Brand Symmetry

'Symmetrical Logos: Rebuild and Make Your Own' 

Humans, and nature, are natural pattern spotters. We are drawn to symmetry, just as bumble bees are in their hunt for pollen. So it is not surprising that most well-known companies have symmetry in their Logos. Which of the below Logos (image from are symmetrical and which aren't? Describe their symmetry?

Your aim is to rebuild the company logos below starting from a small fragment.

You need to feel confident in finding equations of straight lines. If you want more practice or a quick review/reminder try the Straight Line Graphs or  Equations of Lines activities.


Rebuild each of the logos below using lines of reflection. For the last "Jewish Star" applet your teacher may suggest using rotations also to try and find as many different solutions as possible. You can use the worksheet below to help you work out the equations of lines if necessary.

Brand Symmetry

Internet Explorer users (and ipad/iphone users) click on this Direct link Coco Chanel Remake

  Direct link: Union Jack Remake

Challenge: Is the picture of the Union Jack below the same as the real British Union Jack? What are the symmetries in the real Union Jack?

Direct link Jewish Star Remake

When you've finished the challenges above. . .

(1) Try finding your own picture. Using a FREE downloadable photo editor such as (a more developed version of paint with transparent background options), gimp or any of the many other options (Adobe photoshop, Fireworks etc.), trim the picture down to a small symmetrical fragment, erase the background and save as a PNG file (otherwise the background may still show, if using gimp you will need to use the file menu option "Export as" then choose the .PNG format). You can then insert it in a Geogebra page for your partner to start remaking the original. Why not donate to gimp, donate to a euro or two [or more :) ]if you do end up using gimp or paint.

(2) If you resize the picture, whilst maintaining the symmetry, what effect does this have on the equations of symmetry? Do you think it will affect the gradient and the y-intercept or only one of them?

(3) Why not try making your own brand symbols starting from a basic building block – see this Equation Reflections activity for some initial ideas. Then give your partner the original shape you started with, a copy of the image they're aiming for, and see if they can rebuild the original from your fragment.

This is an overview video of how to edit a picture and make its background transparent using the  FREE photo editor (


This is an overview video of how to edit a picture and make its background transparent using the  FREE photo editor gimp (


  • Compare the image fragment in each of the applets above to the image of the complete company logo. Where do you need to place your mirrors to rebuild each logo back to its original form? Can you work out the equations of each of these lines of reflection? 
  • If your teacher has given you a print out of the above you can draw on where you think the mirrors would need to go to help you in finding their equations.
  • Once you think you have worked out the equation of each line, enter them in the "input bar" at the bottom of each applet and press ENTER. Then click first on the fragment of the image, then the mirror line you want to reflect it in.
  • Once you've finished re-building each of the four logo applets, find one on internet or create your own, use a photo editor (photoshop, fireworks etc.) to create a small fragment of it from which your partner can rebuild the original.
  • See the video overview above for further help with using the Geogebra commands on the applets.
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