B8. The Varignon theorem
A theorem with parallelograms
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:
1st. Type the E=Midpoint(a) command.
2nd. Type the F=Midpoint(b) command.
3rd. Type the G=Midpoint(c) command.
4th. Type the H=Midpoint(d) command.
5th. Type the P=Polygon(E,F,G,H) command.
Activate the "Move" tool 
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.
The two curved arrows located in the upper right corner of the Graphics View allow you to reset the activity.
If the activity is correct, you will get 10 points automatically.
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.
The two curved arrows located in the upper right corner of the Graphics View allow you to reset the activity.
If the activity is correct, you will get 10 points automatically.