This picture shows a proof of the Pythagorean theorem because
b
a
b
a
a
C
a
C
a ^ 2
a
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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.
1 answer
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 \( c^2 = a^2 + b^2 \).