okay geometry lesson number one this is like geometry 101 you want to understand some basic terms and how to write the different lines points planes and there were going to jump into some typical questions that you experience in this first geometry lesson so let's go over the terms first so we're gonna work with undefined terms these are terms that are basically accepted as true if we don't have to prove anything we just accept it the first thing is a point and a point basically we represent in geometry as a dot and it's basically infinitesimally small but it just locates a point in space right and so what we do is we just label it with a capital letter like a or you can have another point over here B and so you would just say if you're identifying the point you would just say point A or if you were saying point B point B like that okay now when we talk about a line you know from algebra one you know a line it goes in you know two directions and it keeps going forever and ever right it's a set of points and we know it looks something like this but when you identify a line you want to use two points that are on the line like say for example if you have a point x and y that are on the line the way you write it the notation it's kind of like a pictograph you know our picture like hieroglyphics you would draw x and y and you would draw actually like that line symbol above x and y to indicate that it's a line that it keeps going in both directions or you could say Y X it doesn't matter the order now one thing I want to point out is that a point is actually zero dimensional okay so it's like no dimension whereas a line is 1d or one dimensional when we get to a plane now a plane is like a flat surface kind of like the floor or like a wall or the ceiling right that's 2-dimensional and we generally draw it like a rectangle or a parallelogram to kind of show that you know that it's a flat surface but you have to kind of realize that it keeps going you know in forever and ever like on this flat surface at that level but when you label a plane you can either use like a capital letter like it'll indicate in like the one of the corners of the plane so for example I could call this plane M or what you can do is you can pick three points that are not in a straight line say for example like if this is a B and C I could write this as plain ABC that's another way to do it but you want to make sure that they're not in a straight line now why why do you not want them to be in a straight line well if they're in a straight line like this there is more than one plane or more than one flat surface that could go through those three points so that's why when you draw three non collinear points meaning that they're not in a straight line there's only one plane or one flat surface that goes through those three points so the plane remember is 2-dimensional and then we get to space which is what we think of as you know three dimensional and we'll talk about that a little bit later so we have 0 D 1 D 2 D 3 D now when we move over here segments a segment is like a portion of a line it has basically a beginning and an end right we call these two points where it starts and finishes it as endpoints and so when you write your segment you would pick these two endpoints x and y and you just put like a bar above them so that represents a segment now you can also write it the other way Y acts with that bar above it to indicate that it's a segment and not align with the line symbol above it with array you think of a ray is like a ray of sunshine right it's like there's a photon at the Sun and it's going out from the Sun towards the Earth it just goes one direction it has an endpoint we call this an endpoint but you can think of as like a starting point and it just goes that one direction so this is what we would call ray CD and when you draw the symbol for Ray you always want to draw it to the right so for example with this ray here notice how the Ray is actually going to the left look at the way we're going to write this you're gonna write this as e f and see how the arrow is pointing like towards F it's starting at E right and it's going towards F and it keeps going so that's Ray EF so that's just the convention that it's always drawn pointing to the right even if the Ray is pointing to the left and then opposite rays what does that mean opposite rays well it means that they're going a hundred and eighty degrees opposite one another and together they form a line but the key is you want them to have the same starting point which remember these starting points are called end points and so you would write the two opposite rays here is our TC it starts at iron goes towards T and R s so it starts at R and it goes towards s and keeps going so together it forms line s T or R T or TS you just need two points on the line to to write the line now as far as intersection goes when we talk about intersection we're talking about what points to the objects have in common or you think of intersection you probably think of like where do the two objects cross so if you have two lines they're always gonna cross at a point okay like that unless they're parallel or skew and we'll get into that later but over here when you have two planes these are like two flat surfaces where they cross is actually at a line so if lines intersect across at a point if planes intersect they're gonna cross at a line let me erase the whiteboard I've got some specific questions that you're going to encounter and we'll work through those next okay pause the video if you want and see if you can answer these questions and we're going to go through them together here so what I want you to do is name all these quantities here's will name a point in this diagram here so what do you think so I think there's a lot of answers here there's more than one correct answer but for example we could just say T that's a point or we could say ass or we could say W any of those would be correct you only have to list one for number two you want to name a line so what do you think a good one for a line would be well there's a lot of options here I'm gonna pick maybe like this line right here W X and I'm going to put the line symbol above it to indicate that it's a line that's very important it doesn't matter the order of the points the letters here but you definitely want to put the line symbol above it to indicate that's a line for a segment what do you think would be a good example of a segment well how about if we do from s to X so that would be a sax we'll just put a bar above it now your teacher is going to be very particular about this notation so you want to make sure you really get a good grasp of this don't be too sloppy with it for number four array okay what do you think a good example of array would be I'm gonna say ray XR x are so that means it's starting at X is going towards our and it keeps going notice how that symbol is going to the right even though the ray is going downward right for number five a pair of opposite rays now a lot of times when you're doing these problems if you look at the words very carefully it'll tell you what it is like pair that means like a pair of shoes like two right opposite right so we're thinking 180 degrees opposite rays so a pair of opposite raise a good example would be something like access an X R so we could say X going towards s and keeps going X going towards our and keeps going but they have that same end point end point you think it was a starting point but they're going 180 degrees opposite forming a line what you don't want by the way is you don't want this situation where it's like see how these have like different end points like you don't want them to be alike I'll just see if I can draw like this you wouldn't want this to be let's say this is ABC you wouldn't want to do ray AC in ray ba because then they don't have the same starting point you want it to have the same starting point and then from there go 180 degrees opposite for number six name a plane remember a plane's a flat surface we could say plane a that would be one option right so plane a or you could pick three points that are not in the same flat surface so we could say like x SW so I could say plane x SW you just use three points you want to do four or five six just pick three points that are not in a straight line that defines a plane and then another name for plane a that's kind of funny we just did that one x SW but we could do let's say x RW that's this flat surface as well so that's another option plane x r w for number 8 3 : ear points now we didn't talk about this too much in yet but when you see the word Co that means same and you see the word linear that means like line so we're looking for three points that are on the same line so an example here would be a sax in our so s X and are now three completer points so three points that are in the same plane meaning same flat surface so we could do for example TW and XR in this flat plane B right so let's do X W and T points that is not collinear with line W X so here's line W X a point that's not on that line how about point T that would work a point that's not coplanar with plane be so plane B is this flat surface right here if we want a point it's not in that same plane we could pick R or we could pick s so I'll just say R and then we want to find the intersection of line L and M now we didn't talk about this earlier we were talking about lines but another way that they sometimes label lines is with like a little cursive letter at the end of the line so you can call this like line L like that or you could say a line M okay for this line but the intersection of line L and M where do they cross at point X remember two lines when they cross it cross at a point and then what's an intersection of plane a and plane B so this flat surface and this flat surface where do they cross or intersect you can see they're intersecting right at this line we could say line m or we could say line X W either of those would work so I hope this helped you understand Luud about the notation and an introduction into geometry if you want to see more geometry videos I've got a ton of them on my mario's math tutor YouTube channel you can check out the playlist that I'm going to put right there for you you can use it as you're going through your class if you're trying to review geometry there's a lot of good information there I'll see over in those videos