- A B Cron
The midpoints of the sides of an arbitrary quadrangle form a parallelogram. If the quadrangle is convex or reentrant, i.e. not a crossing quadrangle, then the area of the parallelogram is half as big as the area of the quadrangle. Wikipedia To construct a Varignon Parallelogram
- Create 4 random points (A,B,C,D) on the Drawing Pad.
- Using the segment tool connect the points A,B,C,D,A to form a quadrilateral; change the color of these segments to blue by selecting properties with a <right-click>.
- Use the midpoint tool to find the midpoint of each side.
- Use the segment tool to connect this points, the figure formed is a parallelogram; change these segments to red.
You can <right-click> on segments to add their value to the display or view it in the Algebra View.
- What are the lengths of the opposite side of the midpoint quadrilateral?
- What are the slopes if each side of the quadrilateral?
- What do these results indicate about this quadrilateral?
- What happens if you move any of the free points?