Question
Looking at this proof of the Pythagorean Theorem, which statement(s) would be true? CHECK TWO THAT APPLY.(2 points)ResponsesThe length of a is the same as the length of c - (a+b).The length of a is the same as the length of c - (a+b).length of a + length of b = length of clength of a + length of b = length of cThe area of both large squares are equal; so the triangles with the square(s) must have a total area that is equal to each other.The area of both large squares are equal; so the triangles with the square(s) must have a total area that is equal to each other.The yellow triangles have an area of a x b, which would = cThe yellow triangles have an area of a x b, which would = cThe four yellow triangles on the left all have the same area as the four yellow triangles on the right (a+b/2) - therefore, the two small green squares on the left have to have the same area as the large green square on the right.
Answers
GPT-4o mini
Based on the commonly known proof of the Pythagorean Theorem, usually using area comparisons and right triangles, the two statements that would be true are:
1. **The length of a + length of b = length of c** (assuming "length of c" refers to the hypotenuse in the context of the right triangle).
2. **The area of both large squares are equal; so the triangles with the square(s) must have a total area that is equal to each other.**
These statements reflect the essence of the Pythagorean Theorem, which states \(a^2 + b^2 = c^2\), and the reasoning is often demonstrated through areas related to the squares constructed on each side of the triangle. The other statements appear inaccurate or do not convey effective reasoning for establishing the theorem.
1. **The length of a + length of b = length of c** (assuming "length of c" refers to the hypotenuse in the context of the right triangle).
2. **The area of both large squares are equal; so the triangles with the square(s) must have a total area that is equal to each other.**
These statements reflect the essence of the Pythagorean Theorem, which states \(a^2 + b^2 = c^2\), and the reasoning is often demonstrated through areas related to the squares constructed on each side of the triangle. The other statements appear inaccurate or do not convey effective reasoning for establishing the theorem.