 Keep that handy dandy yellow reference sheet out the front of it face up Probably you want to keep it so you can see it and all we're going to do from now on Jordan is what we've been doing Except you're going to hear me say why convince me prove it and what you need to train your brain is When you see the answer to ask how do I know that that's true? You see the extra step Devin We're going from simply saying here's the answer to saying and this is why it's right shut up Really in a court of law so Example one it says find the measure of each angle and give a reason first of all how big does angle one have to be? Jordan, I totally agree Why what I'd like you to do is find the word on your yellow sheet that describes that I? Think there's a word that begins a letter C that matches this diagram even more is there not Right angle was the definition of the angle, but I think two angles and add to 90 What do we call that from the sheet? So if we were in a court of law Taylor, it would go something like this Jordan would have said 22 degrees I would have said objection your honor calls for speculation and Jordan would have said complimentary and the judge would have said objection over Well, because you've given me the evidence This is the extra step court and you have to memorize all the rules Sydney No, you're gonna not be allowed to have that sheet in front of you But you gotta know like where they are and how to find them Okay angle three how big Marcus Objection your honor calls for speculation Now this one you can either use that or you'll notice just underneath it There's another rule called angles on a line now I'm gonna be really technical Technically you use angles on a line when it's three or four or five angles forming a straight line and Supplementary when there's only two angles forming a straight line that's technically Joe I don't care you can use either of those and I'll figure out you include in that It's a straight line adds to 180 so you can either use supplementary or angles on a line To me they're interchangeable My court of law is a little bit more linear Okay Question seven Angle See F okay C F E That's I'll mark mine up you guys don't need to but that's that one there. How big sorry I heard someone say it 90 objection your honor calls for speculation convince me. I have no idea what you said It is a right angle. I don't think that's the reason though By the way, 90 degrees and saying it's a right angle. Here's what you're saying It's 90 degrees because it's 90 degrees. Did you hear it? We have a special name for that. We call it circular reasoning It's like saying I'm stupid because I'm dumb. You're well. No, you're not giving evidence You're repeating your argument in a different form and hoping that I don't notice that you've done that You've heard me actually confront kids. Why are you late because I just got here That's saying I'm late because I'm late Hear it and you've seen kids do that. So I need a better. I'm gonna say I agree with the 90 How did you know that was 90 Jordan? I? Don't think you looked here Where did you look to figure out that this one had to be 90? This is 90 and what are these two form? Okay, what did we call two angles that formed a straight line? You know what I'm gonna argue that the rule that you used is Supplementary is that okay Emily? Okay, next angle C F D that's That one how big yep Convince me objection your honor calls for speculation. I don't see a rule on there called 35 minus 90 on the yellow sheet Sorry Okay, so Taylor said look if this is 90 these two add to 90 and now We're going to abbreviate complementary as comp. We wrote it out the first time. Yes You can abbreviate that as comp. There is another argument. You could have made as well. You could have also said what Marcus You could also have said or So or What was that when you said? Okay ready angles on Align, and I'm saying you can't abbreviate these because it's lots of writing The same way they do in a court of law. They don't tell you the whole case They say oh in Johnson v. Smith, and you're supposed to look it up and clue in whatever Either of those I would have to accept and now we're getting into diagrams that are complicated enough into arguments That are complicated enough that there's more than one reason Best friends always BFA is that I know BFF is best friends is BFA anything No, okay You can use that now best friends always B F a now that is That one How big Yes, I know you know this and you're doing good and thank you for raising your hand But I want to get other people involved now. I Agree no wait a minute objection your honor calls for speculation. Ah Okay, so here is where we saw the X Which I think is also on your sheet top right corner if I'm remembering correct or near the top right corner Sorry, no never mind. I gave you two columns On the first half of the page near the top right of the first. It's there You find it. Yes. Yes. Yes. Yes. Okay Matt, what did you say the rule was? What did you say the rule was? How about vert? And I'll clue in that that's what you're talking about By the way, I don't know if I've showed you how I remember that rule. Can you all look up for a second? Matt, what letter is that? What letter is that? What's the top half of the X look like? That's how I remember X B vertically opposite whatever works for you, but I Told you I sucked at geometry and I had to come up with all sorts of stuff shake. This was one way You okay with this? Let's keep going this one We're arguing but we're getting marks for arguing which most teenagers don't normally do Be at BFC. That's that guy. How big? Yeah How'd you get 125? Vertically opposite, let me see so you said you looked at that and you added 90 you know what I didn't even see that I agree that works It's not the first one I would have spotted I actually went well Yeah, I trained myself if I'm not sure what to do always look at the previous question because often the previous question is What I need to find the next one so I looked here and I said 50. Oh, I also said or sup or Angles on a line or Alex do we know this? Do we know this? Do we know this? Do we know this? What's that add to? Okay, where is that rule on the sheet? Can you find it? What do we call that one find it on the yellow sheet somewhere? Okay, we're gonna call that the course the court case that we're gonna refer to from now on Aaron for that one is or Angles at Point that means on a quiz from now on I'm gonna ask you for the angle and for the reason It's probably gonna be a half mark and a half mark but for this answer Joe I would take that or that or that now did you hear me say to Alex I didn't even think of that one you guys heard me say that on These quizzes what I'm gonna be doing afterwards all the time is saying now come lawyer with me You may have seen one that I didn't see and I might have marked it wrong And you may actually say no I saw this and it's not oh, I didn't see that and you are right So for this unit when I hand stuff back argue with me because that's part of what we're also trying to practice Jeremiah It's the art of mathematics of logic and reasoning Bifta Be a Bfd be oh Be Fd What angle is that? As a number first of all, please How many degrees okay 180 degrees What's that called on our court reference sheet? It's there No, no, I think I think that I think this is they're not actually one of those on there somewhere. Oh what? Straight is that what it says straight angle? There you go There's our rule. So you should find this sheet handy. Let's do a few more through the page Okay angle one how big now if you're stuck Where would I go looking to try and figure out how big angle one is Joe? What's the only angle they gave me in this question? They gave me a 180. What's the only angle they gave me in this? So, you know what? Because I've told you do these an or if you're finding trouble now I'm seeing some of you are seeing these right away great You can probably drop your guard down and almost do them in any order But if you're having trouble I've said to you do them in order because you can think like the test creator I'm sure this 70 is going to tell me how big angle one is and it's either going to be the same size or add to 180 Because that's the only rule we've ever learned angle one how big well sorry I heard somebody say e and I 70 I agree objection your honor culture speculation. How come? Oh, she even found the rule she said mr. Do it when you have two parallel lines And a line cutting across which you do have a picture of yes. Yes. Yes. Yes. Yes If you can slide one line one angle like snakes and ladders along the line that's cutting across and they overlap perfectly we call that Can I abbreviate corresponding with c o r r? We're gonna Angle two how big Marcus Convince me. You see letter x. Yep Angle three how big Jordan why Sup Or we said you could also call that angles on the line. I'll take that now If somebody said to me joe Well, couldn't I use angles at a point add to 360? This is where I would say Since you don't know this angle yet You can't use a rule that assumes that you know this angle to try and find another angle So Try not to add extra angles if you can avoid it We want the cleanest case. We don't want a bunch of extra legal information that the judge doesn't need It may be right But if the judge doesn't need it why confusing? Does that make sense Courtney? Let's keep going Courtney, what's the only angle they gave me in question 10? So that angle four it's either 65 although They don't look the same size Or it's probably 180 minus 65 is only with two relations. We have I'm pretty sure it is 115 what I'm really saying is why How come Marcus? Uh, let's see that would mean these two formed a letter zed and I don't think they do Matt Okay, now you all have your reference sheet. Yes The one that I forgot to print into here. Give me one second here foundations of math 11 My geometry reference sheet because we're gonna we're gonna handle else on this sheet So you all want to get out that reference sheet for a second And where it says interior angles on the same side of the transversal we're going to add two things First of all if you want the abbreviation it was I a O T T IOT sought first letter of each word But a few years ago after this handouts were made up somebody came along in math in bc and said You know in britain and in europe they use a shorter word for this and people said Oh, they do that would be great because i'm tired of writing interior angles on the same side of the transversal So what i'd like you to write next to here if you want to is co interior You can use that to describe this as well co dash interior The only reason I don't like that is kids get alternate interior and co interior and co responding a little bit mixed up But wait a minute. You got the pictures in the shapes in front of you. I'm gonna say I think you can handle it Okay, so back to our notes to your angles on the same side of the transversal Coint or iot sought it's the same thing In fact, it was the letter c rule right There's your capital letter c their tangles a big zangle five Objection your honor calls for speculation. You're right. How come? What letter are you looking for alternate interior angles? Zed here's how I remember that these go together zed is the last letter a is the first letter. I kind of remember zed Goes into the a sorry. I don't know works for me Zoro angles one year my kids named them zangles. I've had some kids call them But alternate interior is the official court rule Try to think try 12 on your own. I'll do it up here 12 is trickier if you get stuck You can always look up in a few seconds I got these Yes, no Oh, I'm sorry. I hit the button I thought try that again. I got those Where do you guys are we? by the way Jordan in situations where I'm getting two rules you you only have to use one of them But what I'm saying is I take that I take that now This last one and this one you might lawyer with me because there is another way to get angle three Did anybody see the other way to get angle three? What There is a zed So I would have to also accept on a quiz Is there another way to get angle four that I haven't seen? I'm not really seeing Anything there Great question Okay No, no, it's a good quick. What did you do? Did you get 110 or not? So first of all, here's what I said I heard you say did you say the one in the three? What angle are you finding right now? No, no, you what angle did you said you want you asked me what angle two didn't you? Oh, how did I get angle three you asked? I thought he asked me how did I get angle two? Sorry, okay So two ways Like that to the zed or X marks the spot just imagine that line's not there And there you have to use your Sesame Street imagination, which means these two are the same angle Vertically opposite Okay, let's try a couple more In fact a few more and we're done How big is angle one Boston? You might need your calculator for this one unless you're good arithmetic in your head Is it 58? Yes, no. Yeah 58. We're good to 58 Convince me Okay, now what are we going to call that one? Can you find that rule on the gold sheet somewhere? I think it's right above where the triangles start It's all on the front page right now. We haven't done anything from the back page yet It's in small typing. I think right above where the triangles start. I think oh, I think oh, I think What's it say? Louder, I can't hear you. So here's how we're going to abbreviate that one angle sum of triangles Some you're adding them up the angles Triangles except we're not going to write that much. Oh, we'll write it up just this once in our notes But we're actually going to write it this way angle sum of triangle shorter Is that okay? So Your court case that you referred to Boston is I know every triangle adds to 180. We're going to call that angle sum of triangles Okay Angle four how big how big is angle four 29? I think I Yeah, I agree with Sam 29 convince me More specific. What type of a triangle is this? I sock triangle Now the fancy word for this is angles opposite equal sides of an isosceles triangle or equal We're using the properties of the isosceles triangle and I think I gave you a picture of an isosceles triangle on your gold sheet Yes, and I listed the properties. Yes. Yeah Oh, wouldn't it be 34? I don't know. I wasn't doing the math. Is it 34? 180 minus 112 and then divide by two. Yes You also did use angle sum of triangles But really your final step was isosceles triangle having said that Jeremiah I would accept both rules if you said to me. Well, I used angle sum of triangles I'd say fair game But most of you also would have said that's awesome So Alex, how big is angle five then? 146 convince me What's up or angles on the line Or I guess you could argue Hey, this adds to 360 and this one here is 180. You could use angles at a point But hopefully nobody would do that much extra work. I'm also trying to teach you Emily to be lazy and deficient There are often longer ways to get that's probably a short way to get there last page Does getting the hang of this a little bit One extra step. We're saying ask your brain how you know. All right angle four Now you'll notice they didn't give you any numbered angles here. There's no 30 degrees kicking out of you or 52 degrees kicking out of you Angle four how big Jordan 60 objection your honor calls for speculation And you know what? If you look at the definition of the equilateral triangle on that gold sheet Yes, Joe, what does it say next to an equilateral triangle on the gold sheet now that you've got it right side up so you can read it and and Does it say anything else? Okay, I think it says Three sides equal three. What's the sudden abbreviation for? Okay, so read that too. That's the phrase. I'm looking for it And if they're all equal they each equal 60 because they've got to add to 180. So you know what if you write Equa triangle equilateral triangle. Okay, how big is angle five? Now if you're not sure how the heck to find angle five What angle should you look at as for a hint? I would look at angle four first of all I would also look at any other numbered angles that they gave me if there's like a 42 degrees kicking around some But I'm looking at angle four and when I do that I'm going to argue. I think that makes the Zorro's angle zed easier to see Yes, how big is angle five? What do we call the zed rule? alt int angle six how big convince me alex angle sum triangle You notice I even dropped the word of a clue it okay On a test that probably includes the word I'm just what I'm trying to say is can you defend your argument? Can you show me what your reasoning is? And for those of you who say where am I going to use this stuff? This stuff probably never But arguing and trying to convince people that you're right. That's the skill we're practicing Marcus. You going to make it? I'm not so sure No up in there You know what I missed you I was aiming for you and I aimed a little bit to the left there didn't I because danielle boy that got her attention Sorry danielle. You know what next time I'll aim at jordan. That should get Marcus square between the eyes Last one What's the great big shape that you have here? Circle So here is mr. duix one of the many tricks portney if they ever give me a circle did they give me a circle? If they ever give me a circle, I always find all the radiuses all the radii And I put equal hash marks on all of them That's the same length as that is the same length as that is the same length as that You know how I know jordan Because the radius like the definition of a radius was from the center of the circle to the edge A circle is defined as all the same radius Do you see as soon as I do that did you notice a whole bunch of isosceles triangles suddenly appeared? See them So devon they give you a circle put hash marks on the radiuses Okay, I'm going to use the proper math on the radii So All right, how big is angle one? Matt I think you're right if I read your lips correctly. You are correct convince me Isos triangle How big is angle two? convince me Isos triangle How big is angle three? Taylor 110 convince me I think you went like this These are all These are all angles at a point. You said those add to 360 So I think Taylor you went 360 minus this angle minus this angle And then you said if the two remaining angles are the same size What will I do with the degrees that I have left over? Yeah, and the geometry rule you started out using was angles at a point. I agree angles Do we have an abbreviation in English for the word at? Yes, we do I'll take that even Angles at point and you'll notice I didn't even write the word So that's what we're going to be spending leading up to Christmas and after Christmas going over Okay Says homework work on finishing geometry package one just so that I know has anybody finished geometry package one yet Just one person Okay, I was gonna It says once you finish geometry package one hand it in and start on geometry package number two I'm going to hand out geometry package number two on thursday of next week So if you're done, I'm not going to give you new homework. Okay The rest of you you have the remainder of class