[size=200][b]A theorem with parallelograms[/b][/size][br][br][color=#000000]The Varignon theorem (1654-1722) says: The four middle points on the four sides of a quadrilateral are the vertices of a parallelogram. It is very easy to verify with GeoGebra with the following commands:[/color][br][br][color=#9900ff]1st. Type the [color=#000000][b]E=Midpoint(a)[/b][/color] command.[/color][br][br][color=#9900ff]2nd. Type the [color=#000000][b]F=Midpoint(b)[/b][/color] command.[/color][br][br][color=#9900ff]3rd. Type the [color=#000000][b]G=Midpoint(c)[/b][/color] command.[/color][br][br][color=#9900ff]4th. Type the [color=#000000][b]H=Midpoint(d)[/b][/color] command.[/color][br][br][color=#9900ff]5th. Type the [color=#000000][b]P=Polygon(E,F,G,H)[/b][/color] command.[/color][br][br][color=#000000]Activate the "Move" tool [icon]/images/ggb/toolbar/mode_move.png[/icon] and move the vertices "A", "B", "C" and "D", verify that the irregularity of the red quadrilateral does not matter, the new quadrilateral will always be a parallelogram.[/color][br][br][color=#000000]The two curved arrows located in the upper right corner of the Graphics View allow you to reset the activity.[/color][br][color=#000000]If the activity is correct, you will get 10 points automatically.[/color]