Return to the Purplemath home page


Try a demo lesson Join Login to


Index of lessons | Purplemath's lessons in offline form |
Forums | Print this page (print-friendly version) | Find local tutors


Symmetry about an Axis (page 1 of 3)

Sections: Symmetry about an axis, Symmetry about a point, Symmetry and graphing

"Symmetry" is a recognition of the matching-ness of the parts of a shape.

human musculature, with line of symmetry



For instance, the human body is said to have "bilateral" (two-sided) symmetry, because the left and right halves of the body mirror each other, as you can see in the image to the left.



    But this symmetry applies only to the basic framing structure of our bodies; much of our insides, our organs, don't match, as you can see in the image to the right: watch the liver (brown) and the stomach (pink) change sides when the organs are flipped.:


human organs, showing lack of symmetry

The dotted line running down the middle of the left-hand graphic above is called "the axis of symmetry".



If you think of the bilateral-symmetry picture as being drawn on a sheet of transparent plastic with a shish-kebob skewer punched through the dotted line, you could twirl the skewer (and thus the sheet) 180° around and end up looking at the same picture, but from the other side of the plastic sheet:


  Copyright © Elizabeth Stapel 2005-2011 All Rights Reserved


(Note: If this animation experiences occasional breaks, you're probably viewing in Internet Explorer. You might want to upgrade to a more capable browser.)


flipping sheet over axis of symmetry

A figure has as many symmetries as its plastic sheet can have skewers.

For instance, a rectangle can be twirled through its middles, so a rectangle has two symmetries.


a rectangle rotating on its axes of symmetry

A square can also be twirled along its diagonals, so a square has four symmetries.


a square rotating on its axes of symmetry

A triangle might have one or three lines of symmetry, but usually has none:

one line of

three lines of symmetry

no lines of

triangle (isosceles) with one line of symmetry

triangle (equilateral) with three lines of symmetry

triangle with no symmetry

...and a circle has infinitely-many lines of symmetry, since any line through its center (any diameter) is also an axis of symmetry.

Top  |  1 | 2 | 3  |  Return to Index  Next >>

Cite this article as:

Stapel, Elizabeth. "Symmetry about an Axis." Purplemath. Available from Accessed



This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2005-2014  Elizabeth Stapel   |   About   |   Terms of Use   |   Linking   |   Site Licensing


 Feedback   |   Error?