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 triangle An Equilateral Triangle (3 sides)
has 3 Lines of Symmetry
 
  symmetry square A Square (4 sides)
has 4 Lines of Symmetry
symmetry regular pentagon A Regular Pentagon (5 sides)
has 5 Lines of Symmetry
 
  symmetry regular hexagon A Regular Hexagon (6 sides)
has 6 Lines of Symmetry
symmetry regular septagon A Regular Heptagon (7 sides)
has 7 Lines of Symmetry
 
  symmetry regular octagon 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.

  circle symmetry