Use the image to answer the question. Betty is writing a proof of the Pythagorean Theorem using the diagram shown. In the diagram, there is a large square. A smaller square is drawn inside the large square, dividing the large square into a smaller square and 4 small triangles. Step 1: First, I know that the area of a triangle is equal to bh2 . The area of each small triangle would be ab2 . Since there are 4 triangles in the entire square, the area of all 4 triangles together would be equal to 2ab . The area of the small square in the middle can be represented by c2 since the sides each have a length of c . Therefore, the area of the entire large square can be written as 2ab+c2 . Step 2: Another way to think about the area of the entire large square is by looking at its side lengths. The length of each side can be written as a+b , so the area would be (a+b)×(a+b) . Step 3: Since we've expressed the area of the large square in two different ways, now set those two areas equal to each other and then simplify using algebra. (a+b)×(a+b)=2ab+c2 a2+2ab+b2=2ab+c2 a2+b2=c2 In which step of Betty's proof did she make a mistake? Enter 1 for Step 1, enter 2 for Step 2, enter 3 for Step 3, or enter 4 if Betty did not make a mistake in her proof. (1 point) Skip to navigation
Betty made a mistake in Step 1 of her proof. The mistake is in the statement "The area of all 4 triangles together would be equal to 2ab." This statement is incorrect, as the correct area of all 4 triangles together should be equal to ab. Therefore, the correct expression for the area of the large square would be ab + c^2, not 2ab + c^2.
Betty made a mistake in Step 1 of her proof. In this step, she incorrectly calculated the area of all four triangles together as 2ab. The correct area of all four triangles together would be 4ab. Therefore, the correct expression for the area of the entire large square would be 4ab + c^2.
Betty made a mistake in Step 1 of her proof. She incorrectly stated that the area of all four triangles together would be equal to 2ab. The correct area of all four triangles together should be equal to 2ab + c², not just 2ab.
