A discussion on the coordinate method in junior high school geometry competition problems
刍议初中几何竞赛题中的建系法

摘要

本文探讨建系法在初等几何问题中的应用价值，分析其在提高解题效率、简化推理过程方面的作用。本文通过对三个竞赛题的系统分析，揭示建系法如何将复杂的几何推理转化为可程序化执行的代数运算。研究发现，与传统几何法相比，建系法解题过程更直接、思路更清晰，可以将复杂的几何关系转化为清晰的代数关系，减少对辅助线构造和复杂图形推理的依赖，使解题过程更具条理性、规范性和可操作性，在规则图形及数量关系较明显的题目中优势尤为突出。研究表明，建系法能有效降低辅助线构造难度，提供稳定的解题路径[1]，有助于落实数形结合思想、提升学生的几何解题能力。

Abstract

This paper explores the application value of the coordinate method in elementary geometry problems and analyzes its role in improving problem-solving efficiency and simplifying the reasoning process. Through a systematic analysis of three competition problems, the paper reveals how the coordinate method transforms complicated geometric reasoning into algebraic operations that can be carried out in a more procedural way. The study finds that, compared with traditional geometric methods, the coordinate method offers a more direct solving process and a clearer line of thought. It can convert complicated geometric relationships into explicit algebraic relations, reduce reliance on auxiliary constructions and complex figure-based reasoning, and make the solution process more organized, standardized, and operable. Its advantages are especially evident in problems involving regular figures or relatively explicit quantitative relationships. The results show that the coordinate method can effectively reduce the difficulty of constructing auxiliary lines, provide a stable approach to problem solving [1], and help implement the idea of combining numbers with figures, thereby enhancing students’ ability to solve geometric problems.