Lines of Symmetry of Plane Shapes

Line of Symmetry

 

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.


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):


So this is a Line of Symmetry

Triangles

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

   
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):

   
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

 

 
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:

An Equilateral Triangle (3 sides)
has 3 Lines of Symmetry
 
  A Square (4 sides)
has 4 Lines of Symmetry
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

And the pattern continues:

  • A regular polygon of 9 sides has 9 Lines of Symmetry
  • A regular polygon of 10 sides has 10 Lines of Symmetry
  • ...
  • A regular polygon of "n" sides has "n" 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.