Shown here are the three essential steps in a proof of the Pythagorean Theorem. Which statement is justified by the diagram in Step 1?

A) 4 (

AB

2

) = C2

B) B (A + B) = B2 + 2 (

1

2

BA)

C) A2 + B2 = C2

D) (A + B) 2 = A2 + 2AB + B2

Answer: D) (A + B) 2 = A2 + 2AB + B2

Step-by-step explan (A + B) 2 = A2 + 2AB + B2 is correct. The area of the large square can be written as (A+B) (A+B) or, by adding up the areas of the two squares and two rectangles inside it, which are A2, B2, AB, and AB.