Line of Symmetry
Kimberly Hopkins
Jen Kershaw
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Printed: July 7, 2016
AUTHORS
Kimberly Hopkins
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Line of Symmetry
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Line of Symmetry
In this concept, you will learn about symmetry.
Raven has been studying lines of symmetry with her class. When she goes home, she looks at her cat and notices
that his face is symmetrical. She grabs a sheet of paper and holds it in the middle of her cat’s face, then she rotates
the paper to see if the cat’s face has other lines of symmetry. What type(s) of line symmetry does Raven’s cat have?
In this concept, you will learn about symmetry.
Symmetry
In geometry, a figure or an object can have symmetry. Symmetry is having one side that exactly mirrors the other.
Here is a butterfly. Notice that you can draw a line right down the center of the butterfly and one side will match the
other side. Here is what that looks like.
When you can divide a figure or an object into two even matching halves, you say that the figure has line symmetry.
This figure can be divided in one way, vertically. If you tried to divide it horizontally, the two sides would not match.
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Therefore, you can say that the butterfly has bilateral symmetry. Bilateral symmetry means that it has one line of
symmetry that divides the butterfly in half.
A line of symmetry is a line that splits a figure into symmetrical parts. In the butterfly, there is one line of symmetry
that can be drawn to show the two equal matching halves of the butterfly.
Let’s look at a picture of a figure that has more than one line of symmetry.
Here is a cross. This cross has four lines of symmetry. You can divide it vertically and horizontally and both sides
will match. That shows two lines of symmetry.
There are other types of symmetry. There is turn or rotational symmetry. Rotational symmetry means that you
can rotate the figure around a fixed point and it will look the same.
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Chapter 1. Line of Symmetry
This star has rotational symmetry. It looks exactly the same no matter which point is rotated to be at the top. Since
there are 5 points, this is a figure with a rotational symmetry of 5.
Examples
Example 1
Earlier, you were given a problem about Raven and her cat.
Raven notices that her cat’s face looks symmetrical. What type(s) of line symmetry does Raven’s cat have?
First, draw a vertical line down the middle of the cat’s face. Does the line divide the cat’s face in to halves that look
the same?
Yes
Next, draw a horizontal line down the middle of the cat’s face. Does the line divide the cat’s face in to halves that
look the same?
No
Then, state the lines of symmetry.
Vertical
The answer is that the cat’s face has a vertical line of symmetry.
Example 2
Identify the lines of symmetry in the object.
First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
Yes
Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the
same?
No
Then, state the lines of symmetry.
Vertical
The answer is that the object has a vertical line of symmetry.
Example 3
Identify the lines of symmetry in the object.
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First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
Yes
Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the
same?
Yes
Then, state the lines of symmetry.
Vertical and horizontal
The answer is that the object has vertical and horizontal lines of symmetry.
Example 4
Identify the lines of symmetry in the object.
First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
No
Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the
same?
Yes
Then, state the lines of symmetry.
Horizontal
The answer is that the object has a horizontal line of symmetry.
Example 5
Identify the lines of symmetry in the object.
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Chapter 1. Line of Symmetry
First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
Yes
Next, draw lines from the middle of each side to the point opposite of it. Do both of the lines divide the object in
halves that look the same?
Yes
Then, state the lines of symmetry.
One line of symmetry from each vertex to the middle of the opposite side for a total of three lines of symmetry.
The answer is that the shape has three lines of symmetry, one from each vertex to the middle of the opposite side.
Review
Identify the lines of symmetry in each figure or object. Draw them in if possible.
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4.
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5.
6.
Identify whether the following objects have rotational symmetry. If yes, write yes. If no, write no.
7.
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10.
11.
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Chapter 1. Line of Symmetry
12.
Find three other objects. Draw them and identify each line of symmetry. Share your findings with a friend.
Review (Answers)
To see the Review answers, open this PDF file and look for section 9.20.
Resources
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/181950
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