1
00:00:00,740 --> 00:00:07,190
In this video, let's discuss how to identify whether two given lines are parallel or not.

2
00:00:07,440 --> 00:00:10,670
So we have seen various properties in the case of parallel lines.

3
00:00:10,850 --> 00:00:17,240
We have seen that consecutive interior angles will be supplementary, alternate interior angles will

4
00:00:17,240 --> 00:00:22,680
be equal, alternate exterior angles will be equal and corresponding angles will be equal.

5
00:00:22,700 --> 00:00:23,140
All right.

6
00:00:23,330 --> 00:00:27,200
Now, when a transversal intersects two lines, right.

7
00:00:27,440 --> 00:00:34,320
And it's given that a pair of corresponding angles are equal, then the two lines will be parallel.

8
00:00:34,760 --> 00:00:37,220
That's the contours of what we've learned before.

9
00:00:37,250 --> 00:00:44,480
So, for example, you're given two lines that these two lines that it be line and line B and it's mentioned

10
00:00:44,480 --> 00:00:51,980
that there is a transversal C that's intersecting and B and it's given a pair of responding angles are

11
00:00:51,980 --> 00:00:52,520
equal.

12
00:00:52,520 --> 00:00:54,650
C angle one is equal to angle two.

13
00:00:54,860 --> 00:00:57,700
And we know that these two angles are corresponding angles.

14
00:00:57,920 --> 00:01:03,150
So if angle one is equal to angle two line, it will be parallel to nine B..

15
00:01:03,540 --> 00:01:05,830
Now that's one criteria.

16
00:01:05,930 --> 00:01:10,390
Another criteria would be a pair of alternate angles are equal.

17
00:01:10,400 --> 00:01:14,060
You can take alternating angles or alternate exterior angles.

18
00:01:14,360 --> 00:01:20,210
For example, in the same case, if it was given that angle to an angle, three are equal.

19
00:01:20,360 --> 00:01:23,090
We know that these two are alternating triangles.

20
00:01:23,300 --> 00:01:29,210
So if angle two is equal to angle three, then definitely line it will be parallel to line be.

21
00:01:29,570 --> 00:01:30,020
All right.

22
00:01:30,260 --> 00:01:36,680
Now, what is another criteria that we could check if a pair of interior angles on the same side of

23
00:01:36,680 --> 00:01:43,550
the transversal right or consecutive interior angles are supplementary, that means they add up to 180

24
00:01:43,550 --> 00:01:43,980
degrees.

25
00:01:44,180 --> 00:01:47,690
Then also we can say that these two lines are parallel.

26
00:01:47,930 --> 00:01:48,800
What does that mean?

27
00:01:48,950 --> 00:01:51,110
Say, for example, this angle is angle four.

28
00:01:51,260 --> 00:01:58,430
If angle two plus angle four is equal to 180 degrees, then we can be sure that line and line B are

29
00:01:58,430 --> 00:01:58,930
parallel.

30
00:01:59,150 --> 00:02:01,530
So you don't need to check all these criteria's.

31
00:02:01,820 --> 00:02:04,520
You just need to check whether any one of them is true.

32
00:02:04,700 --> 00:02:07,940
If any one of them is true, all of them will be true.

33
00:02:08,090 --> 00:02:12,350
And if any one of them is true, the two given lines will be parallel.