Van Aubel's theorem

The orange dots are at the vertices of a quadrilateral.[br][br]A square is erected on each face of the quadrilateral.[br][br]Blue and green line are drawn joining [br]the centers of opposite squares.[br][br]Drag the orange dots to reshape the quadrilateral.[br][br]Can you explain the observed behavior?[br][br][color=#ff0000][i][b]What problems could/would you set for your students based on this applet?[/b][/i][/color]

Information: Van Aubel's theorem