 and welcome back. Today we're going to talk about the converse of the Pythagorean theorem, converse of the Pythagorean theorem. Basically what we're going to be doing is, instead of using the Pythagorean theorem to solve for sides or for the hypotenuse or something like that of a triangle, we're actually going to use it for something else. So basically, here's what we're doing. If the Pythagorean theorem works, then the triangle is a right triangle. So basically what this does for us is what we can do is we can actually attempt to use the Pythagorean theorem and we can actually figure out if these triangles, these two triangles that I have, these examples that I have right here, we're going to see if they are in fact right triangles or not by using the Pythagorean theorem. Okay, so let's just go ahead and jump into it. Pythagorean theorem I have up here on the right side, a squared plus b squared is equal to c squared if you had forgotten what that was. So this is what we're going to do. We're going to plug these numbers in and see if they work for the Pythagorean theorem and if they don't, well then this isn't the right triangle. Okay, so first thing we got to do is we got to identify, okay, where are my legs? Now on a right triangle, if this is a right triangle, the hypotenuse is always the bigger side. So here's my 13, that would be the hypotenuse, which means the other two sides, 12 and 5 are going to be my legs. So 12 and 5 are going to go in for the legs here and then my 13 is going to go in for my hypotenuse. Okay, so a squared plus b squared is equal to c squared, which means 5 parentheses squared plus 12 parentheses should be, is that going to be equal to 13 squared? Okay, now notice I put a little question mark there because that's the question we're asking, is this going to work? Because we don't know right off the top of our heads, we don't know right away if this is going to work or not. So that's why I got the question mark there. All right, so let's do a little bit of math. Okay, so 25 squared, excuse me, 5 squared is 25, 12 squared is 144, is that equal to 169? Well, actually in fact, 24 plus 144 is 169, so these are in fact are equal. Now what that does tell us though is this isn't an answer and a lot of students get confused at this point. We're not even looking for numbers for answer. Since the Pythagorean theorem worked, since this worked, yes, this is a right triangle. And that would be my answer to this problem, because that's what we're trying to figure out. Is this triangle going to be a right triangle or not? Okay, so that in this case that's where some students get kind of confused. A lot of students think, oh okay, this is my answer because I'm looking for numbers in math class, I always look for numbers. Well actually that's not the case this time. We're using the numbers, interpreting the numbers to answer a certain question. That question was, is this triangle a right triangle? Well in fact, yes it is because the Pythagorean theorem worked. Okay, so let's try that for this triangle over here. Let me change my colors a little bit. Let's try that for this triangle over here. Okay, so 9 is my hypotenuse, it's the biggest side. My legs are 8 and 7. I'm not going to write down the Pythagorean theorem this time. So we got 7 squared plus 8 squared. Is that going to be equal to 9 squared? Okay, well 49 plus 64, is that going to be equal? If I add those together, is that going to be equal to 81? Well right off the bat we can see 40 plus 60 is 100 and then 9 plus 4 is 13. So this is 113, which is definitely not equal to 81. So basically that tells us no, this triangle is not a right triangle. Okay, this triangle is not a right triangle. Okay, again the numbers didn't match up. This side, the legs here, when I add this together it's way too big. So these legs are way too big for this to be a right triangle. So it doesn't really work. Okay, now one argument some students make with this is that, well it looks like a right triangle, so it has to be a right triangle, right? No, no, no. Again, we got to get out of that mode of thinking that just because a triangle looks a certain way doesn't mean it's actually that. So again, it looks like, it looks like, yeah, right here, right there. That looks like a right angle right there. But in fact, that is not a right angle. There is no proof that that is a right angle. Okay, so we cannot assume that that is a right triangle. Okay, and here's the math that actually proves that this is not a right triangle. Since the Pythagorean theorem didn't work, it's not a right triangle. Okay, all right, so that's the converse, the Pythagorean theorem, pretty short video there. Thank you for watching and we'll see you next time.