Pythagorean Theorem by Inductive Reasoning
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The red figure is a square.
1. Why is the magenta space a square?
2. Write an expression for the area of the magenta square in terms of c.
3. Write an expression for the area of the upper magenta square in terms of a.
4. Write an expression for the area of the lower magenta square in terms of b.
5. Write an expression for the total area of the magenta space in terms of a and b.
6. Now, set your expressions for the area of the magenta space from #2 and #5 equal to each other.
7. The Pythagorean Theorem states that the side lengths of a right triangle are related by the equation a2 + b2 = c2, where a and b are legs and c is the hypotenuse. Did this inductive reasoning activity help convince you about the truth of the Pythagorean Theorem? Explain.