Reflection Symmetry

Reflection Symmetry

Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to see, because one half is the reflection of the other half.

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
(also called the "Mirror Line")

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.
reflection parinacota

Line of Symmetry

graph line of symmetry

The Line of Symmetry (also called the Mirror Line) 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.

See these examples (the artwork was made using Symmetry Artist) :

Line of Symmetry
Sample Artwork
Example Shape
graph x axis symmetry art x symmetry shape x
graph y axis symmetry art y symmetry shape y
graph y=x symmetry art y=x symmetry shape y=x
graph y=-x symmetry art y=-x symmetry shape y=-x

Plane Shapes

Not all shapes have lines of symmetry, or they may have several lines of symmetry. For example, 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

I have collected some more examples at Lines of Symmetry of Plane Shapes.