Double Reflections (Parallel Lines)

① This example demonstrates what happens when a polygon is reflected twice across two parallel lines, showing the composite effect of successive mirror transformations. ② Core mathematical concepts include axial symmetry (mirror reflection), composition of reflections, and how parallel-line reflections affect position and orientation. ③ Construction details: Using GeoGebra's Polygon command to create the initial polygon poly1, then applying the Mirror command about two parallel lines a and b to obtain the first reflected polygon poly1' and its corresponding edges a', b', followed by a second reflection of poly1' about one of the lines to produce poly1'', while retaining all intermediate objects (points A, B, C and their images A', B', C', A'', B'', C'') for clear visualization. ④ Suitable for middle/high school geometry or introductory transformation courses, helping students understand iteration and composition of reflections, and the special property that two reflections across parallel lines are equivalent to a translation.