PSA2RAZ - Classwork---Geometry, M1, Lesson 15 (G.CO.A.3)
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1. Draw all lines of symmetry. Locate the center of rotational symmetry.

 

 

 

 

 

 

 

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Part A)

2. Describe all symmetries explicitly.

 

 

 

 

a. What kinds are there?

 

 

 

 

 

 

 

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Part B)

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

 

 

 

 

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part C)

c. How many are reflections?

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part A)

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?)

 

 

 

 

 

 

Modified from EngageNY ©Great Minds Disclaimer

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part B)

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

 

 

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Part C)

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

 

 

 

 

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Part D)

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.

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):