Parallelograms are represented in the left panel by the positions of their vertices and the sides and diagonals joining the vertices.[br][br]They are represented in the right panel by the points in a unit square that have the ratio of the blue to the red diagonal plotted along one axis and the angle between the diagonals plotted along the other.[br][br]If you choose to control the applet from the left panel you can drag the yellow dots to explore the space of parallelograms as seen in the right panel.[br][br]By the same token, if you choose to control the applet from the right hand panel, you can drag the yellow dot and explore the space of parallelograms in the left panel.[br][br]Can any shape parallelogram be generated by the controls in the left panel? If yes, can you prove it? If no, can you give a counterexample?[br][br]Can any shape parallelogram be generated by the controls in the right panel? If yes, can you prove it? If no, can you give a counterexample?[br][br][color=#ff0000][i][b]What problem(s) based on this applet would/could you give to your students?[br][br]What have you learned from this applet?[/b][/i][/color]