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Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

### Making Rectangles, Making Squares

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

# Property Chart

##### Stage: 3 Challenge Level:

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.