L11 : Converse Internal Bisector Theorem - Triangles, Maths, Class 10 Video Lecture

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that you have watched part 1 - part 10
let us do some activity for converse of
interval bisector to let us draw this
two lines now angle and this points once
we have this point what we'll do is add
join this point now here is a trick you
see this this point which I have drawn
here the angle is not liqui-sew
this point when I entry who I assume
that so let's suppose this is 1 2 3 4 5
6 7 8 9 10 11 and this is here again
mine I think so this is X this is y so I
found this point actually such that X by
y is equal to 11 mind once I found this
point I drew this plane here this angle
is equal to this angle I don't know
right I don't know
here it's converse actually here I found
this point first such that X by Y is
equal to 11 by 9 and then you see this I
have to prove that angle Guntersville
going here it's other way round we have
to prove that angle one is going right
to prove what we'll do we'll just take
the compass and we'll observe so what is
observed in any such case we'll observe
that angle 1 is greater angle because it
is activity you have everything in your
hand we can directly measure the angle
MC so what we have done huh here we have
drawn this angle a B this this lines we
have drawn we have joined this point B C
and then the right this point B in such
a way that X by a vice 2011 one line
once you have got this point D you have
drawn is my ad and then we observed an
angle ones were going to do in case of
angle bisector activity we have drawn
this angle such
angle one is going in tune and then we
have seen that X bar Y is equal to
eleven the line in this case is
otherwise we have found this point D
says that X bar is parallel in the nine
and then we have observed that angle one
is going to be a credit converse of
internal angle bisector theorem in a
triangle ABC P is a point on B C such
that D divides PC in race you AV is too
easy then ad is the bisector of angle
this is converse in the know - let's
take this this is triangle ABC and ad is
a point on VC such that it is a point on
VC such that a B by AC that is AD by AC
is equal to B D by DZ that is given that
this is the case then ad has to be the
angle bisector of angle to do this let's
extend this AV extend this and then we
take the compass and make sure that a is
equal to easy this is the point a sorry
this so we have drawn this final we have
measured this AC right let's suppose AC
is X units right same here at X you draw
here you got this point B you got this
point right so you draw the same X Union
you got this point here and we will join
us
that is what we have done here what we
have done we have extended this line
correct you measure AC the same value
here prom cut this here we got a this
point E and then we drawn this so what
we have we have to think that is AP by
AC is equal to BD by DC and also we had
told that AC is equal to a right so AC
is equal to a this angle is going to 1
and this angle either to do so that is
angle 1 is equal to
this is given to us what are you to
prove we have to prove that so let's
suppose this angle is three and this
angle is this 4 so we have to prove that
angle 3 is equal to angle correct that's
all given nothing more now since a be
knock avail
since a B by AC is equal to VD by DC
correct AC is also equal to 8 or we can
say that AV by AE is equal to VC by DC
so in this triangle if you see EBV in
triangle C actually you can see that a B
this value by a this value is equal to
VD by DC correct that means using the
Thales theorem we can say that ad is
parallel to C so we can say that ad is
parallel to see why I wanted to do that
because we want to do to develop a
relation between 1 & 2 & 3 & 4 send it
back to 1 we shear done in the classic
now now since we have proved that ad is
parallel to C now so you can prove that
3 is equal to angle to angle 3 is pin to
angle D Y corresponding again right now
angle 3 is equal to angle 2 also angle 4
is equal to angle 1 why alternate angle
because ad is parallel to C not correct
not 3 is equal to 2 and 4 is equal to 1
we know 3 is equal to 4
how do we know one is going to do since
one is going to give in so please read
over there for 3 is beautiful and that's
what we were supposed to do
C 3 is got to 4 that means ad is the
angle bisector of the del e that is an
angle BAC what we have done here very
simple we have got this triangle we were
told that ad is such that he is such
that a
B by AC is equal to PD by DC we
constructed this AE such that a is going
to AC right and then we have seen that
this applies to Thales theorem we
conclude that ad is parallel to C since
a nice parallel to C we can move that
402 and 3 is equal to 1 right and since
one was built into we can say that 3 is
equal to thank you visit exam Viacom to
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