To determine which statement about the proof is false, let's analyze each option based on the context of the Pythagorean theorem and the provided images:
A. The sum of the areas of the triangles in step 1 equals the sum of the areas of the triangles in step 2.
- This statement is likely true if both steps involve the same configuration of triangles rearranged, which is often the case in proofs of the Pythagorean theorem.
B. In step 1, the sum of the areas of the interior squares equals the sum of the areas of the four triangles.
- This statement is usually true in proofs involving the Pythagorean theorem, where the areas of the squares (a² + b² from the squares of sides a and b) would typically relate to the areas of the triangles involved.
C. The proof shows that a² + b² = c².
- This statement, if the proof is indeed an illustration of the Pythagorean theorem, would be true since the theorem states that the sum of the squares of the two legs (a and b) of the right triangle equals the square of the hypotenuse (c).
D. The area of the interior square in step 2 is equal to the combined area of the two interior squares in step 1.
- This statement is true as per the Pythagorean theorem proof. The area of the square with side c (c²) should equal the combined areas of the squares with sides a and b (a² + b²).
Given the logical analysis, B is the statement that is likely to be false. The areas of the triangles do not equal the combined area of the squares unless specifically shown within the valid context, which often is not the case.