Quadrilaterals
To begin this investigation one should construct an arbitrary quadrilateral using Geometers SketchPad.
Now, lets consider the following:
What polygon is
formed by connecting the midpoints of a quadrilateral?
Another quadrilateral (Is this quadrilateral a special case?—a parallelogram)
What conjectures can be formed concerning congruences, similarities, area and perimeter?
The midpoints form a new quadrilateral that is a parallelogram.
The area of the interior quadrilateral is ½ the area of the original.
Test the conjectures yourself!
Interactive Quadrilateral Applet