GSP Quadrilateral Tessellation Exploration

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Time-40.svg

Objective: Use Geometer's Sketchpad to create a tessellation with quadrilaterals. Doing the construction on the computer allows you to change the shape of your original quadrilateral and see how the tessellation changes.

  1. Run Geometer's Sketchpad (GSP). You should have an untitled window for sketching. If you don't, go to the file menu and choose "New Sketch".
  2. Use the line segment tool to draw a segment. Then draw three more segments to make a quadrilateral.
  3. Construct the interior of the quadrilateral. Choose a color.
  4. Construct the midpoints of all four sides of the quadrilateral.
  5. Rotate the quadrilateral 180° around each midpoint. Color all four new copies with one color.
  6. Your picture should look something like this:

    GSP-quad.jpg
  7. Use translations to finish the tessellation.
  8. Move the corners of the original quadrilateral. Examine what happens when it is not convex.
  9. Add your name to the sketch using the Text palette. Print out your tessellation.
  10. What symmetries does the picture have??

Handin: A sheet with answers to all questions.