Good day students welcome to mathgotserved.com in this introductory geometry tutorial we
going to be going over how to name on goals size and vertices also talk about how to classify
points as being either in the interior of an angle on the angle or being on the exterior
let's take a look at question number one instructions are for us to name the vertex the sides of
the angle and where to name the handle itself and the angle in four ways okay and the angle
in four different ways okay so let's take a look at this angle here for question number
one let's say we have an angle to look something like this in this point here is B on goals
one and have a point on this rate see you have another point on this three a okay let's
start by naming the vertex now the vertex take some different meanings in the context
of the diagram that's we have here the vertex is basically the common points where these
to raise begin okay so that's what's the vertex means so the common points where DC raise
three BC NDE meet is apt points be okay so all the vertex is going to be be now let's
move on to the next parts of our question one which is the sides of the angle okay what
are the sides of the angle these two raise with a common point or vertex be are the sides
of the angle so the sides are going to be we start from both vertex and going to direction
of the two raise so the first sign is BC of the repointing out word is basically means
that be is where the point originates from order rate and any goes in the direction of
C and then the next side of the angle is be a full in the same pattern indicating that
the restarts from b and goes in the direction of a now the last part requires us to name
the angle and four different ways okay so let's go ahead and name the now can name the
angle using the's three points CBN a the the interior points or the vertex is going to
be at the middle okay so were going to name it angle CBA not the first way you can name
this angle you can also name it angle starting from a a BC when you name in the angle's with
these points you have to ensure that the vertex points is at the middle as you can see here
another way you can name this angle is by simply using the vertex I'll for that can
call this angle be and then the last week in the name this angle is by using the numerical
value that's assigned to the angle and that is angle why so those are the four different
ways that you can name this angle why is this important whenever you do we geometry problems
there is in a particular way that the angle will be presented he can be presented using
the numerical representation we could just the given a vertex off the bat or you can
be given the description of the angle using these three points so it's important that
you know the different ways in which to mean an angle so he can basically solve a problem
regardless of whichever format it is presented in now let's go see there another example
in this case will going to look at angle GE our case so were so for the same instructions
as we did in the previous problem opening the vertex the sides and will name the angle
in four different ways okay so it's either so the angle right here and have a point G
and another points oh let's starts with the vertex now what is the vertex in this diagram
the vertex is basically the common points where the two raise originates over the me's
okay so the vertex here is going to be point okay now one of the sides of the angle the
sides of the angle of these two raise which have a common point of origination vertex
.8 so what we're label in the sides remember where going to start from the origin or the
vertex and going to direction of the two points okay so the first side is G the repointing
in that direction indicating that's your starting from key and going in the direction of G and
ales a have Io starting from a and heading in the direction of both so the is an are
two sides of the angle now let's go ahead and name the angle in four ways so what are
the four different ways we can name this angle base on how it is presented here we can name
this angle with his numerical value that's been assigned to these angle so angle for
this one way of naming it. We can also name the angle using the vertex okay so what's
the vertex the vertex here is E so can name the angle angle E we can also name the angle
using these three points GEN all but in whichever direction we choose D has to be the also that
in the center since it is the vertex okay so you can name it angle GE oh or we can name
it angle oh ease G you notice that a is in the middle in these two ways of naming the
angle rights of either the four different ways that you can name this angle presented
here okay now let's take a look at question number three we have a different set of instructions
here for question three we are to name all the on goals that okay so let's consider this
in error right here point okay now it's a we have this diagram here this is vertex o
angle a be in then we have these points on this three we have G here we have point TM
this three in the middle and then we have points P here at the bottom okay so the question
is which on goals how vertex oh angle's with vertex o okay so the first one we can clearly
see that angle a has vertex go right next to it so we have angle a it is one of them
how about angle be on it absolutely angle be has vertex o on it too so let's write it
down angle be aright and is only angle that how vertex over how about the bigger angle
the combination of angle a in the that's angle GE oh the okay so angle GOP also has vertex
o now let's take a look at question number four the last in this clip in question four
we are to state which points on the given figure that are on first of all the point
that the point the points that are on the interior to the point of points that are on
the exterior three the point of points data on angle a PC okay so we're doing multiple
things here let's go ahead and start by giant angle ABC to have angle ABC in the following
configuration so this is point a this is be the vertex angle be our house point see right
here okay so you have point our we have points P we have point X right here on this rate
we have point Q over here and then point M right here okay so let's start with points
on the interior okay so points on that interior of angle ABC let's take a look at what's the
our so what's the interior of angle ABC the interior of angle ABC a basically the collection
of points that lie between these two race okay so the region that these two raise cover
right here it is goes on and on and on and out and kiss get a wider us you go out so
this region that East you raise bound are known as the interior so interior arty collection
of points the serene these two sides okay so if I extend these two sites forever what
points given it is diagram will be bounded by them we can clearly see that point are
in the are in between these two sides what does that mean that means that these two points
are on the inputs here year of angle ABC okay so have points are in P now next question
is what points are on the exterior points on the exterior of angle ABC the points on
the exterior are to points that are not on the line the are not on these raise here and
there not on the interior okay so any point on the outer region that's not bounded by
two raise so anywhere in this region right here going out that's the exterior of the
angle so if you think about this entire space right here on forever okay that's basically
the exterior right here is interior this is on the angle and this region right here
is the exterior okay so let's go ahead and label
the points or indicated the points that are on the exterior we can clearly see that points
am and Q are on the exterior of angle ABC okay so we have points m and Q all right the
last part one of the points down on angle ABC point exactly on Ray be oh I'm sorry read
be a RBC are to points that are on the angle right so if it's on this line it's on the
angle on this Ray okay and if any point on this Ray that point is on the angle okay so
what points are either on Ray be a RBC will be classify are is points on our triangle
ABC so whenever you have an angle you have points that are either on the angle points
in the interior or points in the exterior okay the points on the angle
as indicated earlier points on Ray be a RBC and the only points on the angle is
point X so points us is on S is on our triangle ABC thank you so much for taking the time
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