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This game can be played against a friend or against the computer.
Players take it in turns to click on a dot on the grid - the first player will place blue triangles and the second player will place pink squares.
The winner is the first to have chosen four dots that can be joined to form a rhombus.
Rhombuses can be anywhere and any size.
Clicking on the purple settings cog allows you to select the size of the grid, who the players are, and who goes first.
Once you've played a few times against a friend, you might like to discuss your strategies, and then test them by playing against the computer.
Can you find a winning strategy?
If you are not using the interactive game, you may like to print off some dotty paper.
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?