Reflection Symmetry
Aka: Line Symmetry
Reflection-Symmetric Figures
A figure has symmetry if there is an isometry that maps
the figure onto itself. If that isometry is a reflection, then
the figure has reflection symmetry.
Lines of symmetry can cut through shapes that
have reflection symmetry
Draw in lines of symmetry for each:
A
C
G
none
Segment Theorem:
Figures with reflection symmetry have their
pre-images and images equal distances
from the reflection mirror.
5 in
6 in
10 in
5
6
10
Circle Symmetry:
How many lines of symmetry does a circle have??
Infinite!
Reflection Symmetry is easy to recognize,
because one half is the reflection of the other half.
Here, a dog "Flame“, has her face made perfectly
symmetrical with a bit of photo magic.
The white line down the center is the
Line of Symmetry
The reflection in this lake also has symmetry, but in this case:
•the Line of Symmetry runs left-to-right
•it is not perfect symmetry, because the image is changed a
little by the lake surface.
Folding Test
You can find if a shape has a Line of Symmetry by folding it.
When the folded parts coincide then the fold line
is a Line of Symmetry.
Fold a rectangle one way, and it didn't work.
So this is not a Line of Symmetry
Try folding another direction and it works
So this is a Line of Symmetry
Line of Symmetry
The Line of Symmetry does not have to
be up-down or left-right, it can be in
any direction.
But there are four common directions,
and they are named for the line they
make on the standard XY graph.
x-axis
y-axis
y = x line
y = -x line
Line of Symmetry
Sample Artwork
Example Shape
Line of Symmetry
Sample Artwork
Example Shape
Plane Shapes
Not all shapes have lines of symmetry,
or they may have several lines of symmetry.
A Triangle can have 3, or 1 or no lines of
symmetry:
Equilateral
Triangle
Isosceles
Triangle
Scalene
Triangle
3 Lines of Symmetry
1 Line of Symmetry
No Lines of Symmetry
Quadrilaterals
Different types of Quadrilaterals
Square
Rectangle
Irregular
Quadrilateral
4 Lines of Symmetry
2 Lines of Symmetry
No Lines of Symmetry
Kite
1 Line of Symmetry
Rhombus
2 Lines of Symmetry
Regular Polygons
A regular polygon has all sides equal, and all angles equal:
A Regular Pentagon (5 sides)
has 5 Lines of Symmetry
A Regular Heptagon (7 sides)
has 7 Lines of Symmetry
A Regular Hexagon (6 sides)
has 6 Lines of Symmetry
A Regular Octagon (8 sides)
has 8 Lines of Symmetry
Circle
A line (drawn at any angle) that goes through its center
is a Line of Symmetry.
So a Circle has infinite Lines of Symmetry.
ABCDEFGHIJKLMNOPQRSTUVWXYZ
1. If the alphabet were printed in simple block printing, which
capital letters would have vertical line symmetry?
2. If the alphabet were printed in simple block printing, which
capital letters would have horizontal line symmetry?
BCDEHIKOX
3. If the alphabet were printed in simple block printing, which
capital letters would have BOTH vertical and horizontal H
symmetry?
I
HIOX
O
A
H
I
M
O
T
U
V
W
X
Y
4. Which of the following lettered items possesses line symmetry?
Consider vertical and/or horizontal symmetry.
Circle ALL that apply.
a. the letter F
b. an equilateral triangle
c. the letter X
d. the word BOO
e. a square
f. the word WALLY
g. the letter Q