Transcript for:
Understanding Basic Geometry Elements

in this video we're going to talk about the difference between points lines segments rays angles and stuff like that so the first one is pretty straightforward points you know what a point is that's a point so we can call that point a point b point c and so forth next what is the line if you're taking a geometry class these are some basics that you want to understand a line contains many points and it extends infinitely in both directions so it could have point a point b point c and so forth now you need to be able to name this particular line so you can call it line a b and for lines you need to have both arrows to show that they extend in both directions you can call it ac you can call it line bc you could also call it ba or line ca and we could also say line cb so as you can see with this particular line that contains three points on it that's highlighted there's six different ways in which you can name that line so what about these two lines how can we name it the first line is simply called line l that's it now the second line contains two points that are highlighted so we could say it's line a b or line b a so make sure you know how to name a line if you're taking a geometry course now the next thing we're going to talk about are segments so what are segments and how do they differ from lines so let me draw a picture a segment contains two endpoints it has a beginning and it has an end a line goes on forever in both directions but a segment it has a finite length so this can be called segment a b or segment ba so as you can see there are no arrows so that tells you that it's a segment if we put two arrows on it then we have line a b it's no longer a segment but if you don't see those two arrows there then it's a segment so you need to be able to distinguish segments from lines and in the next example also from rays so what is array in terms of geometry and let's fix that y and that y does not look like a y array has features of a segment and a line array has an endpoint and it has an arrow that's array so let's put some points on it let's call this point a b and c so array has a beginning which starts here and it extends infinitely in the other direction whereas a line extends infinitely in both directions array only extends infinitely in one direction so point a is the endpoint now how can we name this particular array how can we call it we can call it ray a b or ray ac but we have to start at the end point we can't call it ray bc because b is not the end point so with array there's only one arrow a line has two arrows a segment has no arrows so if you see a b with one arrow you know it's array so here's a little matching quiz that i created that can help you distinguish rays lines segments and points so feel free to pause the video and match it accordingly so let's start with number one so we see we have a b and we have an arrow that extends in both directions so we have two arrows that's a line a line extends in both directions so number one is b so i'm going to highlight that in red number two notice that there are no arrows on bc so that has to be a segment and so number two corresponds to answer choice c now number three is not a line or anything always sees a dot so therefore number 3 represents answer choice d which is a point and number 4 by default has to be array array only contains one arrow as opposed to two and so now you know how to distinguish a point from a line from a ray and from a segment now here's a question for you what's going to happen if we combine two rays let's say the first one is called ray a b and this is ray ac so if these two rays meet at point a what will form the combination of two rays produces an angle so we're going to get this particular angle the common endpoint is point a which is also known as the vertex of the angle now you could name this angle three different ways you can call it angle bac or angle c a b either case the common endpoint or the vertex has to be in the middle if you're going to use all three points you could also simply call it angle a and that works as well so you have three different ways of naming this angle so basically angle b a c is the union of ray a b and ray ac so what that means is that this whole angle is basically the sum of this ray a b and the second ray ac so make sure you know the difference between union and intersection which we'll talk more about it later in this video so this is the union symbol and this is the intersection symbol now you don't always have to use letters to describe an angle you can use numbers you can call this angle two or you can call this angle one so you can use numbers to name angles as well so let me give you an example problem let's call this angle one which extends between the first two rays and let's say this is angle two and angle three and let's say this is a b c d and e starting with angle one what are two ways or two other ways in which we can name angle one so angle one can be called angle a b d you could also say it's angle d b a now what about angle two what are two different ways to name angle two and also angle three so angle two you can call it d b e you could also call it angle e b d you can name it in reverse and the process is going to be the same for angle 3. so angle 3 can be called angle e b c or you can call it angle c b e so notice that the vertex letter b has to be in the middle of each of these angles because b is the vertex for angle one two and three so now you know how to name angles now let's move on to another topic now let's start with a line and let's put some points on this line so let's call this point a b c and d so here's a question for you what is the union of segment a b and segment bc how would you represent the union of these two segments so this is segment a b and this is segment bc the union of those two segments is basically just the sum of both of them so that's going to equal segment ac when i think of union i think of addition let's say if a b is 5 and bc is 4 ac is 9. so ac is basically a b plus bc so the union of a b and b c is segment ac now what is the intersection of segment ac and segment bd the intersection is where these two segments meet so this is segment ac and segment bd is highlighted in green now notice that ac and bd they intersect at bc that's where we have both of them so the intersection of ac and bd is simply bc or segment bc now let's say if we have two rays so the first one is ray bc and the second one ray bd what is the union of ray bc and ray bd what's the union of these two well if we put them together as we mentioned before this is going to turn into an angle where the common endpoint is b so the union of these two rays ray bc and bd will give us angle c b d so we've covered this before but now here's my question for you what is the intersection of ray bc and ray bd think about it what's the intersection so where do these two rays where do they meet what do they overlap notice that they meet only at point b ray bc is not part of ray bd they only connect at a point not at a segment or a line so the answer is simply point b so when you deal with union you're like adding two things intersection you find in where the two things meet or where they overlap so make sure you understand the difference between the union symbol and the intersection symbol you