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.