向量法与传统几何法解立体几何题的对比研究

A Comparative Study of Vector Method and Traditional Geometric Method in Solving Solid Geometry Problems

摘要: 立体几何是高中数学几何模块的核心内容，其解题方法主要分为传统几何法与向量法两大类。传统几何法立足立体几何的定义、判定定理与性质定理，依靠空间想象能力进行逻辑推理；向量法以向量的代数运算为核心，借助空间直角坐标系实现几何问题代数化，两种方法各有优劣、适用场景不同。本文通过梳理两种方法的核心内涵，结合典型立体几何例题拆解两种方法的解题过程，分析各自的优势与局限，总结两种方法的选择策略，为高中数学立体几何解题教学提供参考，助力学生灵活运用两种方法破解立体几何难题，提升数学核心素养。

Abstract: Solid geometry is a core content in the geometry module of high school mathematics, and its problem-solving methods are mainly divided into two categories: the traditional geometric method and the vector method. The traditional geometric method is based on the definitions, judgment theorems, and property theorems of solid geometry, relying on spatial imagination for logical reasoning; the vector method centers on algebraic operations of vectors, realizing the algebraization of geometric problems with the help of a spatial rectangular coordinate system. These two methods have their own advantages and disadvantages and are applicable to different scenarios. This paper sorts out the core connotations of the two methods, analyzes their problem-solving processes by combining typical solid geometry examples, examines their respective advantages and limitations, and summarizes the selection strategies for the two methods. It aims to provide references for the teaching of solving solid geometry problems in high school mathematics, help students flexibly use the two methods to solve difficult solid geometry problems, and improve their core mathematical literacy.