DECONSTRUCTING THE TRAPEZOID
Introduction and Background
Polygons can usually be deconstructed (cut up) into smaller polygons. Another way of saying this is that most polygons are really combinations of other polygons. This can be useful information and help with problem solving. In this activity you will explore trapezoids. Remember the definition of a trapezoid: a quadrilateral (four sided) polygon in which only two of the opposite sides are parallel. See the diagram below for an example. Step 1. Build a Trapezoid When you open the GeoGebra file, you see three polygons: a red rectangle, a blue triangle, and a green triangle. Use the MOVE tool
to use these three polygons to construct a trapezoid. If you need to rotate a triangle, click on the Show/Hide Rotator Points option.
Step 2. Deconstruct a Set of Trapezoids
Use the MOVE GRAPHICS VIEW tool 
to move the GeoGebra page up, displaying a set of four parallelograms. Turn on the GRID –it will help with the next constructions.
Now use the SEGMENT BETWEEN TWO POINTS tool 
to construct line segments on the four trapezoids showing how they could be deconstructed into a rectangles and triangles.
Conclusions
What do you notice that makes Trapezoid 4 different from the other three trapezoids?
Trapezoids can be deconstructed into a rectangle and one or two triangles. This conclusion will be useful in later activities involving finding the area of a trapezoid. 