Use the following Floor Tiles Java Applet

• Press the Tessellate button. What do you observe?
• If the pattern would continue, the entire plane could be filled with this pattern of squares. How would you describe this pattern of squares mathematically?
• Change the square to a non-regular convex quadrilateral and tessellate the plane. What did you observe?
• Change the square to a non-regular concave quadrilateral and tessellate the plane. What did you observe?
• Based on what you have observed, develop a definition for a tessellation. What does it mean for a figure to tessellate a plane? Be specific.
• Develop a mathematical argument for why any quadrilateral will tessellate a plane.