Using rotation transformation to solve junior high school geometry problems
利用旋转变换求解初中几何问题

摘要

我们把在平面内将一个图形绕一个定点按一定方向旋转一定角度的几何变换定义为旋转变换，由于旋转前、后的图形全等，因此旋转变换是我们在解决初中几何问题时可以考虑的一种重要手段.在初中几何中，旋转变换类题目灵活多变，常与三角形、矩形、圆等多种载体结合起来，考查角度、线段长度、面积大小、最值等计算或证明问题，这对同学们直观想象、逻辑推理、数学运算能力提出了更高的要求，往往具有一定难度.尤其是题目中不直接给出旋转等信息，同学们在解答时就无从下手,但如果能仔细观察题目条件,巧用旋转变换就能将复杂问题简单化.本文收集部分试题并将其进行归纳进而总结旋转变换类题目的解题策略。

Abstract

We define the geometric transformation that rotates a figure around a fixed point in a certain direction and a certain Angle in a plane as a rotation transformation, because the figure before and after rotation is identical, so the rotation transformation is an important means that we can consider when solving junior high school geometry problems. In junior high school geometry, the rotation transformation class is flexible and changeable, often combined with a variety of carriers such as triangles, rectangles, circles, etc., to examine the Angle, line length, area size, maximum value and other calculation or proof problems, which puts forward higher requirements for students' intuitive imagination, logical reasoning, mathematical operation ability, and often has a certain difficulty. In particular, if the information such as rotation is not directly given in the question, the students have no way to start when answering the question, but if they can carefully observe the conditions of the question, the skillful use of rotation transformation can simplify the complex problem. This paper collects part of the test questions and summarizes them, and then summarizes the solving strategy of the rotating transformation class questions.