okay I hope you like my bleh my mom’s you my pin hole bail hey I got a I shooted a UH automatic ah uh Mathematica CA how do I be Gagne I was rent free a man thank you for looking that up on your under Franklin – back in Ireland I got an iPhone you little poke have you seen I Love You Man yes subtly things like – I like that that was good I like the bar scene yo happen that’s great I love it seen it okay so to prove triangles argument we’re gonna go over two methods today mr. racer fell two methods to prove triangles congruent briefly so check it out do you agree if you drew two triangles like this right okay do you agree that if this side is congruent to this side and this side congruent to this side and this side can go to this side then these two triangles are congruent yes yes okay yeah there’s a rule or like a kind of a definition of proving two triangles the same which all their sides are the same and that’s called does anyone know yeah you know they’re not equilateral no there’s a really I’m written before I’ll tell you right now it’s called SSS oh okay I just I know side sizes yeah so if I were to ask you what proves these two triangles congruent you’d say side side side SSS okay that’s one thing we’re going to do today and now here is another one let’s say if you had a triangle like this and triangle like this and this side was congruent to this side and this side was congruent to this side and the angle between the two congruent sides was also the same wouldn’t that lock this side into place do you think as in this angle is the same here in here in this line you have you any further out this line can’t do this sort of thing that would be a bigger angle yeah so these two triangles are also congruent these two time is also congruent so if you have an S a side and then you have an angle and they have another side that are going to join these will be what SAS Special Air Service it’s the British yeah all up in your mind F an overall up in Europe y’all on the merging hair mama wears beret of American week in America maybe if you are you’d see Barret this is my barrette rubber I’m her own practice I’m I’m uh I’m uh I’m a city folk I’m uh I’m uh I’m gonna have a modern guy come on it’s a satchel I get a lot of compliments on this movie never mind hangover and imagine now he’s still radar and you’re all this in seventeen don’t watch it oh so funny Carlos so funny oh yes comedy all year but don’t watch it you think what’s the baby he’s like the Carlos all right so any questions about these children good now we’re gonna do ways they’re all these local people there’s a total look please at the Boeing he shot from you won’t be money along class Oh what is he asking for side-angle-side come on good question no side angle in the first half

Sasha’s don’t give me that sad face I’m sorry okay go senses you so please draw this one and then we have to given statements given oh my god yeah you say let’s see room sakes can I get it set schecky brunette who with a thirty year of memorization room you guys are insatiable reasons okay no so assume the given statement is the following and let’s just go ahead write the proof statement approve triangle d XC congruent to triangle B X a okay there we go hi Jackie thank you Mike yes knowing mind Zachary X is the midpoint of D be a little bit smarter and I’m to giving you to stand given statements did you just make up his problem no where you go house that’s not to give me a lot of us I’m giving you the giving right here in within the proof someone have to write it twice that’s all all right now we’re ready to killing me now we’re ready to do it I uh I need you I know you got a mess for you you don’t know you need I’m doing Africa where this American when I’ll do know African bongos in France with moretz here we go guys now check it out we’re trying to prove two triangles are congruent water the two ways that we can prove child’s from right now we can draw it out and then over the two laws before OS a as intensive as s right SAS and SSS so within these two let’s look closely at the triangle we want to prove DC x there’s give me DFC so we want to prove that this one is congruent to the exercise this one okay that’s the goal we want to prove the blue one congruent to the red one so let’s go ahead and start to prove this side is the same as this side okay so let’s go in Newtons use midpoint X is the midpoint of DB and X is in point of Verdean bein what is congruent to one yes oh well using the D X plus XP no but that’s not that that’s fine that works you’re doing if X is the middle of DB what is congruent to what yes oh never lose anything else yes DS movie or D axis from how much we have a question yes birthday vertical yeah we’re gonna do that later okay okay we’re talking about science we hold on oh thanks is the midpoint of DB x is the middle of T V then we could say say clean he asks for the class DX can through it to X to B and what gives us the right to say that DX is congruent to X be definition of midpoint right dad uh mid very very well all right so yeah we’re gonna do another one let’s go ahead and mark the picture DX is the same as xB we can go back than that okay so those two are the same all right what’s the second Kourou insane we can make please yes ax congruent to X is C again there could be oh just gonna miss evening uh yeah you can put it in the same line unit also definitely yeah there it is and now you can also mark the picture like so this is the same as that so something that I like to do sometimes is that if I’m trying to prove like SSS or SAS or any one of those actually give myself a

little reminder I say okay I proved one side of the blue is the same as one side of the red so I did an s awesome good s I proved another side of the blue is the same as another side of the red that’s another us to do so I need either another s or an a yes what couldn’t you have liked that the angle above my PDI and CV are going to be equal because they have to make da I’m going to ad yeah does not have to be true not necessarily no no but the point is we don’t even need to mess up da a and C B because they’re not in the realm of our goal as a DC and then a Mary like okay now can we say that DC is the same as a B we’d like to but we can’t we can’t say that DC is the same as a B because there’s nothing given about that is there anything given the only thing that’s given is that X is the midpoint of these two so we can’t make that assumption yet all right so that’s a good that’s a good guess because if we did it we would have SSS 1b but we can’t say alright someone else actually you said it earlier what about you which angle because you can’t move it convincing yes what kind of angles vertical yeah vertical angles so is there an angle in this triangle that’s the same as an angle in this triangle what’s that angle angle oh shoot I said hey I mean that’s a yes oh yeah oh yeah yeah yeah so what’s a single cool angle angle d-bags seen congruent to B all right so let’s do with B right because you know Dean starting at the one notch to the – oh yeah so be so BXI it wouldn’t be wrong technically I wouldn’t mark the wrong B and X a so we could go ahead and mark them in here definition of congruent angles no that’s not definition congruent angles what kind of angles are they vertical angles you decide but there are bruises you could say you could say more clearly vertical angles are congruent or equal and then the guy that’s like a case of describing instead of Ranga yeah I mean if you’re a definition of vertical angles I wouldn’t like loosely you know but this is clearly an explanation is always better an explanation is always better even for this if if a point cost a segment if a point is the midpoint that it cuts it into two equal parts or something like that alright so that is bar a bless you but that’s our a let me P we have an angle between two sides yes yes so can we prove that these two triangles are congruent now yes so we can say angle a student triangle D X C is congruent to triangle B next Hey by what to law yes okay questions on the axiom SAS sure do you understand how if you look up here side angle side basically means that there’s a congruent angle between two congruent sides the other angles between the two sides because we can’t find the to long side all right you can’t find this side or this one we don’t know about this one or this one yet but we can say that this angle is the same as that and so now we have two congruent sides sandwiching one congruent angle angle between two congruent sides okay that was oh okay one more yeah you guys are laughing it up before I’m here much laughter now what is it hard yeah going away it’s all I feel like they’re supposed to make formula for like what you put in which order like their wills for the other no I’m necessarily mourner as long as you get hired so yes definitely okay draw a new triangle please you already seen on the board I’m going to put it up for clear clarity there here we go

C G a triangle okay given statements I’m just going to put right into the proof itself so let’s put that in we’ll say that triangle um a lot of the stuff is set up in and see my loving eyes CET necessities and just distinguish okay last one so there’s our given two given statements and we haven’t proved to do that these two triangles are the same we can go ahead and mark them as in this guy make through it to e d G this guy so let’s go ahead and try it how do we use that isosceles thing yes well you know that the last line is the bottom two lines on it right what about let’s first let’s use isosceles CED as isosceles that means what is the same as what I write let’s do C D and E D okay it’s our system it already it’s given the notches are given but it’s a good question we need to state it in order to say that this triangle is the same as this triangle we need to say this is the same as that else this is the same as that s this is the same as that maybe another s for an A and then you could say SAS semi expensive okay so let’s go ahead and say C D E have you know that these two are the same I thought isosceles so isosceles triangles have two congruent sides we can just give an explanation Oh foreshow okay so there it is and this classifies as an S or an A this yes s so s we need to stay more state more congruence what is the same as what how about this G is the midpoint of Chiz Novartis iggy go CG is congruent to GE right let’s do CG and eg how’s that that’s cool did you see CG CG there’s the same as even now going to be see Jesus name is GE let’s do Ichi because it’s more consistent starting like them again starting out come follow up forcing for this yeah cg d oh you’re right thank you you’re right good job good job that’s great CG D and E G that’s important okay so how do we say that this is the same as that will give us the right to say it yeah definition of midpoint questions on that okay so now we have another s on our way so is there another side that’s the same in this triangle as it is in this triangle one cycle see what thank you is there a side in this triangle this is so well we know that this is the same as that we know that this is the same as that what about the very side GG is DG the same in this triangle as it is in this triangle yeah say it again is DG the same in this triangle as it isn’t miss tribe yeah my equal to GP exactly you have to say it DG so everything you think you have to like you have to stake all three of the SAS or whatever you have sssu significant this will be a success but the rule that says that a sine is equal to itself or something equals to itself do you remember from algebra one your property’s something equals itself is

what property equal equal reflexive raghava every oh like reflection here I go all right we’re on our way it’s the same line though people don’t that can you say DG is no flexing T’s you guys like the other one I know I know see if you can do it if you don’t do it after ten groups then um well by the way you have ten proofs for homework six really yeah six and so s s s can we say that these two triangles are now congruent yeah they are let’s write it triangle and by what role is like a snake okay concerns questions concerns questions I said it twice questions concerns come round here captain uh basically to recap them before we go to recap you need to state what is congruent to wash clearly this is the same as that stated this is the same as that stated this is the same as itself stated then you could go ahead and stir your yes SS s SS yeah the SS s America why do I go like this every time to America America yeah all right so uh say thank you say au revoir merci beaucoup