1. Draw all lines of symmetry. Locate the center of rotational symmetry.

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2. Describe all symmetries explicitly.

a. What kinds are there?

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b. How many are rotations? (Include 360° rotational symmetry, i.e., the identity symmetry.)

c. How many are reflections?

3. Prove that you have found all possible symmetries.

a. How many places can vertex **A** be moved to by some symmetry of the square that you have identified? (Note that the vertex to which you move **A** by some specific symmetry is known as the image of **A** under that symmetry. Did you remember the identity symmetry?)

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b. For a given symmetry, if you know the image of **A**, how many possibilities exist for the image of **R**?

c. Verify that there is symmetry for all possible images of A and B.

d. Using part (b), count the number of possible images of A and B. This is the total number of symmetries of the square. Does your answer match up with the sum of the numbers from Exercise 2 parts (b) and (c)?

Enter a number for your answer, but write out if your answer matches in the text box.