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Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?

Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Printable Image of the problem

There are more than five solutions to this problem - how many can you find?

Can you find them all?

Additional printable copies of the shapes can be found here.

Try changing the question a bit:

For example, design your own set of three shapes (drawn on a square grid, as above), keep the total area 10. How many ways can they be arranged to make symmetrical shapes?
Can you find a set of three such shapes, which have more valid arrangements than the shapes from the original problem?
Can you find three such shapes which can never be arranged to make a symmetrical shape?

This problem is based on one found in the Dime "Line Symmetry A" pack, produced by Tarquin Publications

Click here for a poster of this problem