The application of the problem of "General Drinking Horse" in the jiangsu middle schoolentrance examination
“将军饮马”问题在江苏中考试题中的应用

摘要

最值问题是初中数学中经常被作为重点考察的内容，学生在对最值问题的探究过程中，不仅可以巩固相关知识和提升解题技能，还能感悟其中重要的思想方法。线段最值问题常通过平移、翻折、旋转、相似等方法转化为“两点之间线段最短”、“垂线段最短”等原理来解决。本文以2010-2020年的江苏中考题为例，对将军饮马问题模型进行探讨，系统地总结出在遇到不同的情况时，用不同的手段转化为一般的将军饮马模型[1]，其中主要涉及两定一动型、两定两动型、三动型在四边形、抛物线、半圆、三角形情境中的情况。不论题目如何变换，掌握作对称点的方法与思想就能够将问题迎刃而解了。

Abstract

Most value problems are often examined as a key content in junior high school mathematics, and students can not only consolidate the relevant knowledge and improve the problem solving skills in the process of exploring the most value problems, but also understand the important ideological methods. The problem of line segment maximum value is often solved by translating, folding, rotating, similarity and other methods into "the shortest line segment between two points", "the shortest perpendicular line segment" and other principles. This paper takes the 2010-2020 Jiangsu midterm questions as an example to explore the general drinking horse problem model, and systematically sums up that when encountering different situations, different means are used to transform into a general general drinking horse model [1], which mainly involves two fixed one-acting type, two fixed two-acting type, and three-acting type in the quadrilateral, parabola, semicircle, and triangle situations. No matter how the topic is changed, mastering the method and idea of making symmetry points will be able to solve the problem easily.