Ms. Lokseth
Math 9: Circles, Transformations and Similarity
Lesson 1: Line Symmetry and Reflections
As a consumer, you are faced with ads for products on everything from
billboards to bus stops to websites. Companies spend millions of dollars a
year promoting their brands. They are attempting to get you to identify with
and to purchase their products.
A logo is a graphic used to represent the face of a product or company. It is a
strong marketing tool when used correctly. How can a logo attract attention
and leave a positive impression?
The logo needs to be easily recognizable, memorable, and visually appealing
to the target audience. This means that when a consumer sees the logo, the
consumer knows the product. The company hopes that consumers feel they
are dealing with a reputable company.
Some companies have done a great job at
marketing their products and logos.
Consumers can identify the company and its
logo just by the shape of the product alone.
Can you identify the logos or the companies
that produce the following products?
A logo can be simple or complex, colourful or plain, large or small. What
makes one design more visually appealing than another? It depends on many
factors, including the type and size of the product and its packaging. For
example, a logo on a can of pop can be larger and more complex than a logo
on a pencil.
Ms. Lokseth
Math 9: Circles, Transformations and Similarity
Regardless of its use, all logos have a common goal. They need to be
memorable and catch your attention. Their owners want you as a consumer to
identify with their product. In this lesson you will investigate one strategy
used for creating easily recognizable, visually appealing designs.
Explore
A well-designed logo
 is easily recognizable
 attracts attention
 allows consumers to quickly identify with a product or company
A visually appealing logo shows balance and symmetry. It can be clearly
identified almost anywhere. A design that is too cluttered or not clearly visible
does not connect well with the consumer. The following three milk containers
illustrate good, poor, and bad designs.
The first container shows a symmetrical cow that is proportionally sized and
placed in the centre of the container. The cow is clearly visible and centred.
This allows the consumer to identify the product quickly. This logo uses a
balanced, uncluttered design.
The middle container uses the same cow logo. It is substantially smaller and
placed in the corner of the milk jug. There is a lot of unused packaging space.
This arrangement does not clearly show the consumer what the product is. It
isn’t a balanced design.
Ms. Lokseth
Math 9: Circles, Transformations and Similarity
The third milk jug has the cow’s face completely surrounded by other text and
pictures. The logo is hidden from view and is the same size as on the first
container. The cluttered background means that the cow’s face is not clearly
visible to the consumer.
Which product do you think a consumer will choose?
Chances are the consumer is going to purchase a product that can be
quickly located on the store shelf.
Your unit project will include creating a
logo of your own.
This piece of art was created by Cree elder
Sally Milne. It was made by biting designs
into birch bark. What reflections and
rotations do you see in it?
Reflections on our World
Symmetry is related to motion geometry and
transformations.
Many of the images in our world show translations,
reflections or rotations.
In fact, some scientists believe that the human
mind uses transformations to help visualize the
world around us.
1. A line that divides an object or image into two identical halves is called a ________________________________. How many lines of reflections are there in
the following images? Describe them
Ms. Lokseth
Math 9: Circles, Transformations and Similarity
2. In the following figure the line of
reflection is represented by a
dashed line, labeled r. Describe the
reflected image.
3. Examine the figure.
a) Figure ABC has been
translated to create image A’B’C’.
What rule could describe the
translation?
b) How many ways can we
describe translations? (ie. Words,
symbols)
c) Describe a translation that
would place the image for ABC in
quadrant III.
Note to self: What are the 4
quadrants on this grid?
A transformation moves a geometric figure.
Examples: translations, reflections and rotations.
A translation: slides an image along a straight line.
Ways of describing:
Words – 3 units right and 2 down
Abbreviations – 3R and 2D
Symbols 
Mapping notation: (x,y)  (x + 3, y – 2)
Ms. Lokseth
Math 9: Circles, Transformations and Similarity
Animations:
Butterfly animation
Letter H animation
What do you notice about shapes that have symmetry?
Goldfish Animation
Ring of pencils animation
Letter L animation
Connect
Objects can be folded or reflected onto themselves
to produce a mirror image. Asymmetrical objects
produce figures that do not exactly match up. An
image that gives two identical halves when it is
reflected on itself is said to have line symmetry.
The fold line that divides the object into the two
mirror images is called the line of symmetry.
Objects can have one line of symmetry, many lines
of symmetry, or no line of symmetry.
line symmetry: the term that
describes when an object
produces two identical halves
when it is reflected onto itself
line of symmetry: a line about
which a figure is symmetrical
If a figure can be folded such
that the two parts exactly
match, the fold line would be a
line of symmetry.
The identical halves can
be produced by vertical,
horizontal, or oblique
(slanted) lines of
symmetry.
Example 1: Find lines of symmetry
Each of the following demonstrates line symmetry. State the number of lines
of symmetry and describe each one.
a)
b)
Ms. Lokseth
Math 9: Circles, Transformations and Similarity
c)
Show you know
How many lines of symmetry are possible for each figure? Describe each line
of symmetry as being vertical, horizontal or oblique (diagonal)
Example 2: Complete drawings using symmetry
Each drawing shows half of a figure. The dashed brown line represents a line
of symmetry for the figure. Draw a complete version of each figure.
Ms. Lokseth
Math 9: Circles, Transformations and Similarity
Show you know
Copy each shape. Use the line of symmetry and a method of your choice to
complete each shape.
Complete Lesson 1 Exit Card – Hand in before you
begin the assignment (complete what you can)
Related Text Questions: Pg.