#### Answer

If the side lengths are a, b, and c and $a^2+b^2 =c^2$, then it is a right triangle.

#### Work Step by Step

We consider a triangle with side lengths a, b, and c. We consider the case where the angle is a right angle. If and only if this is the case, the distance c is:
$c= \sqrt{a^2+b^2} \\ c^2 =a^2 +b^2$
If it was not a right triangle, this would not be the case. Thus, if the side lengths are a, b, and c and $a^2+b^2 =c^2$, then it is a right triangle.