 So we left off on example four from lesson five and we're going to go up to just example seven so three more Okay, and what we're doing now Rachel is we're saying can we make a four or five step argument? Can we given some evidence much like a court of law are you pulling in our legal system? It's really based on the same idea. This was one of the reasons the book elements was so revolutionary I hope legal system is based on it. So in example five it wants us to prove Well, what does it want us to show Rob? There's something in front letter H and something okay, it wants us to show it somehow show that these two angles are the same How will I do that? Well one way to do this would be to show Maybe if those two angles are the same and Then if I can show that those two angles are the same Then because every triangle adds to 180 degrees if two of the angles match the third angle has to matter Let's see Rob Read that to me. How do I know? No, how do I ah given this was people's exhibit one and we agreed last day that we're gonna use the letter G as our abbreviation given yes, oh And soon as I write something down Emma I want to label it on my diagram too. So since I just said those two angles are the same I'll put a how about a little check mark and a little check mark whatever symbol that you want to or another way that you Can show two ends are the same page as you can go like this If you draw a little arc right there a little arc right there if you go double hash mark double hash mark Those are the same or triple hash mark triple or single hash mark single hash marker quadruple hash mark quadruple hash mark That's a little bit overkill Whichever method you want to use they're all fine And you'll notice Sam we started leaving the numbers behind we started out last day with angles where I actually gave you Degree values and now we're trying to say let's generalize this so that no matter what these angles were this would still be a true proof Speaking of Sam. What's the next line read it to me? Stop angle G J H. That's this one here. Yep Hey J out. That's this one here. It's saying those two angles are the same. Was that a given? Then there must be a way that I can reason that we must have a binding case precedent already on the books How do I know that these two angles are the same size? anyone ah Vert op Going to our court of law example Tanner I would have said and judge you may recall from people people the vert op that those two angles We refer to our previous case and the judge would say yeah, okay entered into evidence or let it be so noted Law and order huge huge fan of law and order back when it was on Calling what's the last line which I was trying to show Apparently I have enough information to convince my dumb jury that these two angles have to be the same How do I know these two angles have to be the same? Are these two angles the same? Are these two angles the same? What shape is this? What shape is this? What does every triangle add to? 180 so those two match and those two match. What can you say? They match now if you said it was because of angle some of triangle I'd take that if you want to the fancy one is this third angle in Triangle if two angles match the third angle has to match Why Kiara because angles have to add to 180 and so if I have two pairs the third I have to have a third pair automatically But if you wrote angle some of triangle or if you just wrote something like because the two angles match The third one is the same. I'll take that. I'm I'm not gonna be too fussy on some of these Conclusions. I'm gonna be fussy when it's an actual rule from our yellow sheet. Is that okay Joel? Three lines nice proof Two more rhythm Sample six. Oh, this one's a little longer Okay Nicole what are we trying to show? Soon as I see the word parallel this last line right here. I'm either gonna be writing Corresponding or alternate interior or co-interior three parallel line rules. I'm gonna try and force feed either a Z alternate interior or a C Co-interior or an F Corresponding I don't know which one it's gonna depend on the givens Zach, what's the first line? Can you read it to me? Good. How do I know? Okay, let's write that and now let's label that on our diagram DEF that's this one here Equals angle DEG that's this one here equals this one here. You know what I'll use hash marks this time instead of symbols Those all three are the same Before I move on to the next line. What do I now know based on that information? What else do I now know? Can you see it if all three of these angles are the same? What does that mean Jake? They're each 120 and I bet you that's my next line Let's look and see it says angle DEG equals angle DEG This guy equals. What did you say it was Jake? How do you know? Even got the rule angles at a point. Yeah And I'll put a little 120 degrees right there By the way, David that also means this is 120 and this is 120 But since they haven't bothered bringing those into evidence I'm not gonna bother labeling it because I don't want to confuse my jury I will if I have to but for now I always like to try and go with them what we call the most elegant proof the bare minimum of information Speaking of David. What's the next line say? Can you read it to me? equals How big is angle EGH? How do you know? Ah, oh 60 give him. Oh, and you know what Tanner? Let's write that in here 60 degrees right there EGH then it says Oh jury Hello jury dumb jury. We want you to notice something. We want you to notice the angle DEG this guy an Angle DGH this guy our supplementary now. What does supplementary mean? It means that they add to do they? Yes What am I gonna write for a reason? If you said they add to 180 I would take that if I want to sound impressive I would say hey that's the actual definition of Supplementary, but if you just said they add to 180 we're pointing out we want the jury to notice Hey, you who? Hello. Did you notice did you notice they add to 180? They do Why does that help on my last line? Which parallel line rule have I force fed into this diagram is? There a Zed No There's this which one was the sea I heard it here You know what I force fed since these two angles add to 180. I think that's what co-interior said Yes, it said co-interior angles add to 180. I have force fed Interior angles on the same side of the transversal call which we said could be written as co-interior Case closed guilty or innocent if you're a defense lawyer The call am I gonna put 15 of these on your geometry test? One maybe two Ideally, I like to go with one medium one and one easy one If I can't find one medium one and one easy one will be one longer medium medium one last one Number seven used to be number six, but I had to cross it out Okay, this is about as tough. You know what this is probably tougher than I'll throw at you on a test But in your homework ideally we found the homework we find the homework tougher than the test Ashley, what am I trying to show? Okay. I'm trying to show That these two are parallel now there's a few ways to do it Ashley, can you see the potential for a Zed if I use that approach? I'll end up showing that those two angles are the same that might work or I might be able to go all Co-interior e on you if I can show that this and this add to 180 or that this and this add to 180 Which method will I use? I'm gonna let the givens tell me Adrienne read that to me Gk equals GH, how do I know? Oh And is that marked on my diagram for me? No, it wasn't the first few examples that we let's mark that on our diagram Gk I'll put one hash mark is equal to GH. I'll put one hash mark as Soon as I write that there's now something screaming out at me on the diagram Do you see something that has just appeared on a diagram that wasn't there before but now is officially? What do you notice? It's I saw Salise how much you want to bet this next blank line wants me to mention that not only are those two sides the same I'll bet you those two Angles are the same. I'm not sure yet because this is the first time that we have a completely blank line Let's come back to that. What do they want me to write here? Joel, what's this say? Oh? I bet you the next given is gonna go there HK by so you know what? I think you're right Okay now Ready look up Don't write this down I'm gonna do it the long way and then I'll show you a shortcut that you are allowed to do First of all Joel has correctly pointed out that the rule is gonna be I saw Salise triangle I agree with that Page here is the long way and I don't want you to write this down Joel I want to show that this angle and this angle are the same and I could go angle GKH Equals angle Okay, and that is perfectly acceptable, but if you want to do a bit less writing Paul Now that we're getting the hang of this I am okay if you put a 1 there and a 2 there and you write angle 1 equals angle 2 You write that down if you want to You can label angles with diet with numbers if you want to pull or you can use all three letters I don't care what I Find the number is clear. What's angle one? Can you see it? What's angle ghk? I gotta think about it and kind of trace it up I just want now touchy Anna. The next thing it says is given Can you read this and this second line? So these two this here is the next given can you read that to me? HK bisect. What does the word bisect mean? It's an English word. It's not a grade 3 English word. What is the word bisect mean? For me That's intersect close same root word same topics Page and here's the key doesn't just split into two parts splits exactly in half Okay, cuz I can split something into two parts and have them be uneven when they say the word bisect that you know what Worth writing down split exactly in half so When it says HK bisects angle g Kj given I have to explain to the jury what this means Kayla, what is the next rule on my next line say? What's the reason it wants me to use? The whole thing Definition of angle bisector. What does bisect mean? Splits exactly in half, so let's see apparently HK bisects angle g Kj apparently HK splits this exactly in half You know what that means Joel? How big is this angle compared to this angle? How do I know they're the same size? How do I know they're the same size? It's a definition of bisector How about I'm gonna put a little three right there, and I'm gonna say angle one equals angle three Or you could use the three letter approach to I'm fine with that. I find this easy. Oh And I'll put a little Black dot there too that says angle g Hk hey, I think that's angle two Yes Equals angle hkj. I think that's angle three It's a hello This angle and this angle are the same How do we know no, it's not alt-int yet. We're gonna use alt-int to prove that they're parallel How do I know that these two angles are the same size? Can you see? Angle one is the same size as what? Angle one is the same size as what oh if angle one is the same size Angle two and angle one is the same size as angle three Joel hit me with it between the eyes. Sorry. What? Now you can't say they each equal the same thing, but we can use that word I saw Jacob looking madly to look it up. Did you actually remember it? transitivity trans If a equals b and c equals b then a equals c it's that it's that little called a syllogism It's that little bit of three-line reasoning right there so I Now know That angle and that angle are the same which parallel line rule have I forced that into here? Co-interior oh What what what what because what letter do you see see this? None of us see a z you might Yankee person go home, but we see a Zed baby we see a Zed So what's your official homework? I already said you could try number one I haven't yet made up an answer key. I'm gonna try and get one done during class today Or in the next couple of days. I don't have one online yet but for some of these also It really depends on just how you how I'll take if you explain to me how you figured it out So I may use the short formal word like transitivity if you just said they're both equal the same thing I'm good with that. I'll mark this pretty leniently. So I assigned what one two and three and four I think you can try five six seven eight nine Hey bisects and 10 What's this symbol right here mean? What does perpendicular mean? in fact If you look at number 12 no six sorry Given and this angle and this angle are each 90 degrees because that's the definition of perpendicular There I just filled in two for you You can also work on the take home quiz You have the remainder of class today's bell schedule is a little bit weird So I have right now 103 you have till 135 you got a full half hour to win a little way at these when you get them all done in class today I'll go over these on Monday or Wednesday. Well, I'll go over the take home quiz Monday. I'll probably go over these on the Wednesday We're nearly done the unit mentally. I have about two more lessons. I'm shutting up