Simple Combined Symmetries

This applet demonstrates simple symmetry (rotations and reflections in the plane) and how they combine.

Author and programmer: Ron Barrow

UK Years 7-11, KS3, KS4, Foundation and Higher GCSE Mathematics, Grades C - A* - Shape and Space
US - Grades 7 - 10 - Geometry


Instructions below    Waldomaths video    Square Symmetry    Hexagonal Symmetry

[Applet failed to run. No Java plug-in was found.]

How to Use this Applet

This screen has two different modes, Fun Time and Test Time. You can change from one to the other by clicking with your mouse on the circles next to Fun time or Test time.

Fun Time! Just paly around
You'll see a simple shape on the screen, and a list of 7 actions you can do with it. Click with your mouse on one of the little red squares by the actions, and a new shape will be drawn on the screen using that action. Clicking on other actions will draw more shapes, up to four in total. To start again, click the Reset button.
If you click on the little circle below the first shape, you can drag this shape to a new position. All other shapes you have drawn will move too. Try it! It's fun, and you'll be able to see some pretty dance-type movements.

Test Time! Test your understanding
This time you'll see the first shape (with the drag circle at the bottom) and a another shape in a different colour. Your mission (should you choose to accept it!) is to move the first shape onto the second one in a single move, by choosing and clicking one of the seven actions on the left. If you get it right, you see an outline around the second shape and a Well Done! message at the side. If you are not correct the outline shape will appear somewhere else, so you'll have to choose a new action. Try to get it right first time! You can have as many goes as you like by pressing the Reset button.
There is a great deal you can investigate on this screen. Play around and enjoy it, but to get the most out of it you'll have to do some careful thinking!