Class 9 Exam > Class 9 Videos > Lines parallel to same line are parallel to each other (Theorem)
Lines parallel to same line are parallel to each other (Theorem) Video Lecture - Class 9
FAQs on Lines parallel to same line are parallel to each other (Theorem) Video Lecture - Class 9
| 1. What is the meaning of parallel lines? |  |
Ans. Parallel lines are lines that are always the same distance apart and never intersect. They have the same slope and will never meet, no matter how far they are extended.
| 2. How can we determine if two lines are parallel? | |
Ans. Two lines are parallel if they have the same slope. The slope of a line can be determined by dividing the change in y-coordinates by the change in x-coordinates between any two points on the line. If the slopes of two lines are equal, they are parallel.
| 3. Can lines parallel to the same line be intersecting? | |
Ans. No, lines parallel to the same line cannot intersect. Since parallel lines have the same slope and never meet, any line parallel to the same line will also have the same slope and therefore will not intersect with each other or the original line.
| 4. Are there any other conditions to prove that lines are parallel to each other? | |
Ans. Yes, another condition to prove that lines are parallel is the angle between them. If two lines have the same slope and the same angle between them, they are parallel. This condition can be used when slopes are not readily available or when dealing with lines on a coordinate plane.
| 5. Can lines that are not parallel to the same line be parallel to each other? | |
Ans. No, lines that are not parallel to the same line cannot be parallel to each other. Parallel lines have the same slope, so if two lines have different slopes, they cannot be parallel to each other, regardless of their relationship with other lines.
Text Transcript from Video
hello friends welcome welcome to this
presentation from rising pearl hammock
Cohoes oculus roi item bat Callaghan
handles the cd6 key this key topic
headlines and angles
yeah hamari of episode number 9 or those
coop needed here my last few episodes
may hum a kakaka theorem later hey and
we are actually proving these theorems
so our key theorem Agosto lines which
are parallel to the same line are
parallel to each other so you had
theorem though and we are going to prove
why this is true socially should work at
the hair now theorem could also a well
let us look at it up close so the
theorem states that lines which are
parallel to the same line are parallel
to each other
Matlock a hadass turkey other am a
shadow lines later here and actually get
ahead he lie me happy line L and and he
have key line M so again I've got a
those cookie line L and line M parallel
hair type and then manager we will take
one more line line and all those other
other hemay my other maloom hockey line
L is parallel to line m and himeko serum
Alam Hickey line and Joey it is parallel
to M line enjo have that is also
parallel to line m so those are then
what the theorem is telling is that
other if this is true and this is true
it implies that line L is parallel to
line m it's chemically with Nosa lines
parallel to the same line so line L is
parallel to M and line n is also
parallel to M so lines which are
parallel to the same line you have those
are the same line here that is our line
m agar as ahead oh so then those lines
are parallel to each other
so those actually let us find out how
actually we can solve it so this is a
theorem and after a massacre Kaline
struck earth L m and n Homero so then
the carnahan basically like we are
discussing muhammediye jaata hai ki L is
parallel to M and n is parallel to M
then we have to we have to show that L
will always be parallel to n now those
actually now let us actually get to the
proof of this you say hum kacica keep
crews per sec there so the the first
thing goes come check out the heavy have
drawn out lines and chilly a happy we
have actually taken a transfer select
ELISA care to him a BP younger
transversal Pedro key hey Roscoe now
this basically cuts all the three lines
L m and n right so again those become a
lama job then we actually do these
proofs for theorems come start at the
head what is given and then we want to
write to prove and cap proof cut the
head and the actual proof so what is
given what is to be proved what is to be
proven and the actual proof of it so
given hey happy goes the line L is
parallel to line m and also it is given
line n is parallel to line m these are
two things which are given away on a
proof carneros the key line L will be
parallel to line m this is what we want
to prove oh so now how do we prove it so
what we will say is those though we draw
a transversal P as shown in the figure
such that the transversal cuts all the
lines L m and n right now those though
every age of angle a chillyzack at an
angle one is a cat a high angle 2 is a
cat a high angle 3 right
now though so if you take line L and M a
transversal if it cuts parallel lines I
am a loom have that angle 1 will be
equal to angle 2 right Sarkoja way q
because L and M are parallel lines and
you have a transversal that cuts them so
those are these are corresponding angles
right so here the homeric corresponding
angles have corresponding angles they
are equal correct
now those actually a a we think about
line m and line n you have a transversal
P that cuts these two lines so a V then
those two angle 2 and angle 3 should be
equal as well right
UK angle 2 and angle 3 they are
corresponding angles so a girl ein m and
n parallel here which is given to us
then these two angles are equal for the
same reason corresponding angles equal
right width of a camper thing either
first equality thei chillyzack at the
equation 1 or is cook at the equation 2
sub J for those cook from Equation 1 an
equation 2 we get that angle 1 is equal
to angle 2 and angle 2 is equal to angle
3 is equal to angle 3 or we can say that
angle 1 is equal to angle 3 right so
angle 1 is equal to angle 2 and angle 3
will be equal to angle 2 so MUC love
this angle 1 and angle 3 are equal so
now those are they okay if you now take
line L and line n so now other up if you
if you think your line m hey a exist
negative then update over those so
basically what you will see is you have
line L you have KL you have KN and you
have a transversal which cuts these two
lines in such a way that the arc angle 1
and you have the angle three these are
corresponding angles and these angles
are equal
somewhere a higher slope you know from
mark corresponding angles theorem or
corresponding angles axiom that if we
have two lines and if you have a
transversal that tracks two lines in
such a way the corresponding angles are
equal that means that the lines L and n
are parallel so it means this implies
that line L is parallel to line m so
this is what we wanted to prove KL or n
they are parallel lines and this is how
we proved it now so now like having a
papaya kina when you are given this in
an exam so agarrado properly the way you
have to write the proofs of the theorem
so this is how you are going to write
the proof for this particular theorem so
start you will start by you know drawing
the three lines LM n N and those are the
reason we are doing this app notice
calculation for all of these proofs we
want to be very particular that app
exactly how you have to do this in the
exam hum aapke both the carnage are
there but before we should show it to
you we want to actually give you the
proof and of the reasoning behind the
proof first and most a but we want to
make sure that you know exactly how
step-by-step-by-step Asarco examinee so
so for this particular theorem is key
proof Co you want to start it like this
we have three lines LM n n it is given
line L is parallel to M L parallel to M
and n parallel to M and parallel to M
right up Nettie no line a circuit rocky
here we need to prove L is parallel to n
that is hemay a proof Kearney hi L
parallel to n right now we draw a
transversal P intersecting L m and n as
shown in the figure since M since L and
M are parallel we have angle 1 equal to
angle 2
so those are angle 1 angle 2 since L and
M are parallel we have angle 1 equal to
angle 2 corresponding angles are equal
right today is the camera angle 3 now
since M and n are parallel we have angle
2 is equal to angle 3 corresponding
angles are equal so you say I'm like aha
equation 1 is a hammaker high equation 2
from 1 & 2 we get 1 is equal to 2 is
equal to 3 or we get 1 is equal to 3
right whiskey bar those two we we say
that but if we look at lines L and M we
see the transversal P intersects them in
such a way that a pair of corresponding
angles 1 angle 1 and angle 3 are equal
so this implies that angle the line L is
parallel to line n because from
corresponding angles axiom and hence we
say that the theorem is proved so those
the arch case ruby sword made my ugly
baby some film blanket effect we should
react and Awadh
presentation from rising pearl hammock
Cohoes oculus roi item bat Callaghan
handles the cd6 key this key topic
headlines and angles
yeah hamari of episode number 9 or those
coop needed here my last few episodes
may hum a kakaka theorem later hey and
we are actually proving these theorems
so our key theorem Agosto lines which
are parallel to the same line are
parallel to each other so you had
theorem though and we are going to prove
why this is true socially should work at
the hair now theorem could also a well
let us look at it up close so the
theorem states that lines which are
parallel to the same line are parallel
to each other
Matlock a hadass turkey other am a
shadow lines later here and actually get
ahead he lie me happy line L and and he
have key line M so again I've got a
those cookie line L and line M parallel
hair type and then manager we will take
one more line line and all those other
other hemay my other maloom hockey line
L is parallel to line m and himeko serum
Alam Hickey line and Joey it is parallel
to M line enjo have that is also
parallel to line m so those are then
what the theorem is telling is that
other if this is true and this is true
it implies that line L is parallel to
line m it's chemically with Nosa lines
parallel to the same line so line L is
parallel to M and line n is also
parallel to M so lines which are
parallel to the same line you have those
are the same line here that is our line
m agar as ahead oh so then those lines
are parallel to each other
so those actually let us find out how
actually we can solve it so this is a
theorem and after a massacre Kaline
struck earth L m and n Homero so then
the carnahan basically like we are
discussing muhammediye jaata hai ki L is
parallel to M and n is parallel to M
then we have to we have to show that L
will always be parallel to n now those
actually now let us actually get to the
proof of this you say hum kacica keep
crews per sec there so the the first
thing goes come check out the heavy have
drawn out lines and chilly a happy we
have actually taken a transfer select
ELISA care to him a BP younger
transversal Pedro key hey Roscoe now
this basically cuts all the three lines
L m and n right so again those become a
lama job then we actually do these
proofs for theorems come start at the
head what is given and then we want to
write to prove and cap proof cut the
head and the actual proof so what is
given what is to be proved what is to be
proven and the actual proof of it so
given hey happy goes the line L is
parallel to line m and also it is given
line n is parallel to line m these are
two things which are given away on a
proof carneros the key line L will be
parallel to line m this is what we want
to prove oh so now how do we prove it so
what we will say is those though we draw
a transversal P as shown in the figure
such that the transversal cuts all the
lines L m and n right now those though
every age of angle a chillyzack at an
angle one is a cat a high angle 2 is a
cat a high angle 3 right
now though so if you take line L and M a
transversal if it cuts parallel lines I
am a loom have that angle 1 will be
equal to angle 2 right Sarkoja way q
because L and M are parallel lines and
you have a transversal that cuts them so
those are these are corresponding angles
right so here the homeric corresponding
angles have corresponding angles they
are equal correct
now those actually a a we think about
line m and line n you have a transversal
P that cuts these two lines so a V then
those two angle 2 and angle 3 should be
equal as well right
UK angle 2 and angle 3 they are
corresponding angles so a girl ein m and
n parallel here which is given to us
then these two angles are equal for the
same reason corresponding angles equal
right width of a camper thing either
first equality thei chillyzack at the
equation 1 or is cook at the equation 2
sub J for those cook from Equation 1 an
equation 2 we get that angle 1 is equal
to angle 2 and angle 2 is equal to angle
3 is equal to angle 3 or we can say that
angle 1 is equal to angle 3 right so
angle 1 is equal to angle 2 and angle 3
will be equal to angle 2 so MUC love
this angle 1 and angle 3 are equal so
now those are they okay if you now take
line L and line n so now other up if you
if you think your line m hey a exist
negative then update over those so
basically what you will see is you have
line L you have KL you have KN and you
have a transversal which cuts these two
lines in such a way that the arc angle 1
and you have the angle three these are
corresponding angles and these angles
are equal
somewhere a higher slope you know from
mark corresponding angles theorem or
corresponding angles axiom that if we
have two lines and if you have a
transversal that tracks two lines in
such a way the corresponding angles are
equal that means that the lines L and n
are parallel so it means this implies
that line L is parallel to line m so
this is what we wanted to prove KL or n
they are parallel lines and this is how
we proved it now so now like having a
papaya kina when you are given this in
an exam so agarrado properly the way you
have to write the proofs of the theorem
so this is how you are going to write
the proof for this particular theorem so
start you will start by you know drawing
the three lines LM n N and those are the
reason we are doing this app notice
calculation for all of these proofs we
want to be very particular that app
exactly how you have to do this in the
exam hum aapke both the carnage are
there but before we should show it to
you we want to actually give you the
proof and of the reasoning behind the
proof first and most a but we want to
make sure that you know exactly how
step-by-step-by-step Asarco examinee so
so for this particular theorem is key
proof Co you want to start it like this
we have three lines LM n n it is given
line L is parallel to M L parallel to M
and n parallel to M and parallel to M
right up Nettie no line a circuit rocky
here we need to prove L is parallel to n
that is hemay a proof Kearney hi L
parallel to n right now we draw a
transversal P intersecting L m and n as
shown in the figure since M since L and
M are parallel we have angle 1 equal to
angle 2
so those are angle 1 angle 2 since L and
M are parallel we have angle 1 equal to
angle 2 corresponding angles are equal
right today is the camera angle 3 now
since M and n are parallel we have angle
2 is equal to angle 3 corresponding
angles are equal so you say I'm like aha
equation 1 is a hammaker high equation 2
from 1 & 2 we get 1 is equal to 2 is
equal to 3 or we get 1 is equal to 3
right whiskey bar those two we we say
that but if we look at lines L and M we
see the transversal P intersects them in
such a way that a pair of corresponding
angles 1 angle 1 and angle 3 are equal
so this implies that angle the line L is
parallel to line n because from
corresponding angles axiom and hence we
say that the theorem is proved so those
the arch case ruby sword made my ugly
baby some film blanket effect we should
react and Awadh
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Dec 28, 2024 Last updated |
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