Question

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 1

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.