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The converse of a theorem reverses the evidence and the conclusion. The Pythagorean Theorem states that in a right triangle with legs of a and b, and

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asked 2021-06-16
The converse of a theorem reverses the evidence and the conclusion. The Pythagorean Theorem states that in a right triangle with legs of a and b, and hypotenuse c, that \(\displaystyle{a}^{{2}}+{b}^{{2}}={c}^{{2}}\)
a. State the converse of the Pythagorean Theorem.
b. Look back at your work from the problem. What can you conclude about a triangle if \(\displaystyle{a}^{{2}}+{b}^{{2}}={c}^{{2}}\)?
c. Why is this not a proof of the converse of the Pythagorean Theorem?

Answers (1)

2021-06-17

a The converse of the Pythagorean Theorem states that if the sum of the squares of the lengths of the two shorter sides of a triangle equals the square of the length of the longest side, then the triangle is a right triangle.

b. When \(a^2 +b^2 = c^2\), the triangle is a right triangle.

c. Problem \(9-51\) is not a proof of the converse of the Pythagorean Theorem because it only provided examples where some gave conclusions that the triangle are actite or obtuse.

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