Dividing Points of Parallelograms: Geometric Properties of Corresponding Vertice

This GeoGebra applet demonstrates a classic plane geometry property: given any two parallelograms, if dividing points are taken on the segments connecting their corresponding vertices at the same ratio, these four points will invariably form a new parallelogram. Users can interactively alter the shapes, positions of the initial parallelograms, and the ratio parameter to observe the generation of t