The Pythagoras theorem for this diagram is ____.

1. Area of the outer square with side of length (a + b) = Side x side

= (a + b) x (a +b)

= $(a+b{)}^2$ ..... (1)

2. Area of the outer square = $c^2+\frac{1}{2}\left(ab\right)4$

= $c^2+2ab$ .......(2)

Equating (1) and (2),

$(a+b{)}^2=c^2+2ab$

$a^2+b^2+2ab=c^2+2ab$

$c^2=a^2+b^2$

The Pythagoras theorem for the given diagram is $c^2=a^2+b^2$