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Let Us Reflect

Stage: 2 Challenge Level: Challenge Level:1

Ruth has sent in some ideas for the first part of the question. She says you can put a mirror across the middle or diagonally from corner to corner to see the whole square. She sent these diagrams:

square with horizontal line across the middle
square with diagonal line from bottom left corner to top right corner
Gemma from Greenleas Primary School managed to find a few more ways of seeing the whole square, as well as some other shapes:

Mirror square
Siobhan from Daubeny Middle School also sent in a very nice solution. She says:

There are four positions where the mirror can be put and you can still 'see' the whole square: vertically in the centre, horizontally in the centre, and on the two diagonals. So the square has four lines of symmetry. To reflect part of the square to make another shape, half the number of the sides of the shape you want to make would need to be reflected into the mirror. The shape you make will have at least one line of symmetry. The diagrams shows the positions of the mirror to make more shapes.


Thank you for writing to us Siobhan, Ruth and Gemma. Well done!