Reflection Symmetry
Bill Zahner
Lori Jordan
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Printed: April 21, 2016
AUTHORS
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Reflection Symmetry
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Reflection Symmetry
Here you’ll learn how to determine whether or not a shape has reflection symmetry and how to draw lines of
symmetry.
What if you were asked to consider the presence of symmetry in nature? The starfish, below, is one example of
symmetry in nature. Draw in the line(s) of symmetry. After completing this Concept, you’ll be able to draw lines of
symmetry through shapes and objects like this one.
Watch This
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/137546
CK-12 Foundation: Chapter12ReflectionSymmetryA
Learn more about reflectional symmetry by watching the video at this link.
Guidance
A line of symmetry is a line that passes through a figure such that it splits the figure into two congruent halves.
Many figures have a line of symmetry, but some do not have any lines of symmetry. Figures can also have more than
one line of symmetry. A shape has reflection symmetry when it has one or more lines of symmetry.
Example A
Find all lines of symmetry for the shape below.
This figure has two lines of symmetry.
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Example B
Does the figure below have reflection symmetry?
Yes, this figure has reflection symmetry.
Example C
Does the figure below have reflection symmetry?
Yes, this figure has reflection symmetry.
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Chapter 1. Reflection Symmetry
Watch this video for help with the Examples above.
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/137547
CK-12 Foundation: Chapter12ReflectionSymmetryB
Concept Problem Revisited
The starfish has 5 lines of symmetry.
Guided Practice
Find all lines of symmetry for the shapes below.
1.
2.
3
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3.
Answers:
For each figure, draw lines through the figure so that the lines perfectly cut the figure in half. Figure 1 has eight, 2
has no lines of symmetry, and 3 has one.
1.
2.
3.
Explore More
For #1 through #8, determine whether each statement is true or false.
1. All right triangles have line symmetry.
2. All isosceles triangles have line symmetry.
3. Every rectangle has line symmetry.
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4.
5.
6.
7.
8.
Chapter 1. Reflection Symmetry
Every rectangle has exactly two lines of symmetry.
Every parallelogram has line symmetry.
Every square has exactly two lines of symmetry.
Every regular polygon has three lines of symmetry.
Every sector of a circle has a line of symmetry.
9. What type of shape has an infinite number of lines of symmetry?
Find all lines of symmetry for the letters below.
10.
11.
12.
13.
14.
Determine if the words below have reflection symmetry.
15.
16.
17.
18.
19.
OHIO
MOW
WOW
KICK
pod
Trace each figure and then draw in all lines of symmetry.
20.
21.
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22.
Determine if the figures below have reflection symmetry. Identify all lines of symmetry.
23.
24.
25.
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 12.1.
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