Hi! And welcome to the Geometry Tutor and this class we are going to tackle the topic of geometry and most of you guys up until now have studied some algebra which deals with equations and X and Y and Z and things like that solving equations. And then you take this class called geometry and then you go on and you do some algebra too after that and geometry kind to trips people up initially when you take it usually because geometry deals with a lot of pictures and that is sometimes hard for people to get their hands around. Because up until now you have been dealing with equations and nice little problems that are written out in your paper one by one and then when you look at the geometry problem it usually got big complicated looking picture or some diagram or something. And you really just sometimes, it is hard to figure out exactly what to do first and what it important in the drawing.
So we are going to step through the concepts of geometry one by one, step by step, we are going to define a lot of terms because the biggest challenge in geometry really is not the math, the math is really not the hard at all, it is just the terms. What does the problem mean when asked you about an angle or a line or something like that, so we are going to step through those things one by one, we are going to define a lot of terms and we are going to do everything methodically.
So let us just right get started here and let us talk about the simplest thing that you can talk about in geometry which is the concept of a point, okay? I think you all have a pretty good idea of what a point is, we talk about a point in space here or I am going to make a point to you when I am making a presentation, I am going to make a strong, powerful point.
So we use a term point in our everyday conversation but in geometry, again, we are going to be defining a lot of terms but the point is literally just a dot that is really all it is. It is just a dot, okay? So in geometry, when you refer to a point, here is a dot, we are going to call that a point and we are going to give it a label because we are going to have a lot of different points. And we are going to have a label so this point right here at this location on this mark of board is right here and that is point A. You can have another point over here and we can call that point B, okay so you put a dot and a letter here right, and the letter is just a label and you can have another point over here, you know you can call that point S.
So you can define lots of points, this concept is not very hard, a point here, a point here, point here, point here, okay, those are on a plane in three dimensional space I can have a point right here at the tip of my finger, a point right here tip of my finger, over here. And so on and I just label those points A, B, C, D, E, F, G whatever, in order to be able to reference them as I go along.
Okay, so the next thing we are going to talk about is the concept of a line, which is the next most complicated thing in geometry but again, it is not really that complicated I mean I think you all know what a line is, you know, a line is something that goes on and on in one direction, right? This way, here back and forth is called the line or I can point my finger over here, that is way backwards and forwards, that is another line, I can go up and down, that is a line, so a line is just something straight, I mean it is just a simple language we have here but in geometry we need to define it really precisely so that we all know what we are talking about.
Two points define a line and we are going to talk about this here in just a second, two points define a line, a line goes on and both directions through the two points that define it, place two points here. Alright let us talk about this for a second, this is a great example of a really super simple concept but if you were to read this in a book, you got all this words about points and lines and directions and everything else and it can seem complicated, it is really simple.
All that we are saying here is if you have some line, I am going to say there is a line right here, it goes on back and forth here, I am going to put an arrow on this line, on both ends because I am just trying to remind you what you already know. And that is the line goes both directions, it goes in both directions and this arrow means this line goes on forever, up like this and this arrow down here means this line goes on forever down like that, now ask yourself, what information do you have to have other than this picture to define a line.
What do you need to define a line? It takes two points to define a line, let me just show you what I mean. If there is a point here, let us call that point A, just label, that is just a label, that is all it is because a point and space right here and there is a point here, we are going to call that point B, any two points that I pick. I can draw a line through them and these two points are all I need to define that line. I will pick a point here where the tip of my finger is and I pick a point here where my other finger is and as long as I know there is two points, I can take a ruler or a straight edge and I can draw a line through there and then that line can just go on forever and ever and ever as long as it goes through those two points and define the line. So two points is all I need to define a line, so that is important. So it goes forever this way, it goes on forever way, it goes on forever this way and these two points define the line.
So how do you right this down? You know, we said for a point, when you have a point, you just draw a dot and a letter and that dot is how we represent a point. For a line, we are going to write this like this, this line is represented by the two letters AB with the little symbol on the top. So what this is saying is, this line is defined by point A and point B and this little symbol up above just means it goes on forever and ever and ever in both directions which is exactly what we have here.
Now, you can also write it, as BA, again with the same symbol, so what I am trying to say here is, when you have two points that define a line, you just write the two letters down and put the symbol on the top that shows that it is a line and it does not really matter the order here, you just put AB or BA, that does not really matter-because the two points here are defining a line and the line goes often both directions forever and ever. So when you write it down, you can put AB or BA just make sure you have this up on top and everybody will know you are talking about line that goes through these two points.
Now, one more thing I want to talk about before go on is that a point is infinitesimal small, what that means is, a point, when you really think about it, it has no dimension. We talk about the fact that we live in a three dimensional world, right? What does that mean? We have length, width, and height, that is the three dimensions, the three special dimensions that we live in, right, today, in this world that we live in. But a point by definition, even though we are putting this dot on the board and the dot it is a fairly big dot here. But when we really mean, what we are talking about a point, is it is just this place and space, it does not stretch this way because if it did, it will be part of a line. It does not stretch this way and it does not stretch this way, it is just a point, it is just a place and space so it has no dimension, zero dimension. So a point has zero dimensions.
A line goes on and on, in one direction this way and a one direction that way. And we call that, one dimension, a line has one dimension and when you think about it with the three dimensions that we live in, it is length, that is one direction, width that is the other direction and height, which is the other direction. Those are the three directions in which you can move as a three dimensions we have, but a line, when you dram a line in this way and that way, it only exists in this direction, okay, back and forth, it does not go toward you or away from you, it does not go up or down, it only exist along the direction of the line.