Initial Investigation

Quadrilateral Midpoints

Part 1. Draw two quadrilaterals of about the same shape as the ones shown below. Using your midpoint tool, bisect each side of each figure. Join the midpoints of the four sides of each figure in order, so that two new quadrilaterals are formed. What do you notice? What is the relationship of the shape of the interior and exterior quadrilaterals? What about the area? Perimeter? What else could you investigate?

Part 2. Investigate the kind of quadrilateral formed by the angle bisectors of a parallelogram (make sure to construct a parallelogram - not just a figure that looks like one. Again, what is the relationship of this quadrilateral to the type of original parallelogram?

Justify any conjectures that you make with properties, theorems, and/or measurements.