 Welcome geometry students to chapter 8. This is the converse of the Pythagorean theorem. We're going to try an example where the three sides of the triangle are 2, 3, and 4. So please have your paper and pencil ready and follow along with me. We're going to do two parts. Part A, we are just going to check and make sure we have a triangle. We're going to look at the two smaller sides, 2 and 3. They add up to 5. If that is greater than the third side, we do have a triangle. And we have 5 is indeed greater than 4. So yes, we do have a triangle. Now for part B, we're going to check out and see if we have a right acutor obtuse triangle. We're going to take the Pythagorean theorem, which everybody knows is A squared plus B squared equals C squared. And we're going to do the converse, which means we're going to flip it around. So we're going to look at C squared and compare it to A squared and B squared. In this case, C is going to be equal to 4. It's the longest side. 4 squared is 16. Now we're going to compare it to the other two sides of the triangle, and they are 2 and 3. It does not matter what you substitute in for A and for B. So we can substitute 2 or 3 in for A or B. It doesn't matter which one we use. Since they both are legs, so I'm just going to go with 2 squared and 3 squared. So we compare 16, the longest side squared, to 4 plus 9, which is 13. 16 is greater than 4 plus 9, so we have an obtuse triangle.