Geometric Transformation from Square to Cross

This GeoGebra applet demonstrates the geometric transformation of reconstructing a square into a cross shape. Using commands such as Polygon, Rotate, and Translate, it illustrates the mapping relationships of vertices and edges during the transformation. The dynamic model visually presents the geometric principles of figure dissection and reassembly, making it ideal for exploring area-preserving transformations and tangram-style puzzle problems in plane geometry. Students can interactively manipulate the construction to observe how a square can be systematically divided into several polygonal pieces, which are then rotated and translated to form a symmetric cross shape. This hands-on exploration reinforces key concepts including congruence, rotational symmetry, translation vectors, and the conservation of area under rigid transformations. The applet serves as an effective visual aid for understanding dissection proofs and helps learners develop spatial reasoning skills by seeing exactly how each vertex of the original square maps to a corresponding position on the cross. Teachers can use this demonstration in lessons on geometric transformations, symmetry, and area calculations, while students benefit from the immediate visual feedback that connects abstract transformation rules to concrete geometric outcomes.