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Segment Addition Postulate

Added May 09, 2015 •

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plug in and welcome to another video lesson with mr. Roman say we're going be talking about these segment addition postulate and a first we need to talk about some no patient just a little bit of terminology the word postulate means a true statement that does not require proof so something that kind of everyone except without really much approve of it and the next item would be the notation XM when you see the notation of two letters next to each other what that is in kidding is that there are two points on a on a segment X and M and they may or may not be right in a you know you may have X here and I'm here or you may have exit the beginning or and then M and then Z but all Atlee what that means is it saying the distance from X to M on that segment so whatever this distances from here to here that's what this notation is referring to okay so we know already from previous lessons that the notation here means segment XM but this is referring to the distance between X and M  so next we have segments segment AC random what the 20 in the 30-year representing here are the following so we can say that a b is equal to 20 so the distance from 8 is he going to 20 and then we can say that BC is equal to 30 so the distance from B to C is equal to 30 now the segment addition postulate simply States this that the distance from a to c is basically taking the two smaller segments of the 20 in the 30 and adding them together so we could say that 20 + 30 is the distance from 8 which is then 50 so we could say the distance from a to c is 50 based on the segment addition postulate here here's another example of the segment addition postulate let's say that we knew that the distance from a to c was 72 and the distance b2c was 45 so this distance is 45 and this distance here is 72  so really ultimately what we can say then is  Define the distance from A to B we simply would subtract 45 from the 72 because that's the unknown difference and in this case when I take 72 - 45 then gives me a distance of 27 so that I can stay in this case that segments ad the distance of segment ad is 27 it again this is simple example of segment addition saw your notes it says example one if a b is 13 easiest 20 then what is the distance of AC well if here is 13 so I'm going to put that in there and then BC is 20 messed that up hold up okay I fixed it so Abby is 13 in the red there and BC is 20 then we say the distance of AC which is the entire distance would be 33 units okay an example to it says the AC is 40 units and a b is 12 units so then I could say that the distance from B to C would be 40 - 12 which is in this case 28 units example 300 notes it says that by is 4 x + 3 so in this instead of having a number be the value of the distance between be and why it's giving us an expression for the distance between be and why so that's why I wrote and search then we can say that while is 15 so that's an actual value in NBL is 58 so here we won find the value of the distance between by and the value of x so what we're going to need to do here is write an equation and the she is going to be just simply adding the parts of the segments in order to equal the whole so in this case we could say by Nexus 4 X plus 3 plus the 15 so I got the two smaller segments adding them together that should equal 58 in my equation okay so right now I have an equation I know we can solve and then we're going to sell that for it so let's start by combining like terms this would be 18 equals 58 and then we add the 4X subtract the 18 from both sides 4X is equal to  and then we're going to divide by 4 so in this case ex is going to be equal to 10 you're probably thinking won't that's only part of the answer that we're looking for a peer mr. Roman we want the value of x when we also want the value of by well in order to find the distance of by we would simply take the value of x and plug it into this expression to find the value so by is equal to 4 * 10 + 3/4 * 10 is 40 and then add 3 is going to be 43 so we can say distance between bee and why is 43 units and now we've found all of the pieces of this example example for on your notes there is no diagram given however it's going to be helpful for you to be able to draw what is being described so we see here that we have a point is between points T and M on the segment TM so let's begin to draw that we have segment TM  and I will just draw  pretty plainly segment M and then point p some people want to put Point P right in the middle we don't know that he's actually in the middle here so we can actually let's set it off to the side just a little bit again we don't know that it's right in the middle in fact it probably is not in the middle so we have this picture for example for now you can start to put some things into the picture based on the information over on the right here of what we're given so now I've got the parts of the Cigna that were given written on the diagram in the correct order and so now we can write ourselves an equation that we can solve for the whole distance of TM to the whole distance of TM is he with a 14-6 so that's going to be equal to the sum of the two parts the green part plus the blue part has to equal the red part so we can write an equation as this 8x + 1 + 4x is going to be equal to 14 x - 6 and we can solve this equation sore going to start bye bye Twilight terms for x and x equals 12 x and then we're going to add the six of both sides and that's going to give us + 12x equals 14 x + now we're going to subtract the 12 x from both sides which gives us to x equals 7 and then we're going to / 2 on both sides and in this case is going to be equal to 3.3 3.5 but now that is part of what we want to find but in this one let's go ahead and find all the distances that we know that we're going to find over here so TPT M and Kim  and I let start by finding TM so we can say that 14 x 3.5 then minus next 14 or 3.5 49-6 is going to equal to 43 so we can say the distance of TM on the segment is 43 units next we can find the distance from t2p so that's going to be eight times 3.5 + 1 + we would take 8 * 3  that would be 28 and then we add one is 29 so we can say that the distance from t2p is equal to 29 when the other segments we can just simply take 43 - 229 cuz that's going to be the remaining distance 4 p.m. so in this case 40 speed - 29  is going to be equal to 14 so we can say that p.m. is equal to 14  so now you have all three distances for our segments and we know the value of x so we've solved for all the parts

Uploaded by Edgar Villarreal.