This diagram can be used to prove the Pythagorean Theorem.

Question

Which statement would be included as a crucial step in proving the Pythagorean Theorem using this diagram?

(2 points)
Responses

The blue square on the right contains the yellow square + the green square on the left
The blue square on the right contains the yellow square + the green square on the left

The area of the purple and red triangles on the left add to be the area of the yellow square.
The area of the purple and red triangles on the left add to be the area of the yellow square.

The yellow square on the left contains the four triangles on the right
The yellow square on the left contains the four triangles on the right

The yellow square + the green square equal the 2 rectangles on the left

Answer 1

The crucial step in proving the Pythagorean Theorem using the described diagram is:

The blue square on the right contains the yellow square + the green square on the left.

This statement fundamentally captures the relationship between the areas represented in the diagram, illustrating how the areas of the squares on the legs of the right triangle (yellow and green) relate to the area of the square on the hypotenuse (blue). This aligns with the core principle of the Pythagorean Theorem: \( a^2 + b^2 = c^2 \).