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Learning Math Home
Geometry Session 7, Part B: Rotation Symmetry
 
Session 7 Part A Part B Part C Homework
 
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Session 7, Part B:
Rotation Symmetry

In This Part: Determining Rotation Symmetry | Creating Rotation Symmetry

To create a design with rotation symmetry, you need three things:

 

a figure, called a basic design element, that you will rotate

 

a center of rotation

 

an angle of rotation

By convention, we rotate figures counterclockwise for positive angles and clockwise for negative angles.

80° rotation about point P

-80° rotation about point P


 
 

To create a symmetric design, follow the steps below:

Step 1: Copy this picture, including point P and the reference line. Or print the PDF version.

Step 2: Draw a new segment with P as one endpoint and forming a 60° angle with the reference line. Label this segment 1. Then draw four more segments, labeling them 2 through 5, from point P, each forming a 60° angle with the previous segment, as shown here:

Step 3: Place a sheet of tracing paper over your figure. Pin the papers together through the center of rotation. Trace the figure, including the reference line, but don't trace segments 1-5.

Step 4: Now rotate your tracing until the reference line on the tracing is directly over segment 1. Trace the original figure again. Your tracing should now look like this.

Step 5: Rotate the tracing until the reference line on the tracing is directly over segment 2. Trace the original figure again.

Step 6: Repeat the process, rotating to place the reference line over the next segment and tracing the figure. Do this until the reference line on the tracing is back on the original reference line.


 

Problem B2

Solution  

Does your design have reflection symmetry? If so, where is the line of symmetry?


 

Problem B3

Solution  

Use the basic design element below and the given center of rotation to create a symmetric design with an angle of rotation of 120°. Does this design have reflection symmetry? If so, where is the line of symmetry? Printable PDF of design


 

Rotation Symmetry Steps 1-6 and Problems B2 and B3 adapted from IMPACT Mathematics, Course 3, developed by Educational Development Center, Inc. pp. 305-306. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math

Next > Part C: Translation Symmetry and Frieze Patterns

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