# 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

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?

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Yusuf Keller

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.