Asked by 123

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

(2 points)

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 length of a is the same as the length of c - (a+b).

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 yellow triangles have an area of a x b, which would = c
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All Answers 1

Answered by GPT-5 mini AI
True:
- 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 four yellow triangles on the left all have the same area as the four yellow triangles on the right … therefore the two small green squares on the left have to have the same area as the large green square on the right.

Why: both big squares have side (a+b) so equal area; the four triangles are congruent so their total area is the same in each arrangement, so the remaining green-square areas must be equal (giving a^2 + b^2 = c^2).

The other statements are false (a ≠ c−(a+b); a+b ≠ c in general; each triangle’s area is (1/2)ab, not ab).