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

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

.

A. Determine the angle of rotation for each hubcap. Explain how you found the angle.

B. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 1

A. Determine the angle of rotation for each hubcap. Explain how you found the angle.

B. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 1A.

B.There are 5 lines of symmetry in this design.

Hubcap 1A.The angle of rotation is 72º.

B.There are 5 lines of symmetry in this design.

72º

Hubcap 2

A. Determine the angle of rotation for each hubcap. Explain how you found the angle.

B. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 2A.

B.There are NO lines of symmetry in this design.

Hubcap 2A.The angle of rotation is 120º.

B.There are NO lines of symmetry in this design.

120º

Hubcap 3

A. Determine the angle of rotation for each hubcap. Explain how you found the angle.

B. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 3A.

B.There are 10 lines of symmetry in this design.

Hubcap 3A.The angle of rotation is 36º.

B.There are 10 lines of symmetry in this design.

36º

Hubcap 4

A. Determine the angle of rotation for each hubcap. Explain how you found the angle.

B. Some of the hubcaps also have reflectional symmetry. Sketch all the lines of symmetry for each hubcap.

Hubcap 4A. .

B.There are 9 lines of symmetry in this design.

Hubcap 4A.The angle of rotation is 40º.

B.There are 9 lines of symmetry in this design.

40º

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.

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

Follow Up 1.2 #2Create 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 #3Why do you think many rotating objects are designed to have rotational symmetry.