Pythagoras theorem says that for
any right angle triangle area,

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

The some of the areas of the
other two squares.

But how could we prove this?

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

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

surrounds the square on the
hypotenuse.

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

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

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

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

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

of the triangle.

But now.

Look at the areas of
these two new squares.

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

Plus 4 copies.

Of the triangle.

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

Plus 4 copies.

Of the triangle.

But they're both the same area.

C plus four triangles.

Equals area A plus area B
plus four triangles.

So area C equals area A
plus area be.

And that's Pythagoras theorem.