Methodological aspects of teaching 8(9) grade studentstransformation of figures in planimetry

Abstract

One of the most critical topics in Euclidean geometry is the theme of «Transformation of Figures». Mathematics teachers and modern general secondary education system textbooks present this material differently. However, to learn how to use transformation skillfully, it is necessary to visualize them and understand the dynamics of actual operations for obtaining one figure from another. The article discusses parallel translation of figures onto a vector, rotation around a point by a given angle, axial symmetry, and similarity transformations, especially homothety. We believe that the parallel translation should be taught after vectors have been studied, since translation to a vector is closely associated with such transformations of figures. We suggest presenting rotation around a point by a given angle in a purely geometric style, with central symmetry considered a special case of rotation by an angle of 180°. We believe that students should be shown the difference between the aforementioned transformations and symmetry with respect to a straight line, and that the concepts of identical (different) orientation of figures after these transformations should be introduced reasonably. When studying similarity transformations, it is necessary to rigorously prove all properties without exception and present homothety as a special case of similarity. It is also worth proving, based on already known facts, the theorem about the possible decomposition of similarity into a product (composition) of homothety and motion, since after its proof, it will be pretty clear that only those properties of similarity that are common to homothety and motion will be considered properties of similarity. We are also convinced that, in addition to this, it is equally important to introduce students to the described transformations to demonstrate each of them qualitatively using modern digital technologies.