?The following is an outline of a proof of the Pythagorean theorem. Consider a right
Chapter 0, Problem 47(choose chapter or problem)
The following is an outline of a proof of the Pythagorean theorem. Consider a right triangle \(ABC\) and the following figure, which is created by arranging four copies of \(\triangle A B C\) as indicated.
Justify and/or explain each of the following statements.
(a) The entire figure and the figure in the middle are squares.
(b) The area of the outer square is \((a+b)^{2}\) .
(c) The area of the inner square is \(c^{2}\) .
(d) The area of each triangle is \(\frac{1}{2} a b\).
(e) The area of the outer square is equal to the area of the inner square plus the area of the four inner triangles.
(f) Use these results to prove the Pythagorean theorem.
Equation Transcription:
Text Transcription:
ABC
Triangle ABC
(a+b)^2
c^2
1/2 ab
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