### MATH 113: Introduction to Symmetries

This worksheet guides you through an exploration of reflective symmeries.

Work with a partner or two on the following activity. Having two
copies of each handout will be very helpful.
You received a handout with pictures of quadrilaterals on it. Cut out those quadrilaterals.

For each quadrilateral, try to fold it exactly in half, so that the edges of the two halves line up exactly. If you succeed, the line you folded along is called a *line of mirror symmetry*. Trace the fold with a pen -- use a red pen if you have one.

Some quadrilaterals have more than one line of mirror symmetry. Find as many lines of mirror symmery as you can (remember, the outlines have to line up exactly) and trace them with a red pen.

Sketch or trace each quadrilateral and its lines of mirror symmetry in your notebook.

Together with your partner(s), place one quadrilateral on your desk. Take a second copy of the quadrilateral and place it exactly on top of the first. Then pick that second copy up and turn it up side down. Can you make the up side down quadrilateral line up exactly with the quadrilateral that's still on the desk?

For each quadrilateral you sketched in your notebook, make a note of whether it's the same shape right side up as it is up side down. You should notice a relationship between this property and the lines of mirror symmetry -- write that relationship in your notebook.

**Bonus:** For two of the quadrilaterals you were given, the right side up shape doesn't match the up side down shape. Can you find some other way to move the quadrilateral so that it matches itself?