Central and Axial Symmetry: Exploring Triangle Reflections

This interactive applet demonstrates the reflection of a triangle under both central symmetry (point reflection) and axial symmetry (line reflection). It visually shows how a triangle maps to its mirror image across a point or a line, highlighting the correspondence between original vertices and their images. Core mathematical concepts include symmetry transformations, reflection properties, invariant distances, and the geometric relationship between a figure, its mirror, and the symmetry axis or center. The construction uses GeoGebra commands such as Polygon to create the original triangle poly1, Mirror to generate reflected triangles poly1' and poly1'_1 about a point D and a line c respectively, and Line/Segment to draw auxiliary axes and connecting segments. Additional points (A', B', C') and objects (a_1, b_1) are included to clarify vertex correspondences. Suitable for middle school to high school students learning geometric transformations, and useful for teachers demonstrating symmetry concepts in class.