Congruency Transformations: Translation, Rotation, Reflection and Vector Composi

This GeoGebra example demonstrates how geometric transformations such as translation, rotation, and reflection map a figure (e.g., a triangle or an image) to a new position while preserving its shape and size, illustrating the concept of congruency. The core mathematical concepts include congruent transformations, vector translation, rotation angle, mirror reflection, and vectors/planes in 3D space. Construction highlights: using GeoGebra commands Mirror, Rotate, Vector, and Translate, with objects like C, D, pic2, f, pic2', angle, pic2'_1, horizontal, vertical, A, u, pic1, a, b, c, and text1. The vector u and angle control the translation and rotation, while horizontal/vertical references aid positioning. Suitable for middle school to high school students learning properties of transformations, congruence criteria, and dynamic geometry exploration, as well as for teachers demonstrating composition and decomposition of transformations.