After School Booster Group Remember any point is the same distance away from the line of symmetry as its reflection.

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1 Mirror Symmetry Remember the key is that any point is the same distance away from the line of symmetry as its reflection. There are many types of symmetry, but the one that you have learned about at Primary School is Mirror Symmetry. Symmetry shows how two things are not identical but have something in common. It is a way of using that thing in common, by changing one thing so that it becomes the same as something else. Look at the butterfly. The two wings are obviously not identical, but if you looked at one side in a mirror it would look identical to the other side. Mirror Symmetry changes one side of an image by reflecting it in a mirror so that it is the same as the other side of the image. While butterflies are not exactly symmetrical it gives a good idea. When you reflect a shape, ask does this look like a weird shaped butterfly? The line drawn down the middle is very nearly a line of mirror symmetry where a mirror could be placed and when you looked into it the reflection of one side would look just like the hidden side. So in this case, one side of the image is changed by reflecting it in a mirror so that it looks just like the other side of the image. You will often get asked in SATs to complete a line drawing that has a line of mirror symmetry drawn on it. There are a number of key tips to help with this: 1. DO NOT use a mirror to help draw a figure. Some teachers tell you to do this, but it is very likely to lead to mistakes. 2. You may use a mirror to check what you have done, but I don t think that it is necessary and again can be error prone. 3. Some teachers tell you to use tracing paper, trace the image and then turn the tracing paper over and use it to mark out the shape on the other side of the line of symmetry. I am not a fan of this method, finding it clumsy and awkward. 4. Sometimes teachers will tell you to use the fact that lines go a certain number of lines up and across to draw them. DO NOT DO THIS. Use this fact to check results.

2 5. The key technique is to remember that any point is the same distance away from the line of symmetry as. Look at the line joining the white dots. Firstly it is perpendicular to the line of symmetry. Secondly both dots are the same distance from the line of symmetry. 6. So, use lines perpendicular to the line of symmetry, measure the distances and make sure that the points are the same distance along the line as the original. Draw key points and then join the points up with a ruler to make the lines. 7. There will usually be a grid marked on the page for you. This makes part 5 really easy because the lines are already there for you and you just have to count squares. 8. We looked in class as what happens when the line of symmetry is at an angle to the grid, and will have another look in the second example. Example 1. Example 1 has three key points, the corners of the triangle. If we can reflect those in the line of symmetry (the blue line) and then join them up, we have completed the symmetrical drawing. So the top corner is 5 squares from the line of symmetry, so it reflection will also be 5 squares on the other side of the line of symmetry. The grid makes it easy to use perpendicular lines to help this. The middle point is 8 squares from the line of symmetry and the bottom corner is 6 squares from the line of symmetry, so their reflections must also be those distances from the line of symmetry. Drawing the corners in first and then drawing lines between the corners gives us the next figure. Count the number of squares from each corner to the line of symmetry to check that is the same number of squares away. Check your work by noting that the line between the top and middle corners goes up 4 squares and along 3 squares. Check that also does that. Likewise, the line from the middle square goes 2 squares across and 4 up; the line from the bottom corner to the top one is 1 across and 8 up. Check that their reflections do the same thing. So the steps are: 1. Reflect each corner on a shape making sure that is the same distance away from the line of symmetry.

3 2. Join the corners up using a ruler to draw the lines. 3. Check the result by counting how many squares up and across each line goes it should be the same for each line and. 5 squares 5 squares 8 squares 8 squares 6 squares 6 squares Example 2 The previous example was relatively easy since the line of symmetry followed the grid lines. Sometimes in SATs the line of symmetry does not follow the grid lines but is at 45 to them. We use the same idea of points and their reflections being the same distance away from the line of symmetry. We use the same figure as last time, but have the line of symmetry at 45.

4 I have drawn an orange line perpendicular to the line of symmetry from the top corner. Notice that, like the line of symmetry, it goes from corner to corner of each square in the grid rather than along the grid lines. Count the number of squares that it goes through to reach the line of symmetry (4 ½). It also does that on the other side of the line of symmetry and so we know where to put the reflection of the corner. Check this for the other reflected corners. Now check how many squares each line goes up and across (what do you notice?) 4 ½ diagonals 4 ½ diagonals Some examples for you to try:

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6 Answers. I haven t put in all the labels, just enough for you to get the idea. Red is the shape, blue the line of symmetry and yellow the guide lines ½ diagonals 6 ½ diagonals 3 3

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