Question

# 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

Math Word Problem
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?

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.