This picture shows a proof of the Pythagorean theorem because

Question

b

a

b

a

a

C

a

C

a ^ 2

a

C

c ^ 2

b

bc

C

b ^ 2

b

a

a-

b

Figure 4-A

b

a

Figure B

(1 point)

a = b = c so the Pythagorean theorem holds true.

a < b < c so the Pythagorean theorem holds true.

The four yellow triangles are congruent in both large squares and the large squares are congruent, so c ^ 2 = a ^ 2 + b ^ 2

The yellow triangles fill up the large squares just enough to have a small square in each figure.

Answer 1

Therefore, the Pythagorean theorem holds true in this picture because the four yellow triangles are congruent in both large squares, and the large squares are congruent, proving that \( c^2 = a^2 + b^2 \).