L10 : Internal Bisector Theorem - Triangles, Maths, Class 10 Video Lecture

hello friends this video on triangles
part 10 is brought you by exam clear
calm no more fear from example before
watching this video please make sure
that you have watched part 1 - Part I
now let's start with angle bisector
concept what is angle bisector so we
have this triangle let's have this happy
is a triangle then this V Point a this B
point B and this B by C so we have this
point so they are two kind of angle
bisector one is called internal all
right here internal angle bisector and
the second is called external angle by
self let's study both actually so in
first case will go for interval master
so this is the triangle unless suppose
this is the angle E or I believe I want
to find interval investiture at all like
this this is my angle e I treat my
internal angle bisector right so in this
case this angle will be 1 and this angle
we do we are angle 1 will be equal to
angle T but I will be equal so you have
a internal angle and you bisect this do
this line it opposes D ad is called
internal angle bisector now let's draw
action on investor we draw this triangle
we have this point B B and C is a
triangle now now for the same angle E I
want to draw an angle bisector so
external angle is this angle so first
extend this here excitedness this is our
external angle correct this is the
internal angle this is literally now you
draw external angle bisector for this
way what a loop will draw this point
also extend this by because it will meet
somewhere here right now bent of this -
alright so if you see this this angle
it's equals 1 2 3 and this is 4 so here
angle 3 is equal to M it means happen so
this is example of external angle
bisector
so what we have done we have drawn the
same triangle ABC in first case we do
internal angle bisector so we got this
internal angle we drew a line ad says
that angle 1 is equal to angle 2 the
second case V we are supposed to tow
external angle bisector so point a we
extended this because its external angle
this point was a weeks in it because
they wanted at this point wait somewhere
and then we do this angle so we do this
line ad says that angle 3 is equal to
angle 4 so here ad is external angle
wise and here ad is internal angle basic
that is a concept of internal and
external angle its have an activity for
internal angle bisector this draw this
angle once we have this angle then it
installs points all this point ticular
sin find it here also strong sponge now
let's join this point this one you see
this just just way that we have joined
this point here you see this is 1 1 unit
2 3 4 5 6 7 8 9 10 11 11 in its shape
and this is 1 2 3 4 5 6 7 8 9
this is my miniature correct so we have
bought a triangle of sight 11 and 9 and
this is prime now we draw an angle
bisector such that this angle 1 is equal
to half into correct this was 60 degree
in utica th so we do this angle where
angle 1 is equal to angle 2 now let's
put the points this is d it is V this is
V and it is so now that is nothing but 1
1 triangle if you see it is the internal
angle bisector now you may say this
point this is I suppose X and this is
get simplified to measure if you take a
measurement of this BD and DC you will
see that we observe that EC by a B is
always equal to C V by VT
that is 11 by 9 will always be equal to
X 9/5 in this system you take this one
then AC value to be different money that
SOI did you take any angle create angle
bisector and then you observe that this
AC by BD but always be four do CD by
this you can try in your people with a
pen or pencil this will always be this
is an activity Bob will have a theorem
to prove the theorem for internal angle
bisector the theorem says internal angle
bisector of a triangle divides opposite
size interval in the ratio of the sides
containing that angle we have seen this
that if this is the triangle let me
write it be the final this is the final
ABC right and this is the angle bisector
it is angle bisector then a V by AC is
equal to B D by C correct you have the
proof to prove this and stop applying
them and since find them and this is
ABC's it and this is the angle bisector
actually so that suppose this point E is
the angle to prove this let's draw a
line C parallel to e and also and extend
this line to meet at this point Dylan
let's call this one is d why we have
done them because tell mommy no only
Thales theorem so if we have this line
and this line parallel you can use theta
0 property that's why we have extended
the CD parallel to and this angle is 1
second to where angle 1 is equal to
angle 2 and E is parallel to this our
two things we have so what we have to
prove we have to prove that to rule that
a V by AC is equal to V E
by EC in this diagram so let me cancel
this right in this dangle in this
diagram maybe by AC is equal to VD by
easy so what is the application form if
you see send this to a parallel
beep IEC turns on the right-hand side
this one will be equal to a B by any
correct thing and ITV B by just going by
the reverse approach V by easy this is
equal to if you see de by is going to a
be by ad correct by theorem by failure
why because a is parallel to C now we
are supposed to prove that be by AC able
to AV by AC so instead of ad we have to
do AC so if somehow we can prove that ad
is equal to AC our issue is so correct
we can prove that ad is equal to AC a
fish on
so let's see can be proved it is
valuation let's try this this angle 2 is
equal to angle 2 - why because he is
parallel to this so ordinary diagram so
this angle is bent on the side similarly
angle 1 is equal to 1 - I'll put this
one - why because this and this are same
so what we have seen angle 1 is equal to
angle 1 - y corresponding angle and
angle 2 is equal to angle 2 - all
tonight
now since ankle 1 is equal to angle 2 is
already given right given here so we can
say that angle 1 dash is equal to angle
2 - he maker 1 dash equal to angle 2
dash then AC D is a as of lifecycle so
we can say that AC is equal to nd
correct if AC is equal to ad instead of
a ta connect is he here so this equation
I'll put this equation here this
equation will become V by EC will become
a B by HD of 80 a very easy and that is
what I wanted to took hence proved so
thus by using pairs from I approved of
angle bisector theorem that is if a is
my angle is angle bisector than AV by EC
is equal to B by C right
please understand what I have done here
I have just drawn a parallel line
because I knew only things from them and
intestinal if you have parallel line you
can find them ratio V by EC by Thales
theorem becomes a by ad but I wanted to
prove V by BC is equal to AP by AC that
means ad should be pretty easy then
somehow I proved that a B is going to AC
how I approve an angle one decimal -
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