High students so far, we have seen the different angles formed when a transversal intersects two lines.
All right.
So these were the different angles that we came across.
We saw interior angles, exterior angles, corresponding angles, alternate interior angles and alternate
exterior angles, as well as, indeed, angles on the same side of the transversal.
And this is also called consecutive interior angles.
All right, now, over here, these two lines that is line in and line them are not parallel right now.
Let's see the case where a transversal intersects parallel lines.
Well, let's make these two lines parallel.
All right, now you can see that line and line are parallel, right, but they don't intersect with
each other and they are on the same plane.
Now, let's see what is the case with these angles when these two lines are parallel.
Now, the corresponding angles will be equal when Lindemer parallel, that is, you can see angle one
will be equal to angle five and angle four will be equal to handle it.
And the two will be equal to angle six and angle three will be equal to angle seven for the corresponding
angles will be equal when the two lines are parallel.
All right, let's move on to alternating angles.
These angles also will be equal when L and M are parallel.
What does that mean?
Angle three and angle five will be equal.
An angle for an angle six will be equal.
All right.
Now let's move on now.
The alternate exterior angles also will be equal, right?
Why is that so?
We know angle one, angle seven are alternate exterior angles.
Right.
And we have already seen three and five are equal because there alternate interior angles and one is
equal to three because they are vertically opposite angles.
Similarly, five is equal to seven because these two are also vertically opposite angles.
Right.
Therefore, if three is equal to five.
Then definitely angle one is equal to angle seven, and these are alternate exterior angles.
So in the case where a transposon intersects two parallel lines, the alternate interior as well as
alternate exterior angles are equal.
All right, let's move on.
What about interior angles on the same side of the transversal?
Now we have three and six and five and four.
Right.
These are sets of interior angles on the same side of the transversal.
And in the case when the two lines are parallel, these will be supplementary.
That means that three angles, three plus angles, six will give you a 180 degree.
All right, now let's quickly see why that is so we know that angle for plus angle three is equal to
180 degrees, right, because they form a linear pair.
And this is a straight line, right, and we have seen that angle for is equal to Andrew six.
Why is that so?
Because there alternate interior angles, right?
We have that over here.
They are alternating angles.
Therefore, in sort of four, I can write six.
Therefore, angle six plus angle three also will be equal to 180 degrees when these two lines are parallel.
All right.
Now, remember, these angles are also called consecutive interior angles.
What are the different things that we learned in this video, we have seen that in the case where the
transversely is intersecting two parallel lines.
One, the corresponding angles will be equal, the alternating angles will be equal, the alternate
exterior angles will be equal, and the interior angles on the same side of the transversal or the council.
You do indeed.
It angles will be supplementary.
Now, any of these, if they are true, then all of these will be true together.
For example, if point four is true, then point one, two and three also will be true.
So that brings us to our next video, identifying parallel lines.