[Music] [Applause] [Music] [Applause] [Music] um have you done geometry in class already uh yeah we we're on similarity now okay cool um and how do you feel about it sort of are we enjoying it or hating it or i hate it no do you just not see it or what's the reason i've never been a fan of geometry to be honest okay i'm gonna see if i can try and um bring you over to the bright side hi camber have you done geometry in class yet i don't think so much okay okay so you don't have an opinion yet so i have to try and change some opinions but um you've got to go into this open minded we're just going to wait for a couple more people to join and then we're going to get going um and get this new section started if it's just the two of you oh i should have thought of uh some question from the last topic we did at least for you to work on but the others will get here now if you're wanting um i'm i'm not going to tell everyone to write all of these words down because it's going to take too long but if you want to write them down in new books you're welcome to while we wait um hi everyone i'm just giving everyone a few more minutes to join um the call so don't panic if there's silence and you're worried you should be doing something and there are some words up on the board at the moment that we're just gonna talk through but um if you someone who really likes to have your notes with you you're welcome to start writing these things down um we're just gonna we're just gonna give everyone a chance to join the call before we get going while you're here though can you give me an idea can you write in the comments so just say whether or not you've done geometry in school already this year and then give me a number from 0 to 10 on how you feel about geometry so xero you hate geometry it doesn't make sense and 10 you love geometry and everything makes sense so just go into the chat tell me first whether or not you've done geometry in class and then give me a number right okay that's a great number to start with thank you zero oh no no because the numbers coming in are not making me feel good i'm gonna have to try and make these numbers considerably higher over the next four four weeks keep them coming in though so go through to the comments tell me whether or not you've done geometry and then give me a number from 0 to 10 on how you feel about geometry so 0 very bad 10 good okay i will i will take that five oh we are negative numbers again great great if you've just joined just can you go on to the chat for me for a second and just let me know um if you've done geometry in school and where your comfort level is so xero is really bad i hate geometry i don't understand anything in geometry 10 i love geometry i understand it all ah we finally have a high number yes yay progress we have lots of negatives so if you hate geometry you're in good company at the moment okay three that's okay what i do recommend because um we're going to be in geometry for a month so can you please make sure you have a piece of paper or a book somewhere that you can keep safe so separate to where you do all your working and we're going to slowly write down all the reasons on that piece of paper and so then you can use that as a reference as we work forward okay so if you haven't got one with you go find yourself a piece of paper or a book that you can dedicate to geometry reasons i'll give you a couple minutes to go grab that and then we can get going and if you haven't just put your number in the chat me on how you feel about geometry at the moment cool okay so let's get going so for geometry we're going to be on this course for the next month so we have eight lessons on it um we potentially will have two lessons at the end which we're focusing on quadrilaterals but depending on how today goes we may need to stretch out this beginning stuff over two lessons so we're just gonna see how how everyone goes with the questions okay so don't panic i promise we'll cover everything we need by the end of the month so um all i have here at the moment that you can see on your screen is some basic words and some terminology and we're just gonna slowly work our way through this and then we're going to jump straight into some questions now i'm very strict when it comes to having the correct reason and it's because in matric if your reason is wrong you don't get the mark they're not kind they don't think oh i know what this person means it has to be the correct reason and so when we get to talking about reasons it's really really important that you write it down exactly as it should be and that's what you use going forward so that when we learn it in grade nine it stays in our head all the way to metric um yes so i just had a question and geometry is definitely where you have to calculate degrees of angles hopefully because we did equations together and geometry has a lot of equation work we'll be able to make our way through this okay so i'm just going to turn my camera off because i'm going to flip my screen over and we're going to start jumping into geometry okay so let's go so just some basic words just to understand what's going on when we have a point we normally just represent it as like a dot so for example like a c and b those are all different points that we have okay a line segment is where we are joining two of those points so for example this here would be a line segment and we would call that line segment ac so when we're talking about a line that's connecting we talk about the two letters that are joined the two points that are joining it together okay two lines that meets at a point form an angle and these lines um are called the arms of the angle so here we have a b and we have ac and there are two arms and they form this angle here in the middle oh goodness so i'm just going through these words because when i use these words when we're talking it's important that you know what i'm talking about okay so if i'm talking about arms or lines or angles it's important to know what those are a vertex is the point where two arms meet so i could have if i had like a triangle that's a vertex that's a vertex and that's a vertex so i can have more than one vertex in a picture all of those would be a vertex and if you wanted the plural for vertex it's vertice so vertices like that so one vertex many vertices and the angle is the space that is between those two arms okay i'm going over these quite quickly just because um we need to sort of jump into the actual questions this is just to make sure everyone knows what everything is if at any point you don't know what i'm talking about just let me know either either a newton tell me or just tell me in the comments i don't mind either okay all right then this is quite important when we're labeling angles there are different ways that we can label them so first is if i have just a capital letter so if i'm trying to label that angle a over there because it's only one angle a i can actually just say that that's angle a and i have a little like copy like a little hat on a so i'm telling me that it's angle a if i was writing like a b or a c because they're two letters and they are capitals that means i'm talking about lines okay the next way is if i brought in three letters so if i was trying to talk about this angle here i would say well it's between ac and a b right so we kind of follow that path and we say well that angle would be c a b or we could also say b a c doesn't matter as long as a is in the middle because that's where the actual angle is okay yeah i have some subscripts going on so if i cared about let's get a different color since we're in a different question if i cared about this angle here that's shaded i would call it a 1 angle a1 or if i wanted to use my three letters i could say that it is angle c a b so these are just different ways i can say what an angle is and the last way is if they are giving us um variables and we want to know what these different angles are if i wanted to know what that angle is i could just say that that's angle y and this angle here would be angle x so it is just what it is we don't need to have a copy on it or anything so those are just the different ways that we can write what an angle is does anyone need me to sit on this any longer just either just put your hand up as an emoji or let me know okay okay sure no problem do you remember how in algebra we had to kind of learn rules in the beginning because it's like learning a language geometry is the same we have to learn these different rules and these different definitions because it's a language and as long as you understand the language you actually will be fine i'm going to make all of those of you who don't like geometry i'm going to make you love it by the end of this month okay it's good so the first thing we're going to talk about is intersecting lines and this should all be revision from grade 8. so the first rule and that page that i told you to get out that we're going to be referring to a lot this is the first thing that every time i put something in a block like this i want you to put it on that page okay so our first thing the label for in question one um i'm not sure what the what the question means the which label in question one oh we're talking about how i could say what this angle is and i could call that angle just angle a i'm allowed to just say it's angle a that's the only angle there is okay okay so the first thing i want you to write on that piece of paper or that book that you're keeping safe is this rectangle that i've got in here the statement as um and this is just we're keeping this there so that we know what's going on as we move around but basically angles that are all the way around the points add up to 360 degrees and the reason we use for this statement is angles around a point so put this into your um into your book or into your piece of paper that we're keeping safe we're going to add to it as we move through geometry if you feel like you will understand just from the picture you can just write the picture and then just write your um reason next to it if you feel like you're not going to remember that then you can write more information it's up to you that's important for us to start keeping a log of all of this so that when we start adding more things it doesn't get too scary that's okay don't worry okay i'm just gonna give you one more minute to write this down just so that everyone has it and then we're going to look at some questions involving this reason all right let's get going so we're going to start with a nice easy question here i'm going to help you with these first few and then i'm going to let you start trying them yourselves um so what we're doing is we've started geometry and now it's okay for both of you we've started geometry this is the first reason that we've spoken about so don't panic you haven't missed too much yet and all i'm asking is that um you have a piece of paper or a book nearby that you can keep all of your reasons in as we move through the sections something safe and every time i put something in a rectangle i want you to make sure you put that down on that save page okay so that's what they were doing when you guys joined now we're going to start our first examples with it so first example here i'm trying to find x so whenever you see it written like this all geometric statements and reasons that's saying that whenever we say a statement we need to have a reason to back it up and we always put our reasons in brackets next to it okay so be very careful with the formats of what this looks like i'm trying to find this x value over here that would be a point so that would be a vertex and i know that if i went all the way around it would equal 360 degrees so i could say x plus 280 degrees is equal to 360 degrees this is my statement and then i would give my reason in brackets i would say angles round a point that's my reason okay so we have a statement and then we have reason and what we land up creating is an equation and i'm just trying to solve x and i know we spend quite a lot of time doing equation work so you should feel comfortable with it and so all that's going to happen is i'm going to move let's use a different green so you can see i'm going to move that 280 over to the other side so i'm going to say x is equal to 360 minus 280 which means x is equal to 80 degrees okay now this step you don't have to show if you felt comfortable and you could just do it you could just um you could just jump straight to your answer you could actually also go right at the beginning and just say x is 80 and then give you a reason of angles around a point okay i see two hands about either of those questions or they not yeah i need more time on the question that's okay i can sit here for a little bit thank you okay awesome let's go on to our second question yeah [Music] okay okay i'm gonna help you with this one again and then and then let you guys try that one by yourselves okay if you're feeling good then you can sort of try while i'm talking through this as well again this would be my point over here and i know that all of my angles around that point needs equal 360 degrees so i'm just going to write that as an equation so x plus 140 plus x plus 10 plus what's this how many degrees is that little square does anyone remember and 90 yes princess well done that's 90 degrees and all of that together has to equal 360 and my reason is gonna be angles round a point okay we're on a nice little equation here we're going to add our like terms so we've got this x and we're going to add that other x which means we have 2x and then we're going to look at our numbers we have 140 plus 10 plus 90 which gives us 240 and that's equal to 360 degrees then we're just going to move that 240 over so 2x is equal to 360 minus 240 which means 2x is equal to 120 degrees and we're going to divide both sides by two do you see all of this equation work that we did earlier in the year why we needed to do it at the beginning of the year x is equal to 60 degrees so actually the geometry part is only that we have to use this geometry brain is for this first line and then all of this is actually just equation work so if you like the equations then you should like geometry okay i'm going to put cf but b will still be on the screen for anyone who still needs it i would really like for you all to give c a try give it a try by yourselves and let's see if we can get some answers coming in you can just once you've done it don't worry i know i know you're probably still on your first line i'm not trying to rush you once you have an answer you can just put it in the comments or you can unmute and tell me and let me know what value you get for x man yes um like angles at the hey that let me add a point at up to 360 degrees right yes okay okay oh we have our first answer i'm not going to tell you if it's the same as me just yet so we can give others a try a chance but i'm very excited that you have an answer okay two have come in oh and they're the same interesting either you're both right or you're both wrong okay let's start adding so we're going to say all of these together up and equal 360 degrees so 70 plus x plus 10 plus 2x minus 10 plus x plus 70 needs to equal 360 degrees angles around a point okay and so we'll end up 4x plus 140 is equal to 360. if you didn't get that point just double check you're adding i'm going to move that 140 over so 4x is equal to 360 minus 140 which means 4x is equal to 220 degrees divide both sides by 4 and x is equal to 55 degrees okay so some of you were really close well done to everyone who got it right that's absolutely awesome i'm very very happy for those of you who got it a bit wrong you were in the right ballpark so i think what happened is you just made a a small adding error in one of the first few lines so just double check yes see i told you you're gonna like geometry geometry is fun you just have to you have to tell it that you love it until that until it loves you back that's the strategy for geometry okay um i'm going to give you which one should i'm going to give you a um a and b these two they should go nice and quickly they're not horrible ones and then we're going to potentially move down to our second reason depending on people's answers here so a you can actually do in one step if you feel comfortable ah guys i didn't realize i was muted and i've been talking this whole time okay firstly yay your answers coming in are looking beautiful secondly when you um are doing these as practices don't think okay i don't need to write the comments i'm like the reason because i know what it is because the more we write it the better the chances that it sticks in our head and we know what's going on and it's easier for us to remember okay so for a we're looking at that and then we're just gonna say x then well let's say x plus 235 is equal to 360 which means x is 360 minus 235 which means x is equal to 125 degrees so well done for a of 125. um i can see not everyone has finished b b8 so i'm just going to give you a little bit longer to finish off b but i am seeing some good answers coming through if you have finished b you can give c a try for me okay for b we're going to add them all together so 2x plus 2x plus 160 is equal to 360 degrees angles around a point so 4x plus 160 equals 360. 4x equals 360 minus 160 which means 4x is equal to 200 degrees divide both sides by 4 therefore x is equal to 50. so well done to those of you who got that right as well you are doing so well so far very exciting and then c is the last question i'd like you to try with this reason and then we're going to learn our second reason keep uh uh if you are getting an ugly answer for c and by ugly answer i mean if you're getting a decimal please don't panic you're not wrong man yes you scroll down a little bit just sure is that enough thank you ma'am sure no problem oh two different decimals coming in yes um okay lovely answers coming in this is this is an important question to do because sometimes when we get an answer that's a decimal we think we're wrong but remember with all of these questions you can always put it back into it oh goodness sorry zooming in big time over there you can always put it back into the picture with your answer for x and see if you get 360 degrees okay so let's start adding we've got 75 plus x minus 45 plus x plus 30 plus 65 is equal to 360 degrees angles round the point okay and that gives us a beautiful line here of 2x plus 125 which is equal to 360. so 2x is equal to 360 minus 125 which gives us 235 then we divide both sides by 2 and so x is equal to 117 and a half degrees now what i want you to be careful with with a question like this or not get disheartened by is if you have this first line and you've written that beautifully so you have your statement you have your reason and then you made some mistakes along the way in your equation work okay but the answer made sense for what you did you would still potentially get this mark done yet so don't feel like everything was wrong if you make a mistake with your equations you still would have got definitely those first two marks in the first line okay okay our second reason so this is again on that piece of paper or on the book wherever you are writing your reasons i'd like you to put the second rectangle for me so this is saying this angle here which is acd that's this angle plus bdcb which is this angle we're saying if we add those two angles together so what's important is the word adjacent adjacent means next to so they are angles that are next to each other they will equal 180 degrees and the reason is angles on a straight line so just take a moment to put this on that piece of paper on the book wherever you're writing these reasons and we'll go from there remember when we spoke about those definitions at the beginning of this lesson we spoke about arms and adjacent angles have to have a common arm so they have to have one arm that is between them and that's really important because sometimes we think angles are adjacent when they're not so they have to be on either side of an arm okay does anyone need more time here yes please man no problem okay let's move on down so now we're going to be applying this rule so again i'm going to start with two really nice easy examples and i'm going to talk you through them and then i'm going to let you try some alone okay so first one here this is our common arm which means that this angle and this angle are adjacent to each other i know that that might seem very sort of straightforward for a lot of you right now but when these become more complicated it's really important that we understand what adjacent means so that means that these two angles together because they're on a straight line need to equal 180 degrees so i can say x plus 135 degrees is 180 degrees because of angles on a straight line okay sorry my kids at school always give me a lot of hassle for my angles because they say that they look like c's i'm trying really hard to make them all look like angles but you'll have to forgive me all right then we're going to move that 135 over so x is equal to 180 minus 135 which means x is equal to 45 degrees beautiful well done okay second one here's a common arm and here's a common arm which means these angles are all adjacent to each other so all three of those angles together because they're on a straight line need to equal 180. so we would say x minus 10 plus x plus 66 equals 180 degrees angles on a straight line i'm gonna make you prefer the whole of geometry i'm telling you my personal mission 2x plus 56 is equal to 180 degrees we're going to move that 56 over so 2x is equal to 180 minus 56. so 2x is equal to 124 we divide both sides by 2 which means x is going to be 62 degrees so those are just two sort of easy examples i'm seeing the hand them is that a question i want you would you like me to stay here i think i can get another question in with these still on the screen okay so i'd like you to give c a try for me nice easy question don't get a panic you okay answers are coming in have a look so here's our common arm which means this angle and this angle are adjacent to each other so x plus x plus 74 is equal to 180 degrees angles on a straight line so 2x plus 74 is 180 we're going to move that 74 over so 2x is equal to 106. we're going to divide both sides by 2 therefore x is 53 degrees so well done to those of you who got that answer correct awesome okay next two e o e don't eat because you'll need a new rule for e i'll talk to you about e no no so just d for me oh you thought this was a 71 yeah no that was a four sorry but i see why you thought it was a 71 so if you thought it was 71 your answer would be a little bit different um if you're if it was 71 for you you would have gotten an answer of 54 comma 5 degrees uh hmm if you are getting 75 degrees i think you are forgetting about our good friend 90 degrees over here okay let's have a look so there's my common arm there's my common arm which means all three of these angles are going to be adjacent and so x plus x plus 30 plus 90 which is this guy here is equal to 180 degrees angles on the straight yeah yeah the 90 degree was the sneak okay so 2x plus 120 equals 180 which means 2x is equal to 60 which means x is equal to 50 degrees so well done to those of you who got the 3t if you got the 75 you forgot about the 90 and that's okay that's why we do these together and that's why we practice woohoo because you haven't been doing geometry for a while don't panic it'll start coming back it's because there's not like a number attached to it so it's very easy for our brain to kind of skip over it okay this one we have to learn a new rule for but it's not a rule that we use often which is why it doesn't have its own special block but if you would like to put it in a block you're welcome to if we're looking you were right if you are looking at an angle that is just 90 degrees so two adjacent angles that are at 90 degrees to each other we could say here that x plus 70 is equal to 90 degrees we can see that right so we can see that x is going to be 20. but our reason is we would say that they are complementary angles so complementary angles that's what this means complementary it means that they are at 90 degrees to each other so when we are using something that's at 90 degrees we just say comp elementary angle so you could say comp angles is even fine you don't even need the l but this reason is is very rarely used but it is used sometimes so if you would like to put it on your page you're welcome to okay all right oh wait does anyone need more time yes ma'am okay look at things i had this feeling all of a sudden thank you man no problem so now we're gonna i'm gonna give you some of these questions to practice so let's start with these first three uh okay when you start getting answers let me know what you are getting don't forget when you're writing this for every statement you need a reason don't forget to be practicing that on your side actually i have to turn my camera on so that you guys can see how my cat is sitting on me for this lesson right now she's sitting like a parrot i don't know if you can see her she just hopped on at some point and now this is how we're teaching he's so cute it's ridiculous i don't know what she's doing she'd never done this before ma'am mama don't like kids i'm so sorry you definitely would not be enjoying her right now because she's clearly very needy yes yeah there we go if you jump on me like that i'd be very very very scared she sort of just put her paws up so i knew she was on her way but okay cam camera it off again okay i'm seeing some first answers for the cat people i'm non-cat people just be grateful it wasn't on your shoulder okay let's start so x minus 10 plus 125 is equal to 180 degrees and my reason is angles on a straight line okay so x plus 115 is equal to 180 which means that x is equal to 65 degrees okay well done to those of you who got a right awesome consonant where's d what what answer are you working on or is that supposed to be a b okay b here's my common arm which means these are my adjacent angles and so i'm just gonna i'm gonna give you some extra time to finish working this out there we go ma yeah oh yes no okay okay so 2x plus 20 equals 180. which means 2x equals 160 and so x is equal to 80 degrees gorgeous perfect answers coming through excellent okay i'm just going to give you a couple more seconds to work on c and then i'll give you a next question okay here's our common arm and here's our common arm so these are all adjacent angles and so x plus 10 and i hope those of you who forgot the 90 the last time didn't forget it now so plus 90 plus x is equal to 180 degrees angles on a straight line so we've got 2x plus 100 is equal to 180 degrees which means 2x is equal to 80 degrees and so x is equal to 40. and again some really good answers coming through which is excellent okay i am going to give you these last two to do and then we're going to call it a night so we're going to end at the end of e so can you give these last two a try for me and then we're going to carry on with this kind of idea of these intersecting lines in our next lesson so d and e for me and then we will call it a day okay so we all have answers coming in for d let's have a look okay so common arm common arm adjacent adjacent adjacent 20 plus 2x plus 90 equals 180 angles on a straight line so 2x plus 110 is equal to 180 2x is equal to 70 which means x is equal to 35. look at those answers coming in yay good okay last one for the evening e ma'am yes you look so tough yeah but it's not don't panic i promise one sip at a time have some faith in yourself i'll give you a hint on where to start find me why first i wouldn't give you a question that you couldn't do i promise i'm going to help you a little bit for those who are struggling with this first part so that's my 90 degrees so i can say 65 plus y is equal to 90 because of complementary angles okay so therefore y is going to equal 90 minus 65 which gives us 25 degrees okay so we know that this is 25 degrees so that should help you to find x and if you'd already gotten y is 25 that's excellent well done and i just had a look at our time so i'm going to have to keep going so now i'm going to use you could actually just use complementary angles again to find x or you could say x plus 18 plus 65 plus 25 which is our y is equal to 180 angles on a straight line you could have used um complementary angles and so 18 plus 65 plus 25 gives us 108 equals 180 which means x is 72 degrees so very very well done to those of you who got that right i hope that we are feeling a little bit more confident with geometry as we start this journey um and i'm gonna pass over the mic um and screen to tula have a good evening everyone ma'am yeah ma'am can you like just wait for like just a minute yeah i'm okay i'm sure tiller can start speaking before he starts sharing i'm yes no you can um yeah i think you guys can copy that's okay um i just want to know in the meantime how are you guys feeling in the beginning of this msg asked how people felt about geometry and there were some pretty low numbers i remember particularly i think tom like gave like a negative rating or something yeah we got a negative 10 000. yes how are you guys feeling um signing camera adora i think you guys had very low numbers oh okay that's good i see a smile from kamla just give quick numbers you don't have to be perfect at this point but just like are you feeling positive that you'll get better daphne is always like um yeah i'm on the ball over the top yes yeah i like it though ah this is awesome this is awesome oh this is great you guys keep the numbers coming if you haven't voted yet um no this is good and i'm glad that you guys are very positive yeah geometry is fun yes yes it is yeah and it's just like any new thing because i don't think a lot of um a lot of you guys have done geometry before grade nine so it's just a new thing so it's it's it's understandable that it's daunting for a lot of people but as as you've seen now when you have a good teacher teaching you with patience and you also have an open mind it does get better i'm gonna start sharing my screen now i hope um hope that's okay and remember if you don't manage to catch everything now you can always go back to whatobe.co.js and you can re-watch um these lessons um right just go to grade 9 there and all these are recorded and you can rewatch them and copy anything you need to copy so i'm just going to quickly share my screen now so we can let you guys go okay that is the wrong screen okay here we go so as you know we're doing um geometry and we have quite a few lessons um to get through um total of eight lessons good news is we've just finished the one lesson and we'll be continuing with intersecting lines um um on wednesday because we didn't finish that this evening so we'll be doing that and um so yeah just um maybe re-watch this lesson if you need to rewatch it just do whatever you can i know some of you have done it in school maybe you didn't understand it properly just go back to your notes if you have just do whatever you can to prepare yourself um in any way and of course we have at the homework under our tobii app which also tries to prepare you for this so make sure you go to through the lessons onward toby go to geometry of straight lines and then when you click in there under intersecting lines go to equations with complementary and supplementary angles and equations with vertically opposite angles and just do watch the lessons there do the quizzes do whatever you can just to prepare yourself and we'll also have remember on our next lesson on wednesday we'll have the leaderboard so get in as many activities as you can not just for the leaderboard but of course so you can understand but it's a it's a good bonus to have so um i think that's it on my side um do you have anything to add um your mic is off yeah sorry guys i keep on muting myself um no nothing from me i hope you all have a good evening i'll see you on wednesday awesome i'm loving the numbers um and i did do the math and delay yeah it is time you guys have a great sense of humor i love it um i'll see you guys on i'll see you guys on wednesday bye enjoy your evening bye everyone you