Isometries: Transformations Preserving Distances in the Plane

This lecture introduces isometries as geometric transformations that preserve distances in the plane, focusing on the preservation of lines, segments, and the concept of symmetry. It covers definitions, properties, and examples of isometries, emphasizing their role in maintaining geometric relationships. The lecture explores the injectivity and surjectivity of isometries, demonstrating how they map points and figures while preserving distances. Additionally, it discusses the existence of an inverse transformation for isometries and how they maintain alignment of points and figures. Axioms related to isometries, such as the Axiom of Symmetry, are also presented and illustrated through geometric examples.