President Garfield

American president James A. Garfield devised an original proof of the Pythagorean theorem using the following figure. Can you complete the proof?

Source: NCTM Mathematics Teacher

SOLUTION
Area of trapezoid = 2\times area of right triangle abc\;+ area of right triangle cc
Area of trapezoid = half the product of the height and the sum of the bases
Area of triangle = half the product of a base and the height to that base
\frac{1}{2}\left (a+b\right )\left (a+b\right )=2\times\frac{1}{2}ab+\frac{1}{2}c^2
Multiply both sides by 2
\left (a+b\right )^2=2ab+c^2
a^2+2ab+b^2=2ab+c^2
a^2+b^2=c^2

Answer: Given in solution

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About mvtrinh

Retired high school math teacher.
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