0:00:00.000,0:00:00.710


0:00:00.710,0:00:04.040
Let's do a couple of examples[br]dealing with angles between

0:00:04.040,0:00:05.800
parallel lines and[br]transversals.

0:00:05.800,0:00:10.430
So let's say that these two[br]lines are a parallel, so I can

0:00:10.430,0:00:12.680
a label them as being parallel.

0:00:12.680,0:00:15.120
That tells us that they will[br]never intersect; that they're

0:00:15.120,0:00:16.830
sitting in the same plane.

0:00:16.830,0:00:19.690
And let's say I have a[br]transversal right here, which

0:00:19.690,0:00:21.810
is just a line that will[br]intersect both of those

0:00:21.810,0:00:29.930
parallel lines, and I were to[br]tell you that this angle right

0:00:29.930,0:00:39.110
there is 60 degrees and then I[br]were to ask you what is this

0:00:39.110,0:00:40.790
angle right over there?

0:00:40.790,0:00:42.790
You might say, oh, that's[br]very difficult; that's

0:00:42.790,0:00:43.540
on a different line.

0:00:43.540,0:00:46.160
But you just have to remember,[br]and the one thing I always

0:00:46.160,0:00:50.480
remember, is that corresponding[br]angles are always equivalent.

0:00:50.480,0:00:54.020
And so if you look at this[br]angle up here on this top line

0:00:54.020,0:00:57.110
where the transversal[br]intersects the top line, what

0:00:57.110,0:01:00.130
is the corresponding angle to[br]where the transversal

0:01:00.130,0:01:02.140
intersects this bottom line?

0:01:02.140,0:01:04.810
Well this is kind of the bottom[br]right angle; you could see

0:01:04.810,0:01:06.870
that there's one, two,[br]three, four angles.

0:01:06.870,0:01:08.800
So this is on the bottom[br]and kind of to the

0:01:08.800,0:01:10.320
right a little bit.

0:01:10.320,0:01:12.880
Or maybe you could kind of view[br]it as the southeast angle

0:01:12.880,0:01:15.560
if we're thinking in[br]directions that way.

0:01:15.560,0:01:17.930
And so the corresponding[br]angle is right over here.

0:01:17.930,0:01:21.510


0:01:21.510,0:01:23.300
And they're going[br]to be equivalent.

0:01:23.300,0:01:26.910
So this right here[br]is 60 degrees.

0:01:26.910,0:01:29.950
Now if this angle is 60[br]degrees, what is the

0:01:29.950,0:01:31.570
question mark angle?

0:01:31.570,0:01:35.910
Well the question mark angle--[br]let's call it x --the question

0:01:35.910,0:01:39.780
mark angle plus the 60 degree[br]angle, they go halfway

0:01:39.780,0:01:40.690
around the circle.

0:01:40.690,0:01:45.290
They are supplementary; They[br]will add up to 180 degrees.

0:01:45.290,0:01:50.460
So we could write x plus[br]60 degrees is equal

0:01:50.460,0:01:54.300
to 180 degrees.

0:01:54.300,0:01:57.760
And if you subtract 60 from[br]both sides of this equation you

0:01:57.760,0:02:03.515
get x is equal to 120 degrees.

0:02:03.515,0:02:06.970


0:02:06.970,0:02:08.030
And you could keep going.

0:02:08.030,0:02:11.080
You could actually figure out[br]every angle formed between

0:02:11.080,0:02:13.140
the transversals and[br]the parallel lines.

0:02:13.140,0:02:16.390
If this is 120 degrees,[br]then the angle opposite to

0:02:16.390,0:02:19.270
it is also 120 degrees.

0:02:19.270,0:02:22.580
If this angle is 60 degrees,[br]then this one right here

0:02:22.580,0:02:24.600
is also 60 degrees.

0:02:24.600,0:02:28.190
If this is 60, then its[br]opposite angle is 60 degrees.

0:02:28.190,0:02:30.380
And then you could either say[br]that, hey, this has to be

0:02:30.380,0:02:33.800
supplementary to either this[br]60 degree or this 60 degree.

0:02:33.800,0:02:37.030
Or you could say that this[br]angle corresponds to this 120

0:02:37.030,0:02:41.350
degrees, so it is also 120, and[br]make the same exact argument.

0:02:41.350,0:02:43.790
This angle is the same[br]as this angle, so it

0:02:43.790,0:02:45.950
is also 120 degrees.

0:02:45.950,0:02:47.460
Let's do another one.

0:02:47.460,0:02:48.660
Let's say I have two lines.

0:02:48.660,0:02:51.550


0:02:51.550,0:02:52.790
So that's one line.

0:02:52.790,0:02:56.270
Let me do that in purple and[br]let me do the other line in a

0:02:56.270,0:02:57.660
different shade of purple.

0:02:57.660,0:03:00.590
Let me darken that other[br]one a little bit more.

0:03:00.590,0:03:02.030
So you have that purple[br]line and the other one

0:03:02.030,0:03:02.860
that's another line.

0:03:02.860,0:03:04.660
That's blue or[br]something like that.

0:03:04.660,0:03:08.200
And then I have a line that[br]intersects both of them; we

0:03:08.200,0:03:09.305
draw that a little[br]bit straighter.

0:03:09.305,0:03:16.590


0:03:16.590,0:03:25.080
And let's say that this angle[br]right here is 50 degrees.

0:03:25.080,0:03:29.730
And let's say that I were also[br]to tell you that this angle

0:03:29.730,0:03:34.230
right here is 120 degrees.

0:03:34.230,0:03:38.450
Now the question I want to[br]ask here is, are these

0:03:38.450,0:03:40.220
two lines parallel?

0:03:40.220,0:03:44.230
Is this magenta line and[br]this blue line parallel?

0:03:44.230,0:03:46.420
So the way to think about is[br]what would have happened

0:03:46.420,0:03:47.960
if they were parallel?

0:03:47.960,0:03:51.840
If they were parallel, then[br]this and this would be

0:03:51.840,0:03:59.070
corresponding angles, and so[br]then this would be 50 degrees.

0:03:59.070,0:04:00.530
This would have to[br]be 50 degrees.

0:04:00.530,0:04:03.390
We don't know, so maybe I[br]should put a little asterisk

0:04:03.390,0:04:05.490
there to say, we're not sure[br]whether that's 50 degrees.

0:04:05.490,0:04:07.090
Maybe put a question mark.

0:04:07.090,0:04:10.810
This would be 50 degrees if[br]they were parallel, but this

0:04:10.810,0:04:16.020
and this would have to be[br]supplementary; they would have

0:04:16.020,0:04:17.790
to add up to 180 degrees.

0:04:17.790,0:04:19.900
Actually, regardless of whether[br]the lines are parallel, if I

0:04:19.900,0:04:24.380
just take any line and I have[br]something intersecting, if this

0:04:24.380,0:04:28.890
angle is 50 and whatever this[br]angle would be, they would have

0:04:28.890,0:04:31.230
to add up to 180 degrees.

0:04:31.230,0:04:35.200
But we see right here that this[br]will not add up to 180 degrees.

0:04:35.200,0:04:38.000
50 plus 120 adds up to 170.

0:04:38.000,0:04:39.910
So these lines aren't parallel.

0:04:39.910,0:04:42.760
Another way you could have[br]thought about it-- I guess this

0:04:42.760,0:04:45.800
would have maybe been a more[br]exact way to think about it

0:04:45.800,0:04:50.490
--is if this is 120 degrees,[br]this angle right here has to be

0:04:50.490,0:04:53.420
supplementary to that; it[br]has to add up to 180.

0:04:53.420,0:04:57.290
So this angle-- do it in this[br]screen --this angle right

0:04:57.290,0:04:59.940
here has to be 60 degrees.

0:04:59.940,0:05:03.010
Now this angle corresponds[br]to that angle, but

0:05:03.010,0:05:03.930
they're not equal.

0:05:03.930,0:05:06.530
The corresponding angles[br]are not equal, so these

0:05:06.530,0:05:13.810
lines are not parallel.

0:05:13.810,0:05:14.175