 # Delta Math: Segment Addition

Hi I'm is legal here. I'm going to go over for segment. Addition postulate problem given to you on Delta map. Let's get started. We start with the segment addition postulate, which says that if I have segmented AC and a point B anywhere inside that segment. Then the following is true segment. A B plus segment BC is equal to the whole segment.

A D, the way that I like to set up my scrap work is by saying that part one plus part, two is equal to the entire thing. Meaning this part, plus this heart is equal to. B entire thing also I like to have a segment with two end point and one in the middle and then some space to fill in some unknowns that the question gives me let's, get started point. S, is online segment RT, so I'm going to start filling it in I like to fill it in as I read it and point. S is right inside their given s, T. This entire thing is equal to 2 and RT, which is the whole segment is 8 determine link RS. So this is what my diagram look like if you'd like to pause, the video and write this down. In your scrap paper, please do so now we will begin on the scrap work and putting it all together looking at my diagram.

I have part and entire. If I want to make that into an equation I will have X. Plus 2 is equal to the entire thing, which is 8 now in order to solve for X going to take away the two we're going to subtract both sides by two. And then what I'm left with is X is equal to 8 minus 2, which is, and that should be our final answer.

Now, this is just numbers we're going to do one more with. Numbers and then we're going to move on to the equation segments, so I'm going to start with reading and labeling if you want to pause the video and draw this diagram, please do. So now the question reads, wait T is online segment. S, you so I'm going to fill in ask you if you'd like to do it with me as well, that'd be cool, and I have point T's somewhere in between SU given that. S, he is 13 and TU is 5 determine the length of us you. So now this is my unknown I'm going to put this in equation form.

So I. Have 13 plus 5 is equal to X. And then when I combine those two things I have 13 plus 5, which is 18 18 is equal to X. So 18 is my total. Okay.

Now this seems pretty straightforward. But when we start to add equations, it can get a little tricky that's. Why I like to start with my diagram if you'd like to pause the video and write this diagram down, please do so now. So they tell us that point h is online segment, G I. So I have GI have point h. And then they tell me that GH is equal to 2x plus 1. And that H. I am equal to three. They tell me that the whole thing GI is 5, X minus 5, and they want us to determine the numerical length of GH.

Now in order to do that, we need to first stall for, so I'm going to go to my scrap work, and I'm going to plug in this part. One, plus part two is equal to hole part. One is 2x, plus one. So I have 2x plus one, and then I'm adding that to part 2, which is just 3. And that is equal to my entire, which is 5x minus 5.

Now, it's a matter of algebra I'm going to combine like terms. So I. Have 2x I'm going to combine the 1 and the 3. So that I have plus 4 is equal to 5x, minus 5, I'm going to move this up because we might need more space.

Now that I have something that looks a little simpler I'm going to start moving things around I'm going to bring this five over to this side. What that means is that I'm going to add five to both sides. You guys can do this on your scrap paper as well. And now I'm left with 2x, plus well, 5 plus 4 is 9 is equal to 5 now, I'm going to move the 2x to this. Side so I'm going to subtract 2x from both sides, and I'm left with 9 is equal to 5. Minus 2 is 3. Now when I divide both sides by three I'm, just going to use the backslash for division when I divide both sides by three, my final answer is drum.

Roll, please nine is equal to, sorry. Three is equal to X because 9 divided by 3 is 3 and 3 divided by 3 is just 1. So now that we have X is equal to 3 that is not our final answer. What we have to do is plug it into G H. So instead of X I'm going to put 3 and my. Result is 2 times 3, which is 6, plus 1, which is 7, my GH is 7.

Now this was a longer process, but it wasn't a difficult process. So long as you make sure that your diagrams were correct. Now one final one that we are going to do it is very similar to the one that we just did. We have our diagram here. And so if you'd like to draw your own, please pause, the video and do.

So now we have here that point M is online segment, Ln I'm going to start filling this in, so I have point M is online segment, L and I. Have my L I have my N and I have point M somewhere inside there. Now, I'm just filling out values from what they give me LM is 3 X, 3, X, minus 7 and Ln.

The whole thing is X, plus 8, they tell us that m. N, over here is 3 X and that's. How we begin guys really the secret sauce is in making sure that you have this labeled correctly, then they asked us to determine the numerical length of Ln. So we need to solve for X.

And then when we do we're going to plug it into this X, plus 8, let me move this up. Because we might need a lot of space to do this we're going to start with part, one, plus part, two is equal to entire. That means that 3x minus 7, plus part, two, which is 3x is equal to the entire thing, which is X, plus E. Now, it's a matter of completing algebraic steps, I'm going to combine the 3x and the 3x, and I'm going to get 6x. Minus 7 is equal to X, plus 8. So all I did was I combined this. And this to get six and everything I'll stay the same now I'm going to bring this negative seven to the other. Side by adding 7 to both sides, I'm, adding because originally it's subtraction and want to do the opposite operation.

Now that I've added 7 to both sides I'm left with 6x is equal to X. Plus 8, plus 7 is 15. Now in order to get rid of the X on this side, I'm going to subtract by X on both of the sides.

And then my final leg, well close to my final leg is 5x is equal to 15. So I have 5x is equal to 15 what's left to do is to divide 5 by both sides once again, I'm using this backslash, but it's just division. And then I'm left with X is equal to 15 divided by 5 is 3. Now that I have my X I can't, put 3 here that is not correct. What they're asking me for is Ln, I know that Ln is this whole thing. So instead of X here, I'm going to put a 3, and that gives me a grand total of 11.

So Ln is equal to 11 if you are labeling correctly and following this part, one, plus part, Suzy puts a entire. You should have no problem completing these feel free to drop into office hour. If you have any questions.