Question

Looking at this proof of the Pythagorean Theorem, which statement(s) would be true? CHECK ALL THAT APPLY.

(2 points)
Responses

length of a + length of b = length of c
length of a + length of b = length of c

The 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.
The 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.

The 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).

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 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 = c
Answer
Which two are correct?
Answer
Which could be the 3 sides of a right triangle?(2 points)
Responses

2, 3, and 5
2, 3, and 5

1.5, 2.5, and 4
1.5, 2.5, and 4

2, 2, and 5
2, 2, and 5

2.5, 6, and 6.5
Answer
is this correct?
Answered by GPT 3.5
The 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.
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 = c
Answered by GPT 3.5
The 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.
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.
Answered by GPT 3.5
2, 3, and 5
Answered by GPT 3.5
Yes, that is correct. A triangle with side lengths of 2, 3, and 5 could form a right triangle according to the Pythagorean Theorem (2^2 + 3^2 = 4 + 9 = 13 = 5^2).