 Yeah, there's the magic nose. Lesson three, triangles and quadrilaterals. Quadrilateral is a fancy word for any shape with how many sides. Four, triangle has three sides, quadrilateral, that's the triangle of four sides, quadrilateral. First of all, some types of triangles. You may have seen these words before. We have three main types, scalene, isosceles, and equilateral. What makes an equilateral triangle an equilateral triangle? What's special about this guy? Not only are all sides equal, but also all angles are equal. So if every triangle adds to 180 and you know all the angles are the same, for the equilateral triangle, we actually know how big each one of those angles is. How big does each angle have to be if they're all the same and they add to 180? They gotta be 60 apiece. So if you ever see an equilateral triangle, you actually, in fact, frequently what I'll do is I'll put an equilateral triangle somewhere in your diagram, Zach, and I won't give you any angles. Well no, I have, I've given you 360 degrees in there. Now start finding the other ones. Isosceles, we said had two equal sides and two equal angles, sorry. Isosceles at least two equal sides and at least two equal angles. Technically an equilateral triangle is also isosceles because it does have at least two equal sides and two equal angles. It's got three. What's a scalene? Three different sides and not only that, three different angles. An easy way to show that all three angles are different. I'll put an X right there, a check mark right there, and a dot right there. Three different symbols is another way to show that all three angles are different sizes without actually putting any numbers in. Okay, yep. However, I still know what does that scalene triangles angles add to? Every triangle still adds to 180. Then we have one more special triangle, a right triangle, a triangle with a right angle. I'm gonna teach this kind of as though it was new, you may remember this Pythagoras's theorem. I'm just assuming you haven't seen it for a while and you may have forgotten. What makes a right triangle a right triangle? Call if you see a right angle and I'll show that by the little symbol like that. If you have a right triangle, Pythagoras's theorem says if we know two sides, we can find the third side. Does anybody know what the equation that we use for Pythagoras is? Page. Yeah, not A plus B equals, it's close to being alphabetical. It's A squared plus B squared equals C squared, but there's one more thing you must remember and it's about the side that we label C. What always, always, always has to go here. The longest side which has a fancy name? They have a pot, I mean the hypotenuse, yes. Hypotenuse and Rob, I'm gonna put in brackets, your definition, the longest side that always has to go by itself on one side of the equal sign. So in some of your homework today, they're gonna give you a right angle triangle. You'll be able to tell because there's a little right angle symbol. Oh, you're writing stuff down? Good, about time. Example one says find the missing side, give your answer to one decimal place if necessary and we'll try and show our work right on this sheet by writing kinda small. So here's example one, is this a right angle triangle? Yes, then Nicky, I can use Pythagoras. If I had started a fresh page, I'd probably write Pythagoras out each time but do I have it sitting right here? Do I have the Pythagoras equation sitting right there? Then I'm just gonna use that and I'm gonna go straight to numbers. Pythagoras says this, short side squared plus short side squared equals hypotenuse squared. Yeah, Chels, now I go running off to my calculator. X squared equals what? Can someone go eight squared plus 14 squared? Get your calculators out, you need to practice this. I don't know yet. X squared equals 260, how do I get rid of a squared? So for those of you who just got a graphing calculator because you didn't bring your own, the square root button is right here in yellow on the graphing calculators, it's look up second function X squared, 260. And I said give your answer to one decimal place so X equals 16.1. Yes, is that okay? How do you get rid of a squared? You have to square root if you have a squared term to get a squared term by itself, square root. Yep, it's the inverse of squaring. Pardon me, I think 260, is that what you guys said? Yep, so those you have calculators now I'm gonna ask you to make sure you follow along for this next one. Number two, it says find the missing side. Is that a right angle triangle? Then we can use Pythagoras. Do we have Pythagoras written right up here? Then we won't bother rewriting it. Instead we'll start going straight to plugging in numbers. It's short side squared plus short side squared equals long side squared. 5.9 squared plus 3.8 squared equals C squared. Graphing calculator humans, your X squared button is right there. Squared plus 3.8 squared equals C squared equals 49.25. Nicole, how'd I get rid of a squared? Darn right, square root of 49.25. And I get, I guess to one decimal place, 7.0. Shouldn't, sorry? Well, I'll go 7.0 just to be fussy, but yeah, if you just wrote down seven, I wouldn't freak out. Is that okay? How is question three different from question one and two? Yeah, you're gonna find a short side. Now it's still gonna be exactly the same. It's always short side squared plus short side squared equals long side squared, except this time one of my short sides is Y squared plus 24 squared equals 26 squared. How would I get the Y squared by itself? How would I move this over? Y squared equals 26 squared minus 24 squared. I could evaluate the 26 squared and the 24 squared. I'm gonna have to eventually, but it's easier to write that right now than the big number that it's gonna become. In fact, now I'm gonna go to my calculator. 26 squared minus 24 squared equals, I get Y squared equals 100. Nicole, how'd I get rid of a squared? It's gonna be the square root of 100. I think this one works out evenly. Number four, I'm also trying to find a short side. I didn't put a variable there. Hey, how about let's put an X there. What's my equation gonna be? X squared short side plus short side squared equals long side squared. Yes, how would I move this 35 squared over minus it? So X squared is gonna be 60 squared minus 35 squared. And I can go to my calculator now. I doubt this one will work out evenly. It does, it'll be a fluke. I get X squared equals 2375. If X squared equals 2375, how can I figure out how big X is? Square root. And I get 48.7 and I use the answer feature whenever possible. That's less typing, 48.7. Turn the page, hey, you guys figured that out already. What's the difference between these ones and the previous ones? The previous ones, I said, give your answer to one decimal place. Here, they're saying leave your answer as a radical, which is actually less work. Say what? Yeah, I'll show you. So they want us to find short side or long side in example one. So what's the equation gonna be? What squared plus what squared equals what squared? I agree, X squared ends up being 149. If they say leave your answer as a radical, Cheyenne, they're saying, look, all I wanna know is, do you know what to do next? How to get rid of a squared, Nicole? Leaving your answer as a radical means just writing the answer like that inside the radical sign and quit. They're saying, I'm not gonna waste your time going to a calculator. This might be if I wanted to give you a non-calculator section on a test or something like that, this could be how I could do it. I'm not gonna, but in the homework, you're gonna see there's a section where they say, leave your answer as a radical. Means just leave it as a square root, okay? We're gonna skip two, let's jump straight to three. What's the equation gonna be here? How are we gonna get the M squared by itself move this over, right? How? Minus it. Not plus Mr. Deweyck, minus it, Mr. Deweyck, minus it, Mr. Deweyck. What is 20 squared take away 12 squared? Sorry, 256. M squared equals 256. M equals the square root of 256. Now this one works out evenly. So if they say leave your answer as a radical, quickly check on your calculator. If it works out evenly, go one step further. If it doesn't, just leave it as a square root. What is the square root of 256? No, I'll be clear. This is more for what they're doing on the homework. Unless it works out evenly. This one worked out evenly with no decimals, then do it. Like if it's square root of 49, put a seven. Number four, what do those two hash marks mean? Same size, so let's put an X right there. What's the equation gonna be? X squared plus X squared equals 60 squared. Two X squared equals, what is 60 squared? Sorry, how would I get the X squared by itself here? I don't think this one works out evenly. Shayen, I'm gonna leave it as a radical. I'll try it on your calculator, but I'm pretty sure the square root of 1800 doesn't work out evenly. I'm gonna temporarily pause here, because some of you are getting a little bit tired and I wanna give you a chance to practice this before I move on. So right now, if you would be so kind as to get out the geometry package, and I already said that you could do up to S6, okay? I think you can try S7. I'm gonna skip S8.