Axioms related to Corresponding Angles Video Lecture | Mathematics (Maths) Class 9

hello friends this video on lines and
angles part 9 is brought to you by exam
fear calm no more fear from exam 18
let's start with the corresponding Ines
so as I mentioned they are two parallel
lines
these two are corresponding angles okay
or these two are corresponding angles
okay or these two are corresponding
angles or these two more gospel Gators
right so each of these pair is a
corresponding angle correct so there is
no clue for this again you again measure
this if your protector so you see that
these two angles you draw two parallel
lines LNM you draw transpersonal this is
transpersonal use a transversal and then
you see that these two angles are equal
or if you want again drawing one shot it
mean this ln m where L is parallel to M
yes I know
one the stool is e this is 4 this is 5 6
7 8 any naming convention you can given
using protector you can observe that
il-1 will be quite doing in five this
one angle two will be equal to angle six
this one angle 4 will be equal to end of
8 this one angle three will be equal to
angle 7 this one so this is using
observation now since this is done using
observation there is no proof for this
so
as iam a lot right to him why because
using observation I have proved this so
the axiom will be if for corresponding
angles of a transversal intersects
intersects two parallel lines then each
pair of these note they are
corresponding angles corresponding
angles is equal please note this is an
axiom no okay and this is called
corresponding angle axiom okay it is
called corresponding angle axiom
why exam because this is not proved
based on observation we have given this
state okay and let's see the converse of
this is true this is X iam let's see the
converse of the statement is true was
let me write the converse should I write
the converse is in cleaning list the
converse will be if transversal
intersect two lines such that pair of
corresponding angle
is equal then two lines are parallel
okay this is just a plain English
converse it is true or false we don't
know you see that it can be true it can
be fall we can prove that but so in this
case we see that a transversal
intersects two parallel lines then the
angles are corresponding as equal in
this case we see that if the
corresponding angles are equal then the
lines are done okay so now let's true if
this is true or not
okay let's do this first let's let me
write the once again axiom and converse
so I exam say is that if parallel then
corresponding angles equal this is we
have seen observed it so converse is
corresponding angles equal then and this
is true or false we don't know get to
prove it so let us do that so we have to
prove that it is true okay so let us
draw our line CD and let's start to
point if it's mark it be H and then this
P line nearly and we'll draw reminders
from these point vad such that they are
equilibrium this il and this I need such
that these two angles are same the
losses and give some point navier-- -
right we have the line in the edges to
point or these to point B - two angles
and they're equal now you see these two
angles are nothing but corresponding
angles in fact what we can do
is next we can extend these lines so we
are not saying that these lines are
parallel and let me give some value here
and PN is V R so we know that this angle
is angle one let's suppose it's negative
so we know that angle 1 is going to
angle D and is given right so we have to
prove what PQ is parallel to s are
correct because majority construction we
have made the creating this line such a
way that angle 1 is about going to ok
and these are corresponding angles okay
so we had to move that is upon okay so
to prove this what we can do is again if
you see this is all axiom so we have to
use geometric construction so draw
perpendicular line from this point and
if in touch here you see that this angle
is also 90 degree and measure distance
similarly at this point also some other
point draw perpendicular goes down you
see that it is also a Tyrian measure the
distance you see that distance of this
line in this line is same you can do the
same thing into the point is after
extend this and from this point draw
perpendicular you see that the cycle
also 90 degree in this life these are
the same so the distance between this
line PQ and s are is same because you
are amazing the lengths using geometric
um pass for a protractor and scale since
you're amazing the lengthening scale he
had seen that these three lengths are
same
it proves that PQ is parallel to it is
all by geometry construction me apoo
since if you know that it for the exam
and there was no clue for it
similarly using geometry only we have
proved it this is correct right sin it
is correct I can see there
this is a converse eggsy okay so for
corresponding angle we have 2x IAM 1 x
IAM that there are two parallel lines
the transversal which creates if they're
two parallel lines is a transversal
which creates corresponding angle then
these pair of corresponding angles are
equal that is first exam in the second
axiom is that if a transversal
intersects two lines such that the pair
of the corresponding angles are equal
then these two lines are parallel
okay and please note since these are X
gm's
didn't prove it by using any other exams
we have just proved this by observation
by actually constructing it right so you
see the exam itself we have proved by
creating two parallel lines creating a
triangle transpersonal and missing this
values here also what we did was to
prove the axiom we created two
corresponding angles which are same and
then we extended this line and we proved
that these two lines are parallel that
tool that also by using different
reconstruction and that's why it is
axiom thank you visit our website exam
viacom to wash more and more qualities
we should be use you can also attend
free online tests that are there in our
website you can also get access to tons
of free study materials and you can also
find free tutors and mentors in this
website thanks a lot for watching