Interactive Reflections Activity: Exploring Symmetry and Area

① This interactive activity demonstrates the reflection (mirror) transformation of plane figures about a line, visually showing the position, orientation, and area relationships before and after reflection. ② Core mathematical concepts include reflection symmetry, axial symmetry, congruent figures, area conservation, and intersection properties of the reflecting line with polygon edges; it also extends to probability and geometric mean (e.g., probability of random points falling in reflected regions). ③ Construction highlights: Uses GeoGebra commands Line (to define the mirror axis), OrthogonalLine (to draw perpendiculars), Polygon (to construct the original polygon), Mirror (to generate reflected images), and Point (to define key points); objects include original polygon poly1 with edges e,f,g,h, reflected polygon poly1' with corresponding edges, and multiple reflected copies (poly1'_1, etc.), with points E,F,G,H and their images E',F',G',H' controlling dynamic changes. ④ Suitable for middle school geometry (basic symmetry concepts) and high school transformation and area calculations, as well as math lab or inquiry-based learning, helping students understand invariants and symmetry properties of reflection transformations.