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Symmetry - for teachers


Index --- reflective --- rotational --- identify --- make simple, 2, 4 symmetry --- make 3, 6 symmetry --- make snowflake --- examples --- for teachers

This website is about symmetry. It has a couple of exercises for learning about reflective and rotational symmetry, and some examples to practise identifying symmetry. It also lets you design symmetrical picture online. It uses JavaScript to do this. This means that your finished symmetrical picture is not a conventional picture, so you can't save or print it in the normal way. However, there are other ways to do this.

Exercises for learning about reflective and rotational symmetry

There are two simple exercises for learning about reflective and rotational symmetry. In each, you choose a shape (rotational) or letter (reflective) and think about whether it has the right sort of symmetry. Then you test it. The rotational symmetry page rotates the shape. If it isn't rotationally symmetrical, then it will be a different shape after being rotated. The reflective page draws a line, horizontal and vertical, rubs out half the chosen letter, and mirrors the remaining half the other side of the line. If it looks the same as the original letter, then it must have that sort of symmetry.

This page can be used either as a demonstration of why a shape or letter is or is not symmetrical. Or it can be used by students to experiment for themselves in learning how to identify symmetry. Finally, it can be used to test their knowledge once taught (this is rather boring, I think!)

Identify symmetry

There is a page of examples of symmetry. They are small symbols and pictures of many different types of symmetry, and when you click on one, it tells you what the symmetry is. Like the exercises described above, it's best to think before clicking what the symmetry is, and then see if you're right. There are a couple of traps! To be truly symmetrical, the whole of the picture or symbol must rotate or reflect, and the colours must be the same.

This page will tell you if a shape has reflective and/or rotational symmetry. All pictures with reflective symmetry with more than one line of symmetry also have rotational symmetry.

Symmetrical picture designers

There are three online design pages.

The first allows you to create online pictures with reflective symmetry of one, two or four lines of symmetry, or two-fold or four-fold rotational symmetry. You can choose which symmetry and click anywhere within the picture. A square of the chosen colour will appear there, plus further squares in the correct places to keep the picture in the chosen symmetry. You can make a pattern or a picture (although the picture must be symmetrical, of course!) At any time, you can show or hide the line/s of symmetry. Rotational symmetry is about a point rather than a line, so this doesn't show. If you want, you can even choose a random symmetry, make a pattern and see which symmetry it is!

The second designer allows you to create online pictures with reflective symmetry of three or six lines of symmetry, or three-fold or six-fold rotational symmetry. It is based on triangles rather than squares. Triangles are rather slow to process, so in this page, to speed things up, you can only click within part of the picture. This is shown by grid lines which you can hide.

The third designer makes snowflakes! You click within the grid lines (as these are triangles again) to make a triangle white, and click it again to make it black again. The symmetry is reflective with six lines of symmetry (as snowflakes are).

There is a page of examples made using these design pages. I'm sure that people can make better ones themselves, and if anyone sends me some, I'll put them up on the page! But it shows the sort of thing that you can do.

Printing a symmetrical picture

The easiest way to print a symmetrical picture is to print off the whole webpage in the normal way. Then you can cut out the symmetrical picture if you wish.

You can copy the symmetrical picture to a word processor. Then you can print or save it to print later.

Copying a symmetrical picture to a word processor

There are two ways to copy the symmetrical picture to a word processor.

You can high-light the symmetrical picture with click-and-drag. Once you have done this, click on Edit/Copy (top of screen). Leave the webpage and open a word processor file, such as Word. Clink on Edit/Paste in the word processor file and wait a bit, and the symmetrical picture should appear. The format may look a little ragged. Now it is part of the word processor file, you can save it or print it as you wish. I cannot guarantee that this will work with all word processors.

The second way is to screen print. On standard Windows keyboards, there is a key (top right) with Print Scrn or similar on it. When you have the symmetrical picture on screen, click on this. This dumps whatever is on the screen into the 'copy' area (which is called the clipboard). Now go into a word processor file, or any program that handles pictures (such as Paint). Now click on Edit/Paste, and the screen image will appear. This will have more than just the symmetrical picture. If you are in a Paint program, then you should be able to trim it. Whether you do or not, you can now print or save it as you wish.

Saving the symmetrical picture to continue working on it

The methods above preserve the finished symmetrical picture. But you may wish to save a particularly complicated symmetrical picture, and continue working on it in future.

All symmetrical picture design pages have a white box below the symmetrical picture itself (you may need to scroll down). This contains lots of letters or numbers. As you design the symmetrical picture, you will see that the letters change. At any time, you can copy-and paste this collection of letters or numbers (using click-and-drag in the normal way) into a word processor or Notepad or any other file that accepts writing. There you can save it in the normal way. When you wish to continue working on the maze, you can copy-and-paste it back from the word processor file to the white box in the symmetrical picture design page, and click on Regenerate. Wait a short while, and the picture will re-appear.

You could save all your symmetrical pictures this way if you wish, to keep a record of them.

Downloading the webpage to your own computer

If you want, you can download any of these webpages onto your own computer. This will not save any symmetrical picture that you have been working on. But it does mean that you can work on the page even if you're not connected to the internet, and you will avoid internet problems.

  • Go to the relevant webpage
  • Click on File (at top of screen), then on Save As
  • Find the folder on your own computer where you want the webpage
  • Make sure that Save as type: is Web Archive, single file (*.mht)
  • Click on Save
To use the webpage:
  • Go into My Computer or Windows Explorer
  • Go to the folder where you saved it
  • Double click on the webpage that you want

Remember this will only save one webpage. You cannot move from one webpage to another via the links.