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:

ACG 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 TestYou 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-axisy-axis

y = x liney = -x line

Line of Symmetry Sample Artwork Example Shape

Line of Symmetry Sample Artwork Example Shape

Plane ShapesNot 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

3 Lines of Symmetry

Isosceles Triangle

1 Line of Symmetry

Scalene Triangle

No Lines of Symmetry

Quadrilaterals Different types of Quadrilaterals

Square

4 Lines of Symmetry

Rectangle

2 Lines of Symmetry

Irregular Quadrilateral

No Lines of Symmetry

Kite

1 Line of Symmetry

Rhombus

2 Lines of Symmetry

Regular PolygonsA 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 Heptagon (7 sides) has 7 Lines of Symmetry

A Regular Octagon (8 sides) has 8 Lines of Symmetry

CircleA line (drawn at any angle) that goes through its center is a Line of Symmetry. So a Circle has infinite Lines of Symmetry.

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?

3. If the alphabet were printed in simple block printing, which capital letters would have BOTH vertical and horizontal symmetry?

ABCDEFGHIJKLMNOPQRSTUVWXYZA HI

M O T U V W X Y

B C D E H I K O X

H I O X

H I O X

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 trianglec. the letter X

d. the word BOOe. a square

f. the word WALLYg. the letter Q