Let's do this problem in the given figure, find out which pair of lines are parallel.
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Give it a try and then let's do it together.
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We're back.
I hope you have given it a try.
Let's do it together over here.
Let me mark these two angles, this angle, one angle, too, OK?
Now let's check whether nine Abe is parallel to nine city.
If these two lines were parallel and DH is acting as a transversal, we know that consecutive interior
angles or interior angles on the same side of the transversal should be supplementary.
Right.
But one plus two should give you a 180 degree if Abe was parallel to it.
Now, if you add angle one and angle two, you will get your answer as one seventy nine.
Right.
One twenty two plus fifty seven gives you one seventy nine.
That's not equal to 180 degrees.
Therefore Abe is not parallel to city.
All right, let's move on now over here.
Angle two is fifty seven degree and this angle over here is also fifty degrees because they are vertically
opposite angles.
Let me mark this angles three and this one is four.
OK, so we have two angles over here.
Now, if I add three and four, I should get 180 degrees in the case that ECF and they are parallel.
Right, because well F and get Kitty is acting as the transversal.
So if you are angled three plus angle four, that's one twenty three plus fifty seven and that gives
you 180 degree.
Therefore we can conclude that EAF is parallel to get let's that over here.
We have identified two lines that are parallel now over here.
This angle is fifty five degrees.
Therefore this angle over here also will be fifty five degrees because they are vertically opposite
angles.
Right.
All right.
So let me make this angle as angle five.
OK, now angle to angle five.
They are corresponding angles, right.
The corresponding angles for these two lines, Edge and KP and Chris is acting as the transversal right.
The Edge and KP.
These are the two lines and Chris is intersecting both the lines, the series acting as the Transversal.
So we can see that angle to angle five are corresponding angles.
Now, if these two lines were parallel, we know that corresponding angles have to be equal.
But over here and the two is fifty seven degrees and angle five is fifty five degree.
Angle two is not equal to angle five.
Therefore gets is not parallel to KP.
Right.
So is there any other line said set of lines that are parallel.
No, we have seen that these two lines are parallel, we have seen that edge and KP are not parallel.
So definitely E, F and KP also will not be parallel.
Right, because these two are parallel.
Alright now over here we have also seen that it is not parallel to city.
So in this figure which is given the only set of lanes which are parallel is E, f and.
G.H., that is your answer.
Remember, if you have two lines that are parallel to each other and if you find that a third line is
not parallel to one of these lines, definitely that third line will not be parallel to the other line
as well.
Right.
If these two are not parallel, if you keep extending them, they will intersect at some point.
Now, because these two are parallel, they will never intersect.
But if these two are not parallel and these two are parallel, as is the case in this question, therefore,
remember, these two lines also will not be parallel.