Lines of Symmetry of Plane Shapes

Line of Symmetry

dog mirror 

 

Here my 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

Read more at Reflection Symmetry.

Folding Test

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

When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.

Here I have folded a rectangle one way, and it didn't work.

symmetry folding no
So this is not a Line of Symmetry

But when I try it this way, it does work (the folded part sits perfectly on top, all edges matching):

symmetry folding yes
So this is a Line of Symmetry

Triangles

A Triangle can have 3, or 1 or no lines of symmetry:

symmetry equilateral triangle symmetry isosceles triangle no symmetry scalene triangle
Equilateral Triangle
(all sides equal,
all angles equal)
 Isosceles Triangle
(two sides equal,
two angles equal)
 Scalene Triangle
(no sides equal,
no angles equal)
3 Lines of Symmetry 1 Line of Symmetry No Lines of Symmetry

Quadrilaterals

Different types of Quadrilaterals (a 4-sided plane shape):

symmetry square symmetry rectangle symmetry irregular quad
Square
(all sides equal,
all angles 90°)
 Rectangle
(opposite sides equal,
all angles 90°)
 Irregular
Quadrilateral

4 Lines of Symmetry 2 Lines of Symmetry No Lines of Symmetry

 

symmetry kite symmetry rhombus
Kite
 Rhombus
(all sides equal length)
1 Line of Symmetry 2 Lines of Symmetry

Regular Polygons

A regular polygon has all sides equal, and all angles equal:

symmetry equilateral triangleAn Equilateral Triangle (3 sides)
has 3 Lines of Symmetry
 
 symmetry squareA Square (4 sides)
has 4 Lines of Symmetry
symmetry regular pentagonA Regular Pentagon (5 sides)
has 5 Lines of Symmetry
 
 symmetry regular hexagonA Regular Hexagon (6 sides)
has 6 Lines of Symmetry
symmetry regular septagonA Regular Heptagon (7 sides)
has 7 Lines of Symmetry
 
 symmetry regular octagonA Regular Octagon (8 sides)
has 8 Lines of Symmetry

And the pattern continues:

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.

 circle symmetry