The Pythagorean Theorem is a helpful tool for figuring out what type of triangle you have: right, acute, or obtuse.

Here’s a quick review of the theorem:

For a right triangle, the lengths of the sides follow this rule:
a² + b² = c².
In this rule, c is the longest side, called the hypotenuse.

Now, let’s see how to use this to identify the type of triangle:

1. Right Triangle:

   • If the equation a² + b² = c² is true, you have a right triangle.

2. Acute Triangle:

   • An acute triangle has all angles less than 90 degrees. In this case, use this rule:
     a² + b² > c².
     If the sum of the squares of the two shorter sides is greater than the square of the longest side, then you’re looking at an acute triangle.

3. Obtuse Triangle:

   • An obtuse triangle has one angle that is greater than 90 degrees. For this triangle, the rule is:
     a² + b² < c².
     So, if the sum of the squares of the two shorter sides is less than the square of the longest side, it’s an obtuse triangle.

Knowing these rules not only helps solve problems but also helps you understand triangles better. It's a cool way to see how geometry connects different ideas!