Rigid Transformations in the Plane: Preserving Angles and Ratios

This example demonstrates how rigid transformations in the plane (translations, rotations, reflections) preserve key geometric properties: corresponding distances remain unchanged, and the relationships involving angles stay consistent after the transformation. In a connected way, it also links to similarity-type ideas such as ratio and angle characteristics when comparing the pre- and post-image configurations. The main concepts include rigid motion as a distance-preserving transformation, similarity transformations and their ratio/angle behavior (when applicable), and the use of circle-based constraints such as circumcircle (circumscribed circle) to support geometric reasoning. Since no GeoGebra construction commands were provided in the source (the construction summary is empty), the construction process is best inferred from the listed themes: build the initial configuration using geometric primitives, apply the transformation workflow via the transformation functionality, and then verify invariants using angle measurements and circle/circumcircle relations. This is suitable for middle/high-school geometry lessons, classroom demonstrations, and student self-study focused on understanding which properties are preserved under plane transformations.