[left][b]Introduction and Background[/b][/left]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.  [br][br]Remember the definition of a trapezoid:  a quadrilateral (four sided) polygon in which [b][i][u]only[/u][/i][/b] two of the opposite sides are parallel.  See the diagram below for an example.[br][br][b]Step 1.  Build a Trapezoid[/b] [br][br]When you open the [i]GeoGebra[/i] file, you see three polygons:  a red rectangle, a blue[br]triangle, and a green triangle.[br][br]Use the MOVE tool [icon]/images/ggb/toolbar/mode_move.png[/icon]to use these three polygons to construct a trapezoid.  If you need to rotate a triangle, click on the [b]Show/Hide Rotator Points[/b] option.   [br][br][b]Step 2.  Deconstruct a Set of Trapezoids[/b] [br][br] Use the MOVE GRAPHICS VIEW tool [icon]/images/ggb/toolbar/mode_translateview.png[/icon] to move the [i]GeoGebra [/i]page up, displaying a set of four parallelograms.  Turn on the GRID –it will help with the next constructions.   [br][br]Now use the SEGMENT BETWEEN TWO POINTS tool [icon]/images/ggb/toolbar/mode_segment.png[/icon] to construct line segments on the four trapezoids showing how they could be deconstructed into a rectangles and triangles. [b] [br][br][/b][b]Conclusions[/b] [br][br]What do you notice that makes Trapezoid 4 different from the other three trapezoids?  [br][br]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.