Problem 1.2 The angle of rotation is the smallest angle through which a design can be rotated to coincide with its original design.

Rotational symmetry can be found in many objects that rotate about a centerpoint. Determine the angle of rotation for each hubcap. Explain how you found the angle. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 1 Determine the angle of rotation for each hubcap. Explain how you found the angle. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 1 There are 5 lines of symmetry in this design.

Hubcap 1 The angle of rotation is 72º. There are 5 lines of symmetry in this design.

Hubcap 2 Determine the angle of rotation for each hubcap. Explain how you found the angle. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 2 There are NO lines of symmetry in this design.

Hubcap 2 The angle of rotation is 120º. There are NO lines of symmetry in this design.

Hubcap 3 Determine the angle of rotation for each hubcap. Explain how you found the angle. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 3 There are 10 lines of symmetry in this design.

Hubcap 3 The angle of rotation is 36º. There are 10 lines of symmetry in this design.

Hubcap 4 Determine the angle of rotation for each hubcap. Explain how you found the angle. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 4 . There are 9 lines of symmetry in this design.

Hubcap 4 The angle of rotation is 40º. There are 9 lines of symmetry in this design.

Think About it: Is there a way to determine the angle of rotation for a particular design without actually measuring it? Write down your thoughts in your notebook. Make sure you tell me about ones that have lines of symmetry and ones that do not have lines of symmetry.

When there are lines of symmetry 360 ÷ number of lines of symmetry = angle of rotation When there are no lines of symmetry: 360 ÷ number of possible rotations around the circle. 5 lines of symmetry 3 points to rotate it to

Suppose you know the angle of rotation of a particular design Suppose you know the angle of rotation of a particular design. How can you use it to find all the other angles through which the design can be rotated to match the original design?

You can find multiples your angle of rotation until you get 360 degrees for a full rotation.

Follow Up 1.2 #1 Create a hubcap design that has rotational symmetry with a 90º angle of rotation but no reflectional symmetry.

Follow Up 1.2 #2 Create a hubcap design that has rotational symmetry with a 60º angle of rotation and at least one line of reflectional symmetry.

Follow Up 1.2 #3 Why do you think many rotating objects are designed to have rotational symmetry.