Quadrilaterals Inscribed Inside Quadrilaterals
Given any quadrilateral, construct a midpoint on each side. Connect each consecutive midpoint with a segment. What are the properties of the shape formed by joining the midpoints? Does the resulting shape depend on the type of quadrilateral (e.g. convex & concave)? How does the area of the new figure compare to the area of the original quadrilateral?
Suppose you want the new figure to be a rectangle. What quadrilateral would you start with? What quadrilateral would you start with so that the new figure to be a rhombus? What quadrilateral would you start with so that the new figure is a square?
Will the new figure ever be nonconvex?

Related External Resources 
Investigating Properties
In this activity, we'll construct a demonstration sketch which could be used by middle school students to investigate the properties of quadrilaterals.
Problem about Quadrilateral [ java applet ]
A java applet of the above problem.
Mid Rhombus [ GSP sketch ]
A GSP sketch of the above problem.
Submit your idea for an investigation to InterMath.
