Answer
The similarities in the methods are that you need to find the lengths of the shorter sides, add their squares together, and compare this sum to the square of the longest side.
The differences in the methods are:
In an acute triangle, the square of the length of the longest side is shorter than the squares of the lengths of the other two sides; therefore, $c^2 < a^2 + b^2$ or $a^2 + b^2 > c^2$.
In an obtuse triangle, the square of the length of the longest side is longer than the squares of the lengths of the other two sides; therefore, $c^2 > a^2 + b^2$, or $a^2 + b^2 < c^2$.
Finally, in a right triangle, the square of the length of the longest side is equal to the squares of the lengths of the other two sides; therefore, $c^2 = a^2 + b^2$, or $a^2 + b^2 = c^2$.
Work Step by Step
The similarities in the methods are that you need to find the lengths of the shorter sides and add their squares together and compare this sum to the square of the longest side.
The differences in the methods are:
In an acute triangle, the square of the length of the longest side is shorter than the squares of the lengths of the other two sides; therefore, $c^2 < a^2 + b^2$ or $a^2 + b^2 > c^2$.
In an obtuse triangle, the square of the length of the longest side is longer than the squares of the lengths of the other two sides; therefore, $c^2 > a^2 + b^2$, or $a^2 + b^2 < c^2$.
Finally, in a right triangle, the square of the length of the longest side is equal to the squares of the lengths of the other two sides; therefore, $c^2 = a^2 + b^2$, or $a^2 + b^2 = c^2$.
