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平移、旋转、翻折是图形全等变换的三种基本变换,因为一种图形经过其中的一种变换后,虽然位置发生了变化,但具有形状、大小不变的重要特征,所以图形变换的问题常与正方形、正三角形、等腰直角三角形等特殊的多边形综合命题,考查学生用运动变换的思想解决有关几何问题,以此培养学生的综合分析能力及思维(逻辑、逆向、发散)能力.关于“点在特殊多边形内”一类问题,往往需要将原来静止的图形,经过某种变换,构成新的图形,寻求解题途经.
Translation, rotation, and reflation are the three basic transformations of equivalence of graphics. After a graphic has undergone one of the transformations, although the position has changed, it has important features of the same shape and size, so the graphic is transformed. The questions are often combined with special polygons such as squares, equilateral triangles, and isosceles right triangles to examine the student’s thoughts on the use of motion transformation to solve relevant geometric problems, thereby cultivating the students’ ability of comprehensive analysis and thinking (logical, inverse, divergence). With regard to the problem of “points in special polygons”, it is often necessary to transform the original still graphics after some kind of transformation to form new figures and seek solutions.