If it is required to make a pattern that is similar to a original pattern, various similarity descriptions can be used. These similarity descriptions are reflection with respect to an axis, reflection with respect to a point, rotation and translation. By using the coordinate system, the figures and their simlarity descriptions can be presented computationally. Computer graphics are also based on these same principles.

If one of the similarity descriptions returns the pattern to exactly the same place it was originally, there will be symmetry in the pattern. A pattern that is reflected through an axis is said to be symmetrical about an axis. The axis is then called the axis of symmetry.

Example 1

Reflecting the triangle [[$ ABC $]]​ with respect to the line [[$ s $]]​ gives a reflected triangle [[$ A'B'C' $]]​, which is similar to the original triangle.

Example 2

Below, you can see some examples of patterns that are symmetrical about an axis. The axes of reflection are marked in red.