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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 non-convex?



 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.


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