[Music] hey guys Mr bber here this is Lesson 1.1 in this video we're going to look at naming and sketching some different geometric figures now in Geometry there are these things called undefined terms and like the name implies these terms don't have any formal definitions but every math ition around the world agrees as to what these things are and how they're represented we're going to have three undefined terms we'll have points lines and planes those are the three most basic geometric structures that we can create and pretty much everything else that we do in Geometry is based on points lines and planes so our first object is a point and a point is just represented by a DOT you're probably pretty familiar with points from algebra and doing like graphing points help show locations out in space they don't have any actual size to them so even though we can draw these things out with a DOT um they're actually infinitely small we wouldn't be able to see them with our naked eye but we do draw a DOT that's visible just so we can talk about these locations now if we look over on the far right hand side we have a picture we have a DOT with a capital letter written next to it when we're talking about naming points we use that capital letter to help us identify what specific point we're talking about so if we were to name this object drawn out in the picture we would name it point a now our next structure is a line and lines are straight paths that extend in two opposite directions Without End and lines are made up of an infinite amount of points there's two different ways that we can name a line we could use two points that show up on the line or we could use a lowercase letter so if we look at the picture on the right hand side there are two points on this line point B and point c one name we could give to this line is line BC the way we show it's a line is by actually drawing a little line over the top of it with two arrow heads on each end now order is not important when we're naming a line so we could also name this thing line CB again with a line over top with two arrowheads on it now if you also look in the picture there's this lowercase L it doesn't have a point because there's no dot next to it so that's what I'm talking about when I say that we can use a lowercase letter to name this line we could just call this thing line L our last structure is a plane and a plane is a flat two-dimensional surface that extends Without End in all four directions it doesn't go up or down it's just a two-dimensional object but it doesn't stop at these outer lines planes are also made up of an infinite amount of points when we're naming a plane we we use three points on the plane or we use a capital letter so if we look at the three points on this plane we've got Point D Point e and point F so we can name this thing plane DF again order isn't important as long as we just use these three points so it could be e DF it could be fde it could be f d they're all the same plane now if we look down in the bottom left hand corner there's also this capital G that doesn't have a point next to it it's working kind of like that lowercase L above with our line we could name this thing plane G instead of using those three points now while we're talking about lines and planes I do want to mention these things called collinear points and co-planar points collinear points are just points that show up on the same exact line so let's say we had this line drawn out and we had points a point B and point c on it then we would say that points a B and C are collinear since they're all on that same line co- planer works very very similarly so if we had a plane drawn out and let's say we have Point D Point e and point F on this plane then these three points are co- planer because they're all on the same plane they're all on the same flat surface here we've got a few examples to run through with naming some different objects so we've got our picture on the right hand side which we're going to use to help us out number one says we want to give two different names for the line FG now remember order is not important so we could name this thing line GF again putting those Arro heads on the end of each line to show that it is actually a line there's also a lowercase b written next to our line so we could call this thing line B number two says give two other names for plane R so when we're naming a plane remember we need three points we do need to be careful because the three points cannot be collinear they can't be on the same line so we couldn't say HG we couldn't use that combination of three letters since they're all on that same line but we could go like HJ I because Point J is not on that same line or if we wanted to give another name for it we could go g j i again using Point J since it's not on that line with those other points now three wants us to name three collinear points and I kind of gave this one way already these would be points H points G and point I those three things are all on the same line so they're colinear number four if we wanted to name four co-planar points well there's only four points on this plane that we can see it would be Point H Point G Point J and point I those four points are all on that same flat surface a few more vocab words to take a look at we've got a line segment array and opposite Rays again we'll do a description how we name them and then we'll draw out a picture so first for that line segment it's very similar to a line but instead of extending out in both directions we've got a couple of end points and our line stops at those end points so if we take a look at our picture we've got point a on the left side and point B on the right side when we're talking about naming this object we're going to use those end points to help us out just like with a line the order does not matter so we could name this thing ab and we're going to put a little line over top of it now I'm not going to put arrow heads on each end since we're just talking about a segment and it stops at those points we could also name this thing be a since order is not important again not putting the Arro heads on either end since we're stopping at those two end points our next vocab word is AR Ray and we've got one end point which we call called the initial point but then our Ray extends out in One Direction without end so again looking at this picture we've got c as the end point or the initial point and then our Ray extends through Point D and it keeps going and it's got that Arrow Head on the end to show that it keeps going when we're naming array we start with that end point so order is very important here we would name this Ray CD and we'd show a ray over top of it no Arrow Head on the the left side but we will have an arrowhead on the right side to show that we're extending through Point D our last vocab word is opposite rays and these are two rays that have the exact same initial point but extend in opposite directions and when we draw these things out it's going to look like a line but there are in fact two different Rays here if we look at this picture we've got this Ray that starts at e and points to the left through Point F I've got that one highlighted in Red so we would name that Ray EF we've also got this Ray that starts at Point e and then heads out to the right through Point G we would name that one e g so if we were talking about opposite rays we would say that Ray EF and EG are opposites since they're pointing in opposite directions here's another example of doing some naming with a few of our vocab words so number one says we want to give another name for the segment LM so we're talking about this piece of our line that runs between point L and point M the only other name that we could give to that thing is ml because order is not important and we're going to put that segment over the top with no arrows on it number two wants us to name all the Rays that have the end point of K and then we have to identify the pairs that are opposite rays so Point K in the middle is going to be our initial point so we could have the ray that goes from K to J J we could have the ray that goes from K to L working our way around this picture we could have the ray that goes from K to M and our last Ray would go from K to n now as far as the ones that are opposite we would say that KJ and KN n are opposite since they're pointing in opposite directions we've also got Ray k l and Ray k a m being opposites again since those are pointing in opposite directions last thing we've got to talk about is the intersection between some of our objects two lines are going to intersect at a single point so we've got this red line and this blue line I have their intersection Point highlighted if we've got a line and a plane intersecting that's going to happen at exactly one point so I've got this line drawn going straight up and down and then we've got our flat two-dimensional plane part of our line is dotted and the reason that's happening is because our line is passing through this plane so as we're looking at the picture part of our line is actually hidden but it's still there so that's why we show it as being a dotted line on the far right hand side two planes are going to intersect at a line so we've got this blue plane and we've got this green plane again dotted lines showing that part of that would actually be hidden from view um but these two planes are intersecting at this red line that's going to be it for this video thanks for watching