Questions
answered
The diagram shows a larger square divided into a smaller square and four right triangles. The
diagram can be used to prove the Pythagorean theorem.
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Complete the proof of the Pythagorean theorem.
76
9
The area of the larger square found by multiplying its side lengths is
The smaller
square has side lengths of a - b. The combined area of the four triangles and the smaller
square is
which is equivalent to a? - 2ab + b² + 2ab. a? - 2ab +
b2 + 2ab is also equivalent to
. This expression and the expression found by
multiplying the larger square's side lengths both represent the same area. Therefore,
