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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.
