 Okay, we're live using a protractor and With your ruler all I would like you to do using a ruler is to draw Some type of an angle, but I want you to draw it very very specifically What I'd like you to do is to draw a straight line at an angle like this Where's my straight line thingy? I don't know something like that and Then draw another straight line that intersects it kind of I don't know like that Yours will be different from mine and this is where Boston It's tricky for me to explain how to do this on my tablet. I tried to find a virtual protractor I can't find one for free and I don't want to pay ten bucks and find out that it sucks So I'll look around in the summer But for now what I would like you to do once you've drawn kind of sort of vaguely an X I want you to see if you can measure accurately That angle right there using a protractor now, how are you going to do that using that small little thing? Well, let me pause the video recording and I'll explain to you Do me a favor then can you open your books up, please? To it's lesson one from the next unit sort of it's page 105 page 105 page 105 and What we're going to do gone from talking about Inductive reasoning making conclusions and deductive reasoning trying to prove things and we're going to start to do it with shapes You may have done some of this last year or in grade nine or in grade eight It really depends on what your teacher emphasized or not Sydney I'm going to teach it from scratch. So if you remember all this don't be insulted It's I'm assuming you've all forgotten it So says in this unit we will use inductive reasoning and deductive reasoning to determine Relationships between pairs of angles formed by what are called transversals and parallel lines. Oh Heck, let's jump down here. First of all some definitions Can you all underline or highlight the word acute angle? I'm going to ask you to know that word I'm going to use that word and acute angle is an angle between zero and 90 degrees An angle between zero and 90 degrees. How big is 90 degrees? This big a right angle. How big is zero this big so anything in here? Oh, it's acute No, okay a right angle a right angle is exactly 90 degrees and we have a symbol that shows you that it's exactly 90 degrees Adam if you draw a little square or a half square like that That's the symbol for even if it doesn't look it because mr. Do it because drawing it by freehand and it sucks That's meant to be a right angle and we have an obtuse angle and obtuse angle Che is an angle bigger than 90 less than 180 My mom says I'm obtuse. No, that means something different. This is the angle. We're talking about here This is an obtuse angle a straight angle is exactly what it sounds like an angle that forms a 180 degree line Okay, there Courtney. You're really fascinated by the little toy. I can tell You good, okay What's a reflex angle a? Reflex angle is between 180 and less than 360 bigger than 180 and less than 360 What's the reflex angle in this picture here that one that's called a reflex angle Bigger than 180 degrees because it's more than a straight line and the complete rotation is 360 degrees How many degrees are there in a circle? 360 degrees you are gonna need to know these terms and specifically you are gonna need to know Jordan that 360 degrees is a circle most basketball players will have no trouble with that because you call it slam dunk of 360 You have that one memorized and you are gonna need to know that a straight line is 180 degrees So far so good All right A says in each case use a protractor to measure the indicated angles and complete the work so with your protractor right now, can you find how big angle X is and Round off to the nearest five or ten degrees because I think it's supposed to be a fairly even number. I think And I'm gonna grab a protractor Assuming that my screen doesn't distort things What are you getting for angle X? How big? Yeah, I'm getting on my screen. It's like a hundred and thirty seven in a chunk But that could be because my screen is distorting things. Let's call it a hundred and forty degrees How big is angle Y? Sorry, did you measure it or did you use inductive reasoning to figure it out? Oh? You measured it and it was kind of obvious What do angle X and angle Y add to? 180 degrees in fact That's the punchline Jordan that I want to get to Without measuring angle A and angle B. Can you look at them and can you tell me what they have to add to? Pardon me Why I'm not a good answer. I mean you're correct That's the inductive reasoning part, but now we also want to bring some kind of a deductive proof to it What are they formed together when you add them together? What is their base form together? I'll give you a hint straight angle Every straight line is 180 degrees. So can you tell me without measuring angle PQ and R? What do angle PQ and R add to? 180 degrees Angles on one side of a straight line add up to 180 degrees What we're gonna do now is we're going to give that rule a name We're going to say from now on instead of you having to say Those are angles that form a straight line together We're going to give it a name. We're gonna call it supplementary If you say supplementary, I know you're telling me these two angles add to 180 Each one is the supplement of the other X is the supplement of Y. A is the supplement of B P is the supplement of Q and R. Q is the supplement of P and R. R is the supplement of P and Q Yes Turn the page. How big does angle A have to be? Angle A, I don't think can possibly be 180 degrees because 180 degrees is a straight line And I think angle A looks to me about like that. Sorry. I think you're right with 25. What'd you do? Okay 180 minus 155. I agree. How big does angle B Have to be and if you use a calculator go ahead or if you can do the math in your head That's fine, too. How big must angle B be? 61, is he correct? Yes Okay Now we're going to look at a very special shape this X shape the one that I had you draw it being a class and we're gonna See if we can add a new rule to our so right now. We have a rule called century We're gonna see if we can add a new rule We're gonna see if we can do some inductive reasoning and some deductive reasoning so They gave me 80 degrees How big is angle C? Sorry, you're telling me that angle C is exactly the same size as that one there I don't think they look the same to me. This one looks a lot fatter. In fact, this one looks bigger than 90 This one looks smaller than 90 Marcus hundred how come? What's the fancy term that we gave it? Begins letter S and runs with a supplementary Supplementary very good. You okay with that? How big is angle E? 80 convince me Okay, there's another straight line right here. How big is angle D? How big is angle D? Hundred here's the pattern we want to notice here today Matt, how big is this angle here? How big is this angle here? Oh Matt, how big is this angle here? How big is this angle here? We're gonna give that pattern when you have an X and you know that this angle and this angle are the same size and This angle and this angle are the same size rather than prove this four-step little proof anymore There's three-step little proof anymore. We're gonna give that a name First of all, we're gonna erase the highlighter If we have opposite angles at a vertex we call them vertically opposite angles If you have two straight lines that make an X shape First of all the point where they cross right there is called The vertex Can you tell me two angles that have to be the same size in this particular picture? S and R have to be the same size. I don't know what they are, but they got to be the same and In fact, if I knew one of them I could find the other three. Here's an example with numbers Here's a generic example Example A says use a protractor to measure each of the following angles. I disagree I'd like you all just to measure angle A and we're gonna stop We're gonna write that down and then we're gonna see if we can reason our way to what the rest are So can you measure angle A this one right there, please with your protractors? What do you get? I should do this too. Mr. Duke. Are you in about a hundred degrees? I think it's supposed to be a hundred Sorry 110 is it why is a hundred ten on your guys's Okay, so I can't measure the ones on my screen then because my tablet distorts everything That's gonna be a little frustrating And I drop this 110 degrees Now that I know that how big does angle B have to be 110 we call that vertically opposite. How big does angle C have to be? 70 supplementary to angle A or Angle B How big does angle D have to be? Is that a right here thumbs up? Have you guys done this before or not? Is this New or this review? Drilling, okay fine So it says complete the following opposite. We're gonna skip this one opposite angles that a vertex are Equal and in fact we call these Vertically opposite angles Note it says the word vertically refers to the vertex and has nothing to do with being vertical Which is true turn the page So a straight line forms 180 degrees. How many degrees are there in a circle? 360 so If I start here and go all the way around don't write that down. I'll just do that how many degrees must I have just gone through 360 degrees Okay, with your protractor measure angle E, please How big do you get for angle E? Taylor, what'd you get? It's got to be bigger than 90 by eyeballing. Sorry. I Heard hundred and 115 anybody else No, yes 110 110 The consensus seems to be that angle E is 110. How big is angle F that looks a bit bigger than? Looks like about 110 or 120 or something like that How big is angle F? That's this angle right here. I can't hear. I'm sorry 110 again, okay, how big should angle GB? Can you figure it out without actually measuring it and then we'll measure it to confirm it? Alex, what did I say all of these have to add to? It's got to be 360. So I think it's going to be 360 minus 110 minus 110 I think in theory it should be really close to a hundred and forty degrees is it We're going to give that a name as well. I'm not gonna do this second one. I think I've got the idea We call this here angles around a point and angles around a point add up to 360 degrees So example two says calculate the angles marked with letters How big is angle A? How can you figure out how big angle A is Joe? Any guesses and subtract from? Yep, go Does Joe have his calculator? He does. Oh I can like you again Sydney's getting hers out now. Ah people are getting on the bandwagon here be part of the crowd Update your Facebook status. I have my calculator Sam. What'd you get? Hundred Sam says a hundred. Is she right? Wait a minute, Mr. Do it isn't that a letter x shouldn't that be 71 the answer is no How come the x has to be perfect for you to use that vertically opposite rule You notice that this here isn't a continuation of this line here So the x rule the vertically opposite rule it has to be Sydney a proper x like that It can't be an x like that, which you could say well, that's sort of an x. Mr. No, not really That okay? All right Example two The second one let's assume she that they want us to find B first So the question I'm gonna ask myself is how can I find B? How big is B? Why is oh? Here I do have a perfect x Which means that this angle and this angle will be the same size Well, I forgot to turn that off. Mr. Do it now that I know angle B How big is angle C? Joe, how can I find angle C now that I know angle B? What have I just drawn how many degrees? 360 do you know that guy? Yeah, you know that guy You know that guy Did you just figure out that guy? So I can figure out last one same thing as you did over here, isn't it minus 360 good go to it. It's gonna be 360 minus 120 minus 60 minus 55 minus 60 65 Yes, it has to be so let's rehash so far Emily we have supplementary Angles at a point Vertically opposite We're gonna add a couple of more little rules little tricks little shortcuts that we can use Says investigating the sum of angles in a triangle and We're I'm gonna do this one up at the front here really quickly because I don't have enough pairs of scissors to go around Continue says based on this investigation angles in a triangle Matt. What did you say they add up to? 180 degrees every triangle adds to 180 We've got a couple of more little tricks we can use here Says recall the following triangle property. You may or may not recall this In our I saw salise triangle, I won't make you spell it correctly I will make you say it correctly in an I saw salise triangle You have two equal sides and two equal angles Here's how we show this it says verify this property by measuring the sides We're not going to instead. We're going to signify that the sides are the same by using hash marks look up Right now those two sides have different lengths even though they look the same Joe You know how I know that those two sides have different lengths even though they look at the same How many hash marks does this side have on it? This side, how many does this have Soon as I do that what I'm telling you is those are both the same length Okay, or I can also say that the angles are the same. I could do that by going We use little hash marks little symbols It's an easy way especially if you're trying to draw these shea and they're tricky to draw accurately And you're saying they don't quite look the same use the hash marks And I will assume that they are the same This is an isosceles triangle what this means is these two angles are the same size How's that help? Draw yourself freehand a little isosceles triangle right here That looks an awful lot like mine, and I'm going to call this triangle joe Draws You got pick up your hands. I'll actually draw this down. Is this an isosceles triangle? Not yet. Let's make it an isosceles triangle Alex by doing that Okay, and I'm going to tell you one more thing. I'm going to tell you that this angle right here is 28 degrees How big is angle? j o e And how big is angle j e o? Say what? Courtney, here's how you label angles you often will use three letters and Joe means j o e it's this angle right here You go in the order that it's written where the middle letter is where the vertex is J e o j e o means that angle right there Okay, what shape is this Jeremiah? What does every triangle add to? Okay, so I know that this plus this plus this equals 180, but because it's isosceles I know one more thing. So how can I use that to figure out how big each one of them is? Yeah, Marcus 180 take away my 28. I like where you're going so far. Let's do that. I'm like 180 Take away 28. Uh-huh. Let's try that again. 180 take away 28. Uh-huh. Oh I got 152 degrees left for both angles, but if they're both the same They're each 76. Is that what you're saying? Boston that makes sense That that very handy trick that I just showed you right there We're gonna use that an awful lot if you know, it's an isosceles triangle Very handy because you know two of the angles are the same you can find them by dividing by two Joe you okay on Joe or Geo? This one here. I think we can figure out This last one here. I think we can figure out. It says Exterior sides of a triangle What it's really saying is This angle and this angle. Hey What do these two form together? What do these two form together? Taylor straight line. In fact, what was the fancy word begins a letter s runs a supplementary Supplementary so if I tell you that angle C equals 80 degrees How big must angle X be better? Gotta be a hundred gotta be a hundred Why supplementary? So they want us to walk through that bender, but I think I think we see it. Okay, and Instead We're gonna turn the page to page 109 So this is what we're gonna spend some time doing here for the next few days or you'll be using deductive reasoning Inductive reasoning conjectures conclusions for shapes. I like this. It's a nice change from use an equation Rapid how big does angle X have to be? hmm What's angle X sitting in what shape? Matt Triangle and what did we say every triangle adds to? so 180 minus 83 minus 65 Gotta be 32. Yes Okay, here. We have angle a angle B angle C Angle By the way, have you included what the abbreviation for the word angle is it's a little slanty L, right? Sam how big is angle a how can we figure out how big angle a is? Well, I'll give you a hint They only gave me two angles. They gave me a 29 and they gave me a 36 So I'm gonna use one of those guys So I'm now asking myself is angle a forming an X vertically opposite with any of them Is it supplementary to any of them? Is it part of a triangle? I'm running through the little checklist of things that I have here Can you see it? How big is angle a have to be? Yeah, nothing You're awake now Joel's breathing again Mr. A's looking at me like I'm a freak got to keep on the toes say any thoughts how big Okay, let's walk through this. Do you know where angle a is point to it? Yes Yeah First thing I want to notice then is it's made up of this line right here Is that a straight line going to the next angle? Do I know the next angle? Well, how big? How big must these two guys be together? What's every single straight line? So do the math Folks get them come on get your calculators out if you need to do the math no laziness here Shay would you get I agree with you say that was so much fun We're gonna keep going to that beverage now is surging through you you're getting a little caffeine sugar rush excellent Are you ready? Are you ready? So 151 I agree with you angle B Any suggestions here say how I can figure out how big angle B is ah On the other side same thing sure So what will I type into my calculator or do in my head 180 what? It's 180 minus 30 is 150 minus 6. How big I Agree with you 144 degrees mister What's that? This is so much fun. You want to keep going? How can I say no to you Shay? Absolutely? Let's keep going. Let's keep going now angle C angle C Hmm what shape is angle C in Shay? How big is this angle? How big is this angle right here? Ah? Because the one next to it is 90 and those two form a straight line supplementary What does every triangle add to? Good go to it 61 61 No, yes Doing the math in my head. I could be wrong. What's that? You want to finish this one off and get that rosy glow of success? Absolutely. Shay. Let's do that. Let's do that on your own. Can you tell me how big angle D has to be? Yeah, you 54 is he right he is Sit up a little straighter get a little smile. That's that's called success. It feels good doesn't it? I've never felt that before. Yeah, well, there you go first time Raysh and I let's try this next one here. I tend to go alphabetically because I assume whoever created this went alphabetically and Probably I'll use the first one to find the next one to find the next one So if I jump on the last sort of the alphabet I might be stuck So they gave me I think I'm gonna start out with angle P Because P comes first in the alphabet All right over here angle P equals angle Q equals Angle R equals angle S equals. Is there an angle T? Yes, there is Can I can you tell me how big angle P has to be? I agree with you Supplementary or Shay, you know what you can call supplementary for short sup No, okay Keep going Shania angle Q. Is it 69 degrees? Yes, no. Yes, form the straight line right there. Yeah. Yeah. Yeah. Yeah Keep going angle R Hmm. Oh I bet you will use angle Q and angle P to find angle R. That's why I said I go alphabetically all the time It's gonna be 180 minus minus you say 59 59 degrees. Is that right? 5 9? How'd you get that Shania? Why from 180 because this shape together forms up triangle perfect Keep going Angle S. I totally agree 121 oh finish this off. You've done so well and I'll even give you a candy because I like you better than Shay What was that? How could I not? Yeah? 109 how'd you get? Oh, yeah, and by the way again Shay notice This is not vertically opposite X's because it's a crooked X We can't use our these two are the same and those two are the same Otherwise that would have made this question really fall apart really really quick. So sorry what you say it was hundred and what? 109 I agree Boston, what are these two hash marks mean that these two sides are? Which means that these two angles are? Ready Boston, what are these two hash marks mean that these two sides are? Which means that these two angles are? See I Sosley's triangle means two sides and two angles the same which means I can tell you angle D already boss And what's angle D? I totally agree with you and then they want me to find angle E and angle F Let's keep going Boston my friend angle E or 180 minus 34 times 2 or more specifically as a number as an answer 112 yeah, oh how big is angle F? I don't know. You know what first by the way before Marcus points this out to you What we're doing is called geometry. I sucked at it. I'm still terrible at it It was the one thing in math that I'm very very bad at and so I taught myself a mental checklist Where to look to try and find the answer one of the first places I look is at the angle that we just found What angle did we just find? Angle what E do angle E and angle F form anything together? I heard someone murmur it over here Straight line and what's every straight line? Now I can but that's what I would have done with I would so 180 minus 112 is I think 68 Is that okay? Gonna add one more term for you by the way. It says summary We have opposite angles on a line add up to a point add up to 180. We called that supplementary. Let's write down the word supplementary Opposite angles at a vertex are equal vertically opposite angles. That was this one How do I remember that one? Can you all look up for a second? What letter is that right there? I? Agree with you X if I cover it up What letter is that top half form? V for vertically opposite angles You're looking for a dumb way to remember it works for me Angles around a point add up to 360 Angles in a triangle add to 180 says the exterior angle of a triangle equals the sum of the interior opposite angles By the way, it is true. I don't know if you noticed Boston, but 34 plus 34 is 68. I Don't know if you notice, but that plus that gives you that I've never really used that one as a shortcut because almost always I can find this guy and then find that guy as a hopscotcher But we are gonna add a sixth one a sixth term angles that add To 90 degrees are called So angles that add to 180 degrees are called supplementary Anybody know what we call angles that add to 90 degrees Complementary Complementary call. What's your homework two things for you to work on first of all in the workbook? number one number two number four We skipped three five is good Six is good seven eight Sure, nine is good too. I think and then I have for you a great big package of stuff that we're slowly gonna work through I'm gonna tell you which questions you're capable of doing right now It doesn't mean these are all due next class But you want to start them if you finish them and I'll give that to you in just one second here right click pause So put your name on this big great big geometry package number one and uh Okay, mr. Dewick, apparently you haven't printed this up yet Okay, really quickly hang on bear with me reasoning with angles reasoning with angles package number one Right now, I think you folks can do or are capable of doing This first page which is called s2 and s3 and s4 Now am I saying all of that is due next class? No, but you're gonna find when you get pretty good at these you can probably get all the homework done including this far done in class Okay There's a couple of words on here that you might not know congruent means same size But vertically opposite acute obtuse All stuff and I have an answer key I'll put this answer key both online But I'll throw it up here every so often so you can double check for your answers because this one the answers are not attached Does that make sense alex? We're good Fun with drawing and pictures if you can hand in the protractor and the rulers Preferably putting them back in the little plastic thingy That would be wonderful. That would be great and you have the remainder of class to work on this