Algebra 1

First we must define the area of a square: $A(large)=(b+a)(b+a)= a^2+2ab+b^2$. Now we find the area of the small square: $A(small)= c^2$. The area of a triangle is $A(triangle)=ab/2$. Now we can find the area of the large square in a different way: $A(large)= c^2+2ab$, which is equal to the first equation, giving that $a^2+b^2=c^2$