Reflection Symmetry

The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry). It 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

reflection parinacota

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, as the image is changed a little by the lake surface.
 The Line of Symmetry can be in any direction (not just up-down or left-right). To learn more, go to Reflection Symmetry.

Rotational Symmetry

With Rotational Symmetry, the image is rotated (around a central point) so that it appears 2 or more times. How many times it appears is called the Order.

Here are some examples (they were made using Symmetry Artist, and you can try it yourself!)

Order Example Shape Artwork
symmetry order 2 symmetry shape order 2 symmetry art order 2
symmetry order 3 symmetry shape order 3 symmetry art order 3
… and there is Order 4, 5, etc …

Point Symmetry

origin symmetry

Point Symmetry is when every part has a matching part:

  • the same distance from the central point
  • but in the opposite direction.

It is also the same as “Rotational Symmetry of Order 2” above

Create a symmetrical artwork using the following website:

Extension Activity:

Fold a piece of A4 paper. Using stencils or your best artistic skills, write your name on the piece of paper with the folded side towards the bottom of the page. Cut out your name and investigate the below question.

What kind of symmetry is this piece?

Is it a reflection?

Is it a mirror image?

Is it a translation?