Geometric transformations in school geometry

The study delves into the learning progression for school geometry based on transformations proposed by Hung-Hsi Wu. Plane transformations – translations, reflections, rotations, and dilations – are considered. Criteria for the triangle congruence and for triangle similarity, as well as the properties of the graphs of a quadratic function, are proved with their help. Axioms of school geometry used to justify the system of concepts are formulated. The study was motivated by the geometry topic presented in the mathematics curriculum as of 2022 and in the textbooks published.