Sides Of An Angle

good day students welcome to

mathgotserved.com in this introductory

geometry tutorial we are going to be

going over how to name angles size and

vertices we'll 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 the instructions

are for us to name the vertex the sides

of the angle and where to name the angle

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 so let's

say we have an angle that looks

something like this and this point here

is B angle one and then we have a point

on this Ray C and we have another point

on this Ray a okay let's start by naming

the vertex now the vertex take some

different meanings in the context of

this diagram that we have here the

vertex is basically the common point

where these two rays begin okay so

that's what the vertex means so the

common point where these two rays are a

B C and B a meet is at point B okay so

the vertex is going to be B

now let's move on to the next part of

our question 1 which is the sides of the

angle ok what are the sides of the angle

these two rays with a common point or

vertex B are the sides of the angle so

the sides are going to be we start from

the vertex and go in the direction of

the two rays so the first side is BC or

the Ray pointing outward this basically

means that B is where the point

originates from or DeRay and then it

goes in the direction of C and then the

next side of the angle is be a following

the same pattern indicating that the

race starts from B and gules in the

direction of a now the last part

requires us to name the angle in four

different ways

okay so let's go ahead and name the

angle now we can name the angle using

these three points C B and a B the

interior point or the vertex is going to

be at the middle okay so we're going to

name it

angle CBA that's the first way you can

name this angle you can also name it

angle starting from a a b c when you

name in the angles with these points you

have to ensure that the vertex point is

at the middle as you can see here

another way you can name this angle is

by simply using the vertex alphabets you

can call this angle B and then the last

way you can they name this angle is by

using the numerical value that's

assigned to the angle and that is angle

one so these are the four different ways

that um you can

this angle why is this important

whenever you're dealing with geometry

problems there isn't a particular way

that the angle will be presented it

could be presented using the numerical

representation or you could just be

given a vertex alphabet 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 name an angle so you can

basically solve a problem regardless of

whichever format it is presented in now

let's consider another example in this

case we're going to look at angle G yo

okay so we're still following the same

instructions as we did in the previous

problem we're gonna name the vertex the

sides and we'll name the angle in four

different ways okay so let's see this is

the angle right here and we have a point

G and another point O let's start with

the vertex now what is the vertex in

this diagram the vertex is basically the

common point where the two rays

originates or what he needs

okay so

the vertex here is going to be point E

okay now what are the sides of the angle

the size of the angle are these two rays

which have a common point of origination

vertex point E so while we are labeling

the sides remember we're going to start

from the origin or the vertex and go in

the direction of the two points okay so

the first side is eg the ray pointing in

that direction indicating that you're

starting from E and going in the

direction of G and then you also have a

Oh

starting from E and headin in the

direction of O so these are the 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 based on how it is presented

here we can name this angle with this

numerical value that's been assigned to

this 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 we can

name the angle angle e we can also name

the angle using these three points G E

and O but in whichever direction we

choose he has to be the alphabet in the

center since it is the vertex okay so

you can name it angle GE o or we can

name it angle o e G you notice that E is

in the middle in this two ways of naming

the angle all right so these are 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

structions here for question three we

have to name all the angles that um have

vertex oh ok so let's consider this

scenario right here make this point okay

now let's say we have this diagram here

this is vertex o angle a B and then we

have these points on this ray we have G

here we have point t on this Ray in the

middle and then we have point P here at

the bottom okay so the question is which

angles have vertex o angles with vertex

o okay so the first one we can clearly

see that angle a has vertex o right next

to it so we have angle a as one of them

how about angle B does it have vertex o

on it absolutely

angle B has vertex o on it too so let's

write it down and we'll be alright

are those all the angles that I'm

hypertech's oh how about the bigger

angle the combination of angle a and B

that's angle g-o-p 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're to state which points on the given

figure

that are on first of all the point that

the point of points that are on the

interior to the point of points that are

on the exterior three the point of

points that are on angle ABC okay so

we're doing multiple things here let's

go ahead and start by drawing angle ABC

so we have angle ABC and the following

configuration so this is point a this is

B the vertex angle B and we have Point C

right here okay so we have point R we

have point P we have Point s right here

on this Ray we have point Q over here

and then point M right here okay so

let's start with the points on the

interior

okay so points on the interior of angle

ABC let's take a look at what they are

so what's the interior of angle ABC the

interior of angle ABC are basically the

collection of points that lie between

these two rays okay so the region that

these two rays cover right here

it just goes on and on and on and on and

keeps getting wider as you go out so

this region that is to raise bound are

known as the interior so interior are

the collection of points between these

two sides okay so if I extend these two

sites forever what points given in this

diagram will be bounded by them we can

clearly see that points R and P are in

between these two sides what does that

mean it means that these two points are

on the interior of angle ABC okay so we

have points R and P now next question is

what points are on the exterior points

on the exterior of angle ABC the points

are on the exterior are the points that

are not on the line they are not on

these rays here and they're not on the

interior okay so any points on the outer

region that's not bounded by these two

rays 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 go forever

okay that's basically the exterior right

here is the interior this is on the

angle and this region right here is the

exterior okay so let's go ahead and

[Music]

label the points or indicate the points

that are on the exterior we can clearly

see that point and

and Q are on the exterior of angle ABC

okay so we have points m and Q all right

the last part what are the points that

are on angle ABC the points that lay on

Raby oh I'm sorry ray ba or BC are the

points that are on the angle okay 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 ba or BC

those will be classified as points on

triangle ABC so whenever you have an

angle you have points that are either on

the angle points on the interior or

points on the exterior okay so points on

the angle as indicated earlier are the

points on ray ba or BC and the only

point on the angle is Point s so Point s

is on point s is on um triangle ABC

thank you so much for taking the time to

watch this presentation really

appreciate it you found the contents of

this tutorial helpful in your study of

the foundations of geometry to give us a

thumbs-up your positive feedback is very

valuable and supportive to us if you

have any questions or comments on the

material recovered in this presentation

or any geometry concepts in general just

place your questions in the comment

section below and we'll be more than

glad to support you we update videos to

our YouTube page in the

the basis so do subscribe to our channel

so you can get updates to those great

tutorials more resources can be found on

mathgotserved.com thanks again for

watching and have a wonderful day

goodbye