M、N,则线段MN长的取值范围是____.分析要求线段MN长的取值范围,首先要解决与MN长相关联量的问题.若连结PM,PN,分别与AB,AC边相交于点D,E,由轴对称的性质可知,AB,AC分别垂直平分线段PM,PN,即D,E分别为PM,PN的中点,因此,DE为△PMN的中位线,所以有MN=2DE.这
In this paper, a middle school exam questions, for example, to explore the moving point background of the line most commonly used method for reference. Subject (2016 Sanming exam) as shown in Figure 1, equilateral △ ABC, AB = 4, P is BC edge On the moving point, point P on AB, AC symmetry points are M, N, then the length of the line MN is ____. Analysis of the required length of the line MN range, we must first solve the amount associated with the MN If the connection PM, PN, respectively, AB, AC edge intersection at points D, E, from the axisymmetric nature, AB, AC, respectively, perpendicular bisector PM, PN, that D, E were PM, PN Therefore, DE is the median line of △ PMN, so there is MN = 2DE