First Construct (on paper) the Quadrilaterals that satisfy the list below:
Any time you encounter unfamiliar
terminology consult the mathematical dictionary at Math.com
or a general dictionary at merriamwebster.com
Or email the authors at m2t2geo@www.mste.uiuc.edu
Jot this info down in a table you
create similar to the one below.
You may also print this page and fill in the table.
Angles (Measures,
Relationships, Interior Sum) Quadrilateral - - - Parallelogram - - - Rectangle - - - Square - - - Rhombus - - - Trapezoid - - -
These figures have been constructed in the sketch below so that you may experiment with them and explore some of their properties (It is Java-based so if you cannot access it download the real sketch here and use The Geometer's Sketchpad to open it, available from Key Curriculum Press).
These figures and their diagonals have been constructed in the sketch below (It is Java-based so if you cannot access it download the real sketch here and use The Geometer's Sketchpad to open it, available from Key Curriculum Press). Use the buttons to make figures appear. Figures will overlap, use the hide button to hide an obstructing figure.
Diagonals form congruent
triangles? How Many if so? Quadrilateral - - - - Parallelogram - - - - Rectangle - - - - Square - - - - Rhombus - - - - Trapezoid - - - -
After completing the activities above you should have a fair idea of how these quadrilaterals compare with one another.
Use the next figure (or draw on your own) a Venn diagram that graphically depicts their relationships. A Venn diagram looks like this...
where groups 2, 3, and 4 are members of group 1. And, group 4 is also a member of 2 and 3. Try it out below with the figures you have just experimented with.
Extensions
Now the final exploration we will make with our quadrilaterals is the exploration of midpoints and the figures created when those midpoints are connected. Experiment with the sketch below to determine the relationships that exist when you create a figure from the midpoints of the sides of a quadrilateral. Fill in the table that follows as well.
These figures and their midpoint figures have been constructed in the sketch below (It is Java-based so if you cannot access it download the real sketch here and use The Geometer's Sketchpad to open it, available from Key Curriculum Press).
Quadrilateral - Parallelogram - Rectangle - Square - Rhombus - Trapezoid -
We don't want to spoon-feed you the responses to these questions but as you have completed the previous tables you should have noticed certain properties of quadrilaterals. You should also be able to communicate those properties to someone else. Try it out! See if you can explain the following scenarios involving quadrilaterals.