TFish Angle Addition Puzzle: Supplementary Angles via Rotation

This example demonstrates a TFish-style geometric construction where rotations produce a configuration that enables angle-addition verification. It uses supplementary-angle relationships to confirm the target angle equations visually and computationally. The key math concepts are angle addition, supplementary (and related) angle properties, angle preservation under rotation transformations, and the way structured construction points lead to consistent angle labels. Construction relies on GeoGebra commands Point (for many labeled construction points such as A, B, C, D, E and their primed counterparts), Segment (to create the defining lines/edges), Rotate (to generate the rotated counterparts that align the angle chains), and Angle (to measure and display the resulting angles like α, β, γ, δ, ε, ζ, etc., together with the corresponding primed-angle labels). The design is intended for learners studying geometry proofs with dynamic geometry tools, and it works well for middle school through early university audiences practicing transformation geometry and reasoning about angle relationships.