The question asks to explain why the sum of the areas of the two white squares in Figure 2 is the same as the area of the white square in Figure 1. Here's a breakdown:

• Figure 1 shows a large square with side length $c$ (diagonal), and four triangles inside it, which leave a smaller square with area $c^2$ in the middle.
• Figure 2 splits the area into two squares, with areas $a^2$ and $b^2$, and the same four triangles.

The key is understanding that both figures represent the same total area, rearranged differently. The triangles are congruent in both figures, and the total area in each figure must be the same, so the remaining white areas must be equal. This is the geometric proof of the Pythagorean theorem:

$a^2 + b^2 = c^2$.

Now, looking at the answer choices:

1. "The combined area of the four triangles is equal to the area of the large white square." — This is incorrect because the triangles' combined area is not equal to the white square's area in Figure 1.

2. "In each figure the total area is equal and the area of the 4 triangles is equal, so the remaining white area in each figure must also be equal." — This is correct. It explains that since the total area and triangle areas are the same in both figures, the white areas must be equal.

3. "In each triangle, the length of side a plus the length of side b equals the length of side c. That means that $a^2 + b^2 = c^2$." — This is a true statement, but it doesn't directly explain why the areas are equal geometrically. It's a different form of proof.

The correct answer is the second option: "In each figure the total area is equal and the area of the 4 triangles is equal, so the remaining white area in each figure must also be equal."

Would you like any further details or have any questions?

Here are five relative questions for further exploration:

1. How does the Pythagorean theorem relate to right triangles in general?
2. Why does rearranging the triangles in different figures not change the total area?
3. What is the algebraic proof of the Pythagorean theorem?
4. Can the Pythagorean theorem be used in non-Euclidean geometry?
5. How can you prove the Pythagorean theorem using similar triangles?

Tip: When solving geometry problems, visualizing the total area and how parts fit together can help in understanding the relationship between shapes.