 Okay. We got our first problem laid out for specifically geometry and we're going to deal with this as a two-plane, two-dimensional geometry problem. And because we have no numbers you can consider this to be a proof. Now at the end I'm going to tell you what the different types of ways it would have laid out the problem for it to be a proof. But let's deal with this the way it is and solve for whatever variables we need to solve for and see how it works. Okay. Now the problem is laid out in this kind of format. What you have to really understand is when you read problems, you want to go through read through this whole thing, but when you read problems you're gonna have to continuously go back and recheck to see what the parameters are that they gave you. Okay. Now our first sentence says B is the midpoint of AC. Now they haven't told us any coordinate system so we can draw this in anywhere we want. So what we want to do is read through the problem once just to get an idea of what it's all about and then go back and start off from the beginning and lay it all out. Okay. So B is the midpoint of AC. C is the midpoint of BD. D is the midpoint of BE. Now if you try to solve this in one shot you're gonna have a seriously hard time because there's a lot of little variables there. So let's do this one step at a time. Okay. B is the midpoint of AC. Okay. So let's draw AC. Here's A, point A, and point C. And B is the midpoint of AC. So B is going to be right in the middle. So here's our point B. Let's go to the next sentence. C is the midpoint of BD. Now we don't have it D, but if C is the midpoint of B and D, so D has to be somewhere here. So what we know right now is this guy is equal to this guy and this guy is equal to this guy. That means it's also equal to this guy. So right away we're starting to get a picture of what this question is going to look like. Let's go to third sentence. D is the midpoint of BE. Now we don't have an E, we just have to put it in. We've got to make sure we put it in the right place. D is the midpoint of BE. D is the midpoint of BE. So we're going to approximately put it where it should be. So we've got a problem made out. Now if D is the midpoint of BE, then this guy equals this guy. Okay. Now one thing to keep in mind is D double ticks or a legitimate symbol used in math to say it's just basically copying the word from up top. So instead of writing down is the midpoint of every time, I'm just going to use double ticks. And this is the sort of format I'm going to use throughout all the videos. Okay. So keep this in mind. These double ticks basically mean the word up top. Now let's look at the questions. What are they asking us? If BC is W, solve for DE and AE. So let's lay this down. If BC is W, so the length here is W, solve for DE, we want to solve for this and solve for AE. And we want to solve for this. So we want to find out exactly what this is and we want to find out what this is. Okay. What to do to get the answer, we go through logic reasoning. Now what they're going to do in a question in a test or homework, they're going to ask you to lay everything down properly. So what we're going to do, we're going to verbally go through it. On the website, I'm going to lay it all down, write it all up for you guys so you see how it's going to be, it should be presented in an exam or at a homework assignment. Okay. Now let's take a look at this. BC is W. Now this guy, C was the midpoint of BD. If this is W, then this guy is W. That's logical. That makes sense. Now D was the midpoint of B and E. So this length here is got to be equal to that length there. Agreed? Now what's this length here? That's W plus W. So this length here is 2W. If that's 2W, then that's 2W. So we just solve for the first part of the question. DE is 2W. Now what we want to do is figure out what AE is. Okay, let's take a look at AE. Now this guy, C was the midpoint of BD and that equaled W. Well when we're laying out the problem, B was the midpoint of AC, right? B was the midpoint of AC and we marked it down ourselves to remember that this length was equal to this length. So what that means is this is also W. Now this is the trick in mathematics specifically in geometry. When you figure something out with a problem, you use symbols to visually remind yourself what they are and that's what math is about. It's a visual representation with geometry specifically is visually laying out a problem for yourself where you can recognize patterns. So by making a tick here, we didn't have to go back through the whole thing to realize that this was equal to this. We laid it out so it would become easier for us to solve it without the whole problem. So that guy is W. Now all we've got to do is figure out what AE is. So all we do is just add up what the lengths are. That's W. That's W. That's W. So that becomes 3W and that's 2W. 3W plus 2W is 5W. So this guy becomes 5W. So we just solve for question one. Now the way this works is the reason that using variables becomes super powerful is because you can put in numbers instead of the letters and it will apply for any number you put in there. So instead of W, let's assume they said BC was 15. So if BC was 15, then you wouldn't have to go through this every single time to solve for it. Once you did it and they came along and said, hey, what's the length between from A to D? All you would know is go W, W, W. So that's 3Ws. That means that's 3 times 15. So from here to there would be 45. What would it be from here to there? From A to E. It would be 5 times 15. And that's the power of solving problems with variables because you no longer or dependent are just specific numbers for a specific problem. It's a general solution. It applies everywhere for any type of problem that they give you which had all of these parameters associated with it.