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Samantha from Hamlin sent us her work on this problem. She found that it is possible to choose cards so that all of the boxes can be filled in. In fact, she chose cards so that she could fill in all of the boxes using a 1x1 square! Here is her example :

  Has all equal angles Has rotational symmetry Has more than 1 axis of symmetry Has area of 1 unit
Has more than 2 equal angles        
Has more than 1 right angle        
Has more than 2 equal sides        
Has 2 pairs of parallel sides        

Well done to Christine, Peter, Rebecca and Josh from Ely St John's School who found two more ways to choose cards so that all the boxes could be filled in. They decided to use rectangles as well as squares. Here is one of their solutions.
 
  Has more than 1 axis of symmetry Has all equal angles Has more than 2 equal angles Has 2 pairs or parallel sides
Has more than 1 right angle square square  square square
Has more than 2 equal angles square square square square
Has area of 1 unit
 
square square square square
Has area of 2 units
 
rectangle rectangle rectangle rectangle

George found that it is possible to choose cards so that none of the boxes can be filled in. Here's the example he sent us:

  More than one axis of symmetry Just two pairs of parallel sides Rotational symmetry All angles equal
Just one axis of symmetry        
Just one pair of parallel sides        
Just two equal angles        
One right angle        


If anyone has had a go at these questions using the triangle cards, do send your solutions to the secondary team.