1. Reflection Symmetry
Aka: Line Symmetry

2. 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.

3. Lines of symmetry can cut through shapes that have reflection symmetry
Draw in lines of symmetry for each: A C G
none

4. Segment Theorem:
Figures with reflection symmetry have their pre-images and images equal distances from the reflection mirror.
5 in 5
6 in 6 10
10 in

5. Circle Symmetry: Infinite!
How many lines of symmetry does a circle have??
Infinite!

6. The white line down the center is the
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

7. 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.

10. You can find if a shape has a Line of Symmetry by folding it.
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

11. Try folding another direction and it works
So this is a Line of Symmetry

12. 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

13. Line of Symmetry
Sample Artwork
Example Shape

14. Line of Symmetry
Sample Artwork
Example Shape

15. Not all shapes have lines of symmetry,
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

16. Irregular Quadrilateral
Quadrilaterals
Different types of Quadrilaterals
Irregular Quadrilateral
Rectangle
Square
4 Lines of Symmetry
2 Lines of Symmetry
No Lines of Symmetry

17. Kite
Rhombus
1 Line of Symmetry
2 Lines of Symmetry

18. A regular polygon has all sides equal, and all angles equal:
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 Hexagon (6 sides) has 6 Lines of Symmetry
A Regular Octagon (8 sides) has 8 Lines of Symmetry
A Regular Heptagon (7 sides) has 7 Lines of Symmetry

19. 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.

20. 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?
B C D E H I K O X
3.  If the alphabet were printed in simple block printing, which capital letters would have BOTH vertical and horizontal symmetry?
H I O X
H I O X

21. 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