Discuss the strategy of solving similar triangles from a mock test question for the high school entrance examination
从一道中考模拟试题谈相似三角形的解题策略

摘要

我们将对应角相等、对应边成比例的两个图形称为相似图形。图形的相似是初中数学平面几何中极为重要的一个内容，是中考数学中的重点考察内容。相似三角形的知识有两个方面，一是源自相似三角形自身，二是与全等图形、相似图形有着密切的关系。通常以压轴题的方式出现在中考试卷中，对学生的解决问题能力提出了较高的要求，同时会涉及到数形结合、分类、方程、函数等多种数学思想方法。本文对一道2023年上海市嘉定区中考二模填空压轴题，采用一题多解的形式探讨相似三角形的解题策略，以期学生掌握初中数学基础知识、基本技能，提高分析问题、解决问题的能力，进而提升学生几何直观、模型观念、逻辑推理等数学核心素养。

Abstract

We call two figures whose corresponding angles are equal and whose corresponding sides are proportional similar. The similarity of figures is an extremely important element of plane geometry in middle school math, and it is a key examination in the middle school math test. The knowledge of similar triangles has two aspects, one is derived from similar triangles themselves, and the other is closely related to congruent figures and similar figures. It usually appears in the middle school examination paper as a finale question, which puts high demands on students' problem solving ability, and at the same time, it will involve a variety of mathematical ideas and methods, such as combination of numbers and shapes, classification, equations, functions and so on. In this paper, a 2023 Shanghai Jiading District Secondary School Examination second-mode fill-in-the-blank finale questions, using the form of one problem with multiple solutions to explore similar triangles solution strategy, in order to students to master the basic knowledge of junior high school mathematics, basic skills, to improve the analysis of the problem, problem solving ability, and then enhance the students' geometric intuition, the concept of modeling, logical reasoning and other mathematical core literacy.