 So on your reference sheet we have the parallel line rules which appear about one-third of the way down next to this get your reference sheet out Maggie if you don't have the yellow sheet out you want to get the yellow sheet out very handy Next to where it says interior angles on the same side of the transversal. This was the official rule for years and then around 1990 some of the BC math teachers said this is a lot of writing to write out and I abbreviated a yacht saw I took the first letter of each word But they still said that's a lot of writing and then a British math teacher here in BC said, oh We don't call it that in Britain. We call it co-interior Which is way shorter So if you want to use that Sierra, they're interchangeable Okay, I think in the answer keys because I the answer keys were made before they went to this shortcut It will say interior angles on the same side of the transversal, but if you say co-int co-interior, I'll take that Meanwhile back to what we were looking at So we're looking at number 14 and number 16. Sorry on page s6 It wants us to prove which of these lines are parallel. What does parallel mean mean never crosses Some of these look like they're parallel Devin these two look like they're parallel these two look to me like they're parallel and These two look to me like they're parallel, but they might not be For them to be parallel I have to be able to prove it They have to fit one of those parallel line rules and if they don't if they violate one of those parallel line rules I know they can't be parallel okay UW that one which line do you think it's parallel to? Tty So the suggestion is that UW is parallel to TY and that symbol for parallel Two vertical bars. I usually draw the parallel symbol slanty because I'm concerned if I do that if it's an 11 So I slant mine convince me What parallel rule can you see which proves that these must be parallel? So looking either at corresponding or alternate interior or what? Convince me where I agree with you by the way Ah Liam nice this 80 can slide over in fact the letter. I told you look for was a big letter F Liam You're saying hey do it. That's a big F on its side Well played Okay What's another set of parallel lines well the next one I looked at was these two here? They look parallel Are they Matt's shaking his head no convince me Okay, they violate corresponding for them to be parallel both of those would either have to be 65 or 60 so even though they look parallel to the naked eye They're not what's another set of parallel lines well the next one I looked at was These two are they? Yes, so first of all Sam says yes, they are I'm gonna write Q you or you could write you Q. I don't care is parallel to RT Convince me it is if you say it louder with authority like you know it now I want you to say it like you're calling to play in basketball with authority so that everybody says you're right go for it Co-interior oh now co-interior was when you had to parallel lines and the angle inside them the interior angles They're not the same instead. They add to what? 180 that was also called interior angles on the same side of the transversal, which is a multiple to say yes, I practiced Much easier to write Co-in so on these questions Excuse me tonight on these questions number 16 number 17 number 18 It's saying can you find two sets of parallel lines and prove it One of the reasons we like geometry Shea is the rules are what we call if and only if rules the rules that work both forwards and backwards Let me give you an example of a rule that doesn't work forwards and backwards If it's raining, it's cloudy is that true if it's raining. It's cloudy. Is that true? Yeah, if it's cloudy, it's raining. Is that true? No, that's not a rule that works backwards However with geometry rules if it's corresponding it's parallel if it's parallel it's corresponding One implies the other they both work So you can use them to prove to go backwards You can say if I know it's parallel I can find a corresponding or a co-interior or an alternate interior or if I know there's an alternate interior or a Corresponding or a co-interior pattern that I know it's parallel. Can you also then turn please to? number 13 on page number 13 On page s9 Did I talk about number 13 with you folks? Or even number 12 if you want to on page s8. Let's talk about number 12 on page s8 Number 12 on page s8 Number 12 on page s8 Sesame Street is brought to you by what shape What I've said to you is if you ever see a circle and they put a dot at the center You have a whole bunch of idiases. Can I stop saying radius is and can I say ready? I because the plural of radius is ready. I and I want to feel like a nerd So I'm saying ready. I from now. You have a whole bunch of ready. I and every radius All of the ready. I must be the same length soon as I see a circle Alex The first thing I do is this that's saying that's the same. That's the same. I put hash marks on every radius Why is that helpful Boston as soon as I do that? What kind of a triangle is this now? Not equilateral got to be fussy Equal lateral means three sides are the same. There's no way three sides are the same Look at your yellow sheet where it says triangles What kind of a triangle is this now? I saw Salis Back any time you have a circle for example in number 13. There's a whole bunch of I saw Salis triangles there Trust me. There are okay Last thing I want to talk about Since Boston brought up the term quadrilateral quadrilateral means four sides. Can you find quadrilaterals page s10? page s10 and Now you also want to look at the yellow sheet where it says quadrilaterals, which I think is the right-hand side. Yes Okay We're gonna do a couple of these together and then I'm gonna turn you loose Angle one how big 105 objection your honor calls for speculation convince me Liam Nice By the way, you'll probably end up memorizing vertically opposite and the parallel line ones because they show up so often and prop supplementary They're the most common ones the other stuff you by the way, you don't memorize any of them But you're lazy. You'll get tired of looking them up All right How big is angle to Alex is typing away on her calculator, which means she's seen something Alex how big is angle to? 45 convince me What did you do on your calculator? I have no idea so what why 360 on your yellow sheet under quadrilaterals? What's the first thing it says? Some of the quadrilaterals is 360 remember last day we have the sum of the triangle was 180 We call that angle sum of triangle probably call this angle sum of what you know what? Angle Some of and there's my abbreviation for a quadrilateral. I drop four-sided shape You can write quadrilateral you can write quad and How did she find it? She said every four-sided shape every four-sided shape adds to 360. So if I go 360 minus 90 minus angle 1 minus 120 I Get 45 what does every four-sided shape add to? 360 why Devin angle sum of quad what shape is Bear look at your yellow sheet figure it out Matt Trapezoid so right now. I'd also be looking at all my trapezoid stuff on my yellow sheet and take it from there Oh, look Matt will be a good way to abbreviate trapezoid. I'll take trap sure I Won't take trap from you though Zing over some of their heads I'll let you try three and four on your own, but oh you got some parallel lines. You can work some stuff here Hey, let's look at Pony what's pony? Simon, what's pony? Okay, now you can write out parallelogram. Here's what here's my abbreviation for parallelogram Parallel oh gram You can write up parallelogram, but you're gonna watch the number of L's and ours usually because parallel is not the easiest work But wait a minute. I have a symbol for parallels two parallel lines Okay, oh Then it says P y This line Equals what? What's this line the same length as? You're right. I heard someone say it Why oh, let's look at our sheet. Let's see. What does it say about parallelograms? You How about off sides equal Right opposite means the facing sides. They're equal to each other and that's a little rule right there So you have parallel line parallelogram rules right here and you have rectangle rules Right here. Oh and a rectangle is also parallelogram So not only do all of these apply all of these apply we looked at quadrilaterals a few days ago Quadrilaterals are a bit trickier most of the stuff I'm going to give you on a test is going to be based on is going to be based on it's going to be based on Triangles, so I am going hmm. Hmm. Hmm. I Am going to add today Let's see on Page s13 did I give you number 14 on did I give you page? Sorry s. Yeah, did I give you page s13? I Knew to that one did I no no no no in the package though if you keep turning the pages is It in there or not? No, okay? What all did I give you in why don't I grab a geometry package? Because this is the great big document, but I didn't print it all a photocopy at all. This is my original So I gave up to s9 And there's an s10. I like s11. I like then you get to This page yes Okay, these ones are cool Here Simon these ones you'll like because in these ones Look at the answer. Am I also asking for a reason or am I just asking for the angle? You can see because there's not a spot for the reason But for most of these you're gonna have to hop scotch your way and some of these like especially this page These are nasty if you get some of these I'll actually ask you to explain it to the class because some of these I can't get little brain teasers if you're wanting an idea of what's harder than I'll ask on the test These ones here What's that Danielle you'd like to try one? Okay, let's try one shall we let's try Number 11 number 11 You guys have number 11. It's gonna be on the very back. I think yeah, they're close to it This one Danielle, what do they want me to find in number 11? Danielle, we are proud Canadians when we cross the border we say z but here in Canada We are proud. We are proud. What do we say say this angle again for me Danielle like a good Canadian girl xz y Wee-wee you can even throw a little French in there if you went want to x say that again, sorry X Z well, oh, you know which one they want me to find that guy How I'll put a little loop there and that's what I'm gonna try and get to What's the only angle they gave me in this question I'll start with the 80 and I'll say what else do I know because of that? What else do I know because of that 80? What does this angle tell me? Marcus oh You've been said letters. I would have just said the one next to it, but sure that's a hundred How does that help? What can I figure out now? Oh? Boston what kind of triangle is this? Yeah, you do Can you look at your yellow sheet under triangles, please as I've said several times before now and Try and figure out which one of those matches this particular little pattern here Are you on number 11 in front of you? So can I do this? Oh, hang on Boston wait a minute. You're you know what? So that's not acceptable raising your hand and saying mr. Duke, where are we that's much more acceptable So find it we are on page. What are we on page s? Okay, Boston are you ready? Here we go not mad at you yet nice and big for you So we just said that's 80. That's a hundred. By the way, what would the rule be if I'd asked for it? No So Supplementary so Right, okay Whatever stupid way you want to mix up, you know, what's up, right? Oh? Okay, Boston what kind of triangle is this? Yes Boston what can you tell me about these two angles then? More specific since this is a hundred how big do they have to be each how big is this? What shape is this? What's every triangle add to? No, no, no It's on your sheet. You're looking at you seconds Sorry 180 so that's a hundred what's left and If each of these angles are the same because it's isosceles how big is each one? Yes, let's fill those in What do I know now? Oh, this is also 40 Vertically opposite if you want it to be fussy. Oh What kind of triangle is this? Isosceles so how big is this one? So these ones here these last two pages are gonna be hopscotching questions like that and Let me tell you from prior experience if you get 1920 or 21 if You get 22 did I give you 22 23 and 24? Okay, if you get these three, I'm impressed You have the remainder of class and the assignment is this whole here package It's not due next class, but I'm giving you more homework on a different packet next class Okay I'm shutting up