Activity 2: Graphic Design: Using Symmetry to Create Corporate Logos (Grade Level 6–8)
The Geometry of Bicycle Designs 
Using Symmetry to Create Corporate Logos 
Patterns and Weaving 
Career Connections 
More Math Concepts
Standards:
Standard 3: Geometry and Spatial Sense (Transformations and Symmetry)
* These standards have been adopted and are based on the information from Principals and
Standards for School Mathematics: Discussion Draft, October l998, National Council of Teachers of Mathematics.
Objectives:
 Describe three types of symmetry
 Categorize symmetric figures based on type of symmetry
 Create figures using different type of symmetry
Activity
2
Three simple types
of symmetry are reflection, rotation, and translation. In each case,
we start with an original image and, using symmetry, we can transform
it.
Reflection symmetry
is sometimes called "mirror" or "flip" symmetry. It's easy to see why.
A butterfly (see below) may have reflection symmetry because one side
is a mirror image of the other.
Notice that a vertical line down the center of the butterfly's body serves
as what is called the "line of symmetry."
The letter A
has reflection symmetry similar to the butterfly.
1. Look at the letters
of our alphabet below. Organize the letters according to which ones have
reflection symmetry into three groups: the letters that have reflection
symmetry with a vertical line of symmetry (like the letter A), those
with a horizontal line of symmetry, and those with both vertical and
horizontal lines of symmetry.
A B C D
E F G H I J K L M N O P Q R S T U V W X Y Z
A second type of
symmetry is called rotation symmetry. You produce rotation symmetry by
turning an object. By rotating the flag on the left 90 degrees, we produce
a new flag.
The third type of
symmetry is translation symmetry. It is produced by moving the object
forward, backwards, or in any direction but do not flip or turn it. The
heart shape below (which has reflection symmetry) was translated to three
other shapes (or positions).
2. A graphic artist uses symmetry to create designs that become the symbol
for companies. These are called corporate logos. Look at the nine examples
below (ai). Can you tell which ones have reflection, rotation, or translation
symmetry? For each logo, describe the symmetry you find and how symmetry
might have been used to create the logo.
3. Design your own
logo. Notice that many logos start with a basic shape, a rectangle, a
diamond, or an oval, and then the artist uses symmetry to create the
design. The Mitsubishi company logo below began with a diamond that was
rotated 120 degrees, then another 120 degrees from that.
a. Pick a basic
shape from among those below.
b. Cut out at least
three copies and use reflection, rotation, or translation symmetry to
create your own logo.
c. Write a description
in your own words of the type or type of symmetry you used to create
your logo.
The
final figure was achieved by a combination of refection and rotation.
One original triangle was first placed on the page, an identical copy
was reflected horizontally. Two triangles were rotated 90 degrees.
One left in place, the other reflected vertically. The base of each
triangle was superposed, then the rotated group was superimposed over
the center of the base of the other pair.
Students should
be encouraged to use color to enhance their designs:
