# GSP Quadrilateral Tessellation Exploration

From EscherMath

**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.

- 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".
- Use the line segment tool to draw a segment. Then draw three more segments to make a quadrilateral.
- Construct the interior of the quadrilateral. Choose a color.
- Construct the midpoints of all four sides of the quadrilateral.
- Rotate the quadrilateral 180° around each midpoint. Color all four new copies with one color.
- Use translations to finish the tessellation.
- Move the corners of the original quadrilateral. Examine what happens when it is not convex.
- Add your name to the sketch using the Text palette. Print out your tessellation.
- What symmetries does the picture have??

Your picture should look something like this:

**Handin:**
A sheet with answers to all questions.