Dynamic Rhombus: rotate and mirror to control shape and angles

This example demonstrates how to build a dynamic, adjustable rhombus in GeoGebra, where the figure can be repositioned and reshaped using geometric transformations while preserving rhombus properties. Key concepts include rhombus symmetry, angle constraints (Angle, including parameters such as α and β), and distance/length conditions (Distance). Algebraic relationships (and related numeric constraints) help maintain the required geometric structure, while cosine/angle relationships support interpreting or controlling directional/angle measures. The construction relies on the provided GeoGebra commands and objects: Segment and Circle for establishing sides and auxiliary loci; Rotate and Mirror to generate and update symmetric/rotated points (e.g., A/B/C and derived points such as a′/c′, F′/G′); Polygon to display the rhombus as poly1 and poly2; Distance to measure quantities like distanceAD and distanceBC, together with TextAD/TextBC for labeling; and Angle to compute and show angle values such as β and α. Suitable for middle-school geometry lessons, dynamic geometry demonstrations, and student activities on parameterized geometric construction and transformation-based reasoning.