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Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. What is the area of the square? From this formula for the area of this square derive a formula for the area of the trapezium.

Now write down the area of the trapezium as the sum of the areas of the three right angled triangles.

Use these results to give a proof of Pythagoras Theorem explaining each step.

*This proof is credited to James A. Garfield (1876) the 20
^{th} President of the United States.*