Exploring Composite of Three Reflections Across Parallel Lines

① This example demonstrates the composite effect of reflecting a figure successively across three parallel lines, revealing how multiple reflections combine into a single transformation. ② The core mathematical concepts are reflection transformations and their composition: two reflections across parallel lines yield a translation, while three reflections across parallel lines yield a reflection (or a glide reflection), involving symmetry, translation, and vector operations. ③ Construction details: Based on the summary, the GeoGebra commands used include Line, Point, Segment, OrthogonalLine, Vector, Translate, and Polygon. Objects such as points (A, B, C, D, E, F, I, J, K), lines (a, b, c, f, g), segments, vector v, and polygon poly1 are defined. The step and Reset buttons control animation stages, and MoveMe provides interactive dragging to explore the transformation dynamically. ④ This is suitable for high school or early college students learning geometric transformations, and for teachers demonstrating the algebraic and geometric properties of reflection composition, enhancing spatial reasoning and logical thinking.