Exploring Lines of Symmetry: Geometric Construction and Mirror Transformation

① This GeoGebra example dynamically demonstrates the construction of a line of symmetry (mirror line) for geometric figures, visually showing how symmetric shapes are generated through reflection. ② Core mathematical concepts include axial symmetry, mirror transformation, relationships between symmetric points and segments, and the distribution of geometric elements such as incircles and ellipses under symmetry. ③ Construction highlights: the Line command creates the symmetry axis, the Mirror command reflects points A, B, C and segment a to produce corresponding points A' and segment b, while the Segment command connects relevant points; an image pic1 is inserted for visual aid. The construction involves objects A, B, C, a, A', b, and pic1, illustrating a step-by-step build from basic elements to composite figures. ④ Suitable for middle and high school students learning geometric transformations and symmetry properties, and for teachers demonstrating the fundamental role of symmetry axes in plane geometry, helping to understand the relationship between symmetry and congruence.