When proving the Pythagorean Theorem, we use the given diagram. The area of the large square is equal to the area all four triangles, plus the area of the inscribed square. Which mathematical sentence demonstrates this? A) a2 + b2 = 1 2 ab + c2 B) a2 + b2 = 4( 1 2 ab) + c2 C) a2 + 2ab + b2 = 1 2 ab + c2 D) a2 + 2ab + b2 = 4( 1 2 ab) + c2

we know that

[area of one triangle]=a*b/2
[area all four triangles]=4*[a*b/2]------> 4*(1/2)ab

[area of the inscribed square]=c*c-----> c²

[area all four triangles +area of the inscribed square]=4*(1/2)ab+c²----> equation 1

[area of the larger square]=(a+b)*(a+b)-----> a²+2ab+b²-----> equation 2

equals 1 and 2

4*(1/2)ab+c²= a²+2ab+b²

therefore

the answer is the option
D) a2 + 2ab + b2 = 4( 1/2 ab) + c2