Static Demo of a Turn–Turn (Turn-Turn) Transformation

This GeoGebra example demonstrates the geometric effect of a “turn–turn” (turn–turn) transformation: applying consecutive transformations (notably rotations around specified centers) produces corresponding points, angles, and polygonal configurations that match a designed symmetry pattern. It centers on core topics such as rotation as a geometric transformation, angle construction/measurement, and the resulting relationships among transformed vertices and drawn segments. Construction uses the commands Line, Rotate, Angle, and Polygon, with objects including two rotation/angle parameters (α, β), rotation centers (Center1, Center2), base points (A, B, C, D, E, F), their related counterparts (a, b, c, d, e, f), and primed images (A′, B′, C′), along with labels such as γ, δ, q1, c_1, d_1 to track the key angle/position constraints. Suitable for high school through early university audiences, for teaching and exploring composition of transformations and geometric proof strategies.