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Pythagoras theorem says that for
any right angle triangle area,

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see the area of the square of
the hypotenuse equals A plus B.

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The some of the areas of the
other two squares.

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But how could we prove this?

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Let's start by making a second
copy of the diagram.

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On the left hand copy will
draw this square. It just

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surrounds the square on the
hypotenuse.

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And on the right-hand copy will
draw this square.

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Again, it just surrounds the
squares on the other two sides.

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Now these two knew squares we've
drawn are both the same size.

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In each case, the side of the
new square has length little A

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plus littleby. The sum of the
length of the two shorter sides

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of the triangle.

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But now.

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Look at the areas of
these two new squares.

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The one on the left is made up
of square, see.

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Plus 4 copies.

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Of the triangle.

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The one on the right is made up
of squares A&B.

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Plus 4 copies.

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Of the triangle.

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But they're both the same area.

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C plus four triangles.

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Equals area A plus area B
plus four triangles.

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So area C equals area A
plus area be.

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And that's Pythagoras theorem.