I will begin by assuming that most of you have had some exposure to the Geometer's Sketchpad-3. As a preview to GSP-4, you might want to try to:

• create a non-special quadrilateral;
• change the labels of the vertices;
• measure its angles, and show that the sum of the angles remain constant even as the shape of the figure is dynamically changed;
• construct the interior of the figure, color it red, and measure the area;
• display a table that shows the perimeter and area for different quadrilaterals.

To illustrate how the Sketchpad can be used to explore some basic geometric relationships, follow the sequence of steps below.

• Begin with a new sketch. In Edit >> Preferences >>Text, make sure that ÒAs Objects Are MeasuredÓ is checked.
  
  
• Construct a non-special quadrilateral.
  
  
• Construct the midpoints of all of the sides; connect the midpoints to form a midpoint quadrilateral. Observe the shape of the midpoint quadrilateral as, in turn, you grab-&-drag each of the vertices.
  
  
• Make as many conjectures as you can about this inner figure.
  
  
• Describe how you could confirm or deny the correctness of each conjecture.
  For example, one conjecture is that the inner figure is a parallelogram. You could confirm or deny that by measuring the slopes of both pairs of opposite sides. (How else could you confirm this?)
  
  
• If the inner figure is actually a parallelogram, what reasonable explanation might there be for this?
  
  

• Exploration: Assuming the inner figure is always a parallelogram, under what conditions is the inner figure:
  
  
  • a rectangle?
    
    
  • a rhombus?
    
    
  • a square?
  
  
  
• We know that midpoint triangles have the special property of being one fourth the area of their "parent" triangles. Are there any special properties for the midpoint polygons (formed by connecting consecutive midpoints) for other types of polygons?