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Write countersign proof

what would lose Jenna so what I'd like to do is show you how to write a to comp proof using the segment addition theorem so when writing the two comp proof basically what we want to do is take all the information that we have and then put it down on a sheet of paper or in my case I'm going to be writing it down on the board so typically you're usually going to be given some information that's going to be written out or you're going to be given a figure in this example I'm going to actually given both I'm given a figure as well as some information so let's take the information on a two column proof what we have is we have two parts we have a statement and a reason and the reason is kind of like your justification okay so what we want to do is take all the information that we have put it down on you know on the board and kind of organize it and then can see alright how is that going to help us now prove because the goal of a proof is to be able to prove that a B is equal to a 2 am even though we might know hey I know this is true I know that works we got to provide step-by-step justification that our that order us to come to that conclusion we just can't say well I know it's true and that's you know QED it's all done so we're going to have a statement and then a reason so the first and easiest statement always do is start with what you know you know get your building blocks what is the bate what is everything you're given so in this example you know we have a figure and we don't need to write you know that you know we have a length a B a segment you know that's given but let's write down some of the information that we're given and you can see from this point they give us that M is in midpoint of a B so that is a great thing to write down as a given so I'm just going to write M is the midpoint of a B okay and why do we know that M is the midpoint of a B because it is given so we're just going to write given now they won't tell you that M is the midpoint unless they wanted you to use the definition of midpoint somehow or that the fact that we have a midpoint somehow so we other think you know what does the midpoint mean why do we why would they tell us about the midpoint and how could we use that to prove to you know help us use that well the main thing is you know of the midpoint remember a midpoint is basically a point that's in between two other points and if those two points on a line then that midpoint kind of you know bisects that line basically cuts that line in half so therefore both two segments are now going to be equal so we have this nice long segment here a B since M is the midpoint that now makes both those two segments congruent equal and measure so now what I can say is a M is equal to the length of M B and that is because that's the definition a lot of times we can destroy definition of DF but I'll writes the whole thing out definition of midpoint okay so we have the definition of the midpoint now the next thing is you know what else can we do now I started off by saying we're going to use this segment addition theorem and that's going to be kind of the highlight of what we'll be doing here you know sometimes you might be using it sometimes you might not but I think it's a good way to start if you're kind of stuck well we know that whenever you have a segment if you have a point that breaks up that segment the sum of the two parts that you broke your segment up to are always going to add up to the whole segment right it doesn't matter you know if I take a segment doesn't matter how many times I cut it up the sum of all those little parts is still going to equal my whole segment and that's basically with the segment addition theorem States so I can write a M plus M B is equal to a B and that is my segment addition zero okay so now we have all this information we written down basically everything we know as well as everything that we can think of that would be important here comes the trick the tricky part how do we take all this information out and then write it into a justification you know a meaning that we can say that proves a B is equal to two times a.m. okay so what that comes up with the kind of trick part it's going to happen over and over and that's why we want to get practicing this you to look at it you know think about this we're trying to get to AMS we know that a.m. and MB are congruent right they're equal and measure and so we could say that that's a.m. and that's technically a.m. as well right so am is equal to Mb which we said there so if they're equal to each other then it doesn't matter which one I use right I could substitute one for the other and that's going to that's what we're going to use for this next up is substitution rather than writing MB there's no mb in my proof right you always want to look at what you're in what are you trying to prove and if you have a length that you're that's not going to be in it try to see how could you maybe eliminate it or you know substitute in for another value to help you with your proof so what I can do is say a.m. plus a.m. I don't need to write M be because MB is equal to a.m. so a.m. plus a.m. is equal to a B why because I used substitution I substituted I substituted in the length of M be in for a.m. now I have a M plus a.m. which is going to be two am so I can just write you know a B is equal to 2 a.m. right and then the reason you know therefore I can just write simplify okay and then we can just use my box to say my and proof my proof is complete okay you can also read write the other way and then you know switch it around if you want to go through those extra steps okay so on the next one next example is we have a two column proof so we automatically know well let's just get our statement and reason we know that's what we're going to be using so let's write the statement reason and a lot of times I get with students you know and they're having trouble with proofs which you know I think many people have you know can feel feel your pain and going through it and one of the ways to say well I'm just going to get started with it I know I'm going to have used to comp proof and let's just go and get started with writing down you know what I'm given I might not even know what all this stuff means but I'm just going to write it down in my proof so I'm going to say that lying C E is congruent to lying Fe I don't know why cube under than that and I could say e D is congruent to eg and why is all that true because it's given all right so now once I wrote it down there let's actually see how is this actually going to make sense how is this going to help me and then I you know writing this stuff down is great you know possibly it might give you some partial credit on a test or homework but I mean it's helpful to visualize everything so you know I always like to if I if it's in a book I like to redraw kind of the figure so therefore I can write it and kind of visually see what it's going on so we have light segments that are congruent that means they're equal in measure so I'm going to use tick marks to show that they're congruent so it says C e is equal to Fe ok and then e D is equal to e G okay so how can we use this information now to our basic advantage how can we you know simulate a lot of this information well one thing that I kind of notice here is I know that again I've taken a segment and I've broken it apart over here we took a segment and we broke it up by using the midpoint well here we're taking a segment and we're breaking it up by using an intersecting line so therefore we can use the segment addition theorem again I don't know if that's going to help us or not obviously by the title of this video you know that it is going to help us but when you're thinking of a problem that you don't have really any information for you know if you know that you have a segments being broken up well hey you can write it down maybe it'll help you maybe it won't but you gotta at least try you know try to see if it can help you out so let's go ahead and write a segment addition here I'm if if I have this length CD you can see that CD is being broken up by C II and II D so I can say that's line c e + seee is length of C e is plus the length of IDI is equal to the length of CD okay and that is going to be your segment addition okay now what's important though is again remember going back to that substitution rule right again the end is we want to we want to prove that CD is equal to FG so you know one thing I can do is well see E is equal to Fe and II D is equal to eg and Fe and you GE are equal to FG so I don't know let's just try substitute in and see what happens so I can also say that edie plus eg is also equal to CD because all I did is these two are equal to each other or these two are congruent to each other and these two are congruent to each other right that means they're equal in measure so I can just use substitution okay then let's go and take a look at this and you could say that if you look at again well we know that by substitution u d+ e g is equal to CD but by the segment addition theorem we know that dry right though don't see is equal to fe oops - wrote that wrong sorry is that fee and i teach you so FEG okay but we also know that F E Plus E G is equal to F G why are those equal to each other because the segment addition theorem now you have by substitution eg + e e I'm sorry f e plus e G is equal to CD by the segment addition theorem you have FP plus e G is equal to FG well therefore we can say that CD is equal to F G right and that's again by just using substitution now they want to show that they are congruent well if things are equal and measured that means they're congruent so I'm just going to rewrite this as CD is congruent to F G because since they're equal measure that means they're congruent so I'm just going to say the definition of congruence and when you're finished with your proof you can use a nice little box or you can also just write cute Leedy okay so there you go then jumping that is how you write a two column proof using segment addition Theory thanks