[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.71,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.71,0:00:04.04,Default,,0000,0000,0000,,Let's do a couple of examples\Ndealing with angles between
Dialogue: 0,0:00:04.04,0:00:05.80,Default,,0000,0000,0000,,parallel lines and\Ntransversals.
Dialogue: 0,0:00:05.80,0:00:10.43,Default,,0000,0000,0000,,So let's say that these two\Nlines are a parallel, so I can
Dialogue: 0,0:00:10.43,0:00:12.68,Default,,0000,0000,0000,,a label them as being parallel.
Dialogue: 0,0:00:12.68,0:00:15.12,Default,,0000,0000,0000,,That tells us that they will\Nnever intersect; that they're
Dialogue: 0,0:00:15.12,0:00:16.83,Default,,0000,0000,0000,,sitting in the same plane.
Dialogue: 0,0:00:16.83,0:00:19.69,Default,,0000,0000,0000,,And let's say I have a\Ntransversal right here, which
Dialogue: 0,0:00:19.69,0:00:21.81,Default,,0000,0000,0000,,is just a line that will\Nintersect both of those
Dialogue: 0,0:00:21.81,0:00:29.93,Default,,0000,0000,0000,,parallel lines, and I were to\Ntell you that this angle right
Dialogue: 0,0:00:29.93,0:00:39.11,Default,,0000,0000,0000,,there is 60 degrees and then I\Nwere to ask you what is this
Dialogue: 0,0:00:39.11,0:00:40.79,Default,,0000,0000,0000,,angle right over there?
Dialogue: 0,0:00:40.79,0:00:42.79,Default,,0000,0000,0000,,You might say, oh, that's\Nvery difficult; that's
Dialogue: 0,0:00:42.79,0:00:43.54,Default,,0000,0000,0000,,on a different line.
Dialogue: 0,0:00:43.54,0:00:46.16,Default,,0000,0000,0000,,But you just have to remember,\Nand the one thing I always
Dialogue: 0,0:00:46.16,0:00:50.48,Default,,0000,0000,0000,,remember, is that corresponding\Nangles are always equivalent.
Dialogue: 0,0:00:50.48,0:00:54.02,Default,,0000,0000,0000,,And so if you look at this\Nangle up here on this top line
Dialogue: 0,0:00:54.02,0:00:57.11,Default,,0000,0000,0000,,where the transversal\Nintersects the top line, what
Dialogue: 0,0:00:57.11,0:01:00.13,Default,,0000,0000,0000,,is the corresponding angle to\Nwhere the transversal
Dialogue: 0,0:01:00.13,0:01:02.14,Default,,0000,0000,0000,,intersects this bottom line?
Dialogue: 0,0:01:02.14,0:01:04.81,Default,,0000,0000,0000,,Well this is kind of the bottom\Nright angle; you could see
Dialogue: 0,0:01:04.81,0:01:06.87,Default,,0000,0000,0000,,that there's one, two,\Nthree, four angles.
Dialogue: 0,0:01:06.87,0:01:08.80,Default,,0000,0000,0000,,So this is on the bottom\Nand kind of to the
Dialogue: 0,0:01:08.80,0:01:10.32,Default,,0000,0000,0000,,right a little bit.
Dialogue: 0,0:01:10.32,0:01:12.88,Default,,0000,0000,0000,,Or maybe you could kind of view\Nit as the southeast angle
Dialogue: 0,0:01:12.88,0:01:15.56,Default,,0000,0000,0000,,if we're thinking in\Ndirections that way.
Dialogue: 0,0:01:15.56,0:01:17.93,Default,,0000,0000,0000,,And so the corresponding\Nangle is right over here.
Dialogue: 0,0:01:17.93,0:01:21.51,Default,,0000,0000,0000,,
Dialogue: 0,0:01:21.51,0:01:23.30,Default,,0000,0000,0000,,And they're going\Nto be equivalent.
Dialogue: 0,0:01:23.30,0:01:26.91,Default,,0000,0000,0000,,So this right here\Nis 60 degrees.
Dialogue: 0,0:01:26.91,0:01:29.95,Default,,0000,0000,0000,,Now if this angle is 60\Ndegrees, what is the
Dialogue: 0,0:01:29.95,0:01:31.57,Default,,0000,0000,0000,,question mark angle?
Dialogue: 0,0:01:31.57,0:01:35.91,Default,,0000,0000,0000,,Well the question mark angle--\Nlet's call it x --the question
Dialogue: 0,0:01:35.91,0:01:39.78,Default,,0000,0000,0000,,mark angle plus the 60 degree\Nangle, they go halfway
Dialogue: 0,0:01:39.78,0:01:40.69,Default,,0000,0000,0000,,around the circle.
Dialogue: 0,0:01:40.69,0:01:45.29,Default,,0000,0000,0000,,They are supplementary; They\Nwill add up to 180 degrees.
Dialogue: 0,0:01:45.29,0:01:50.46,Default,,0000,0000,0000,,So we could write x plus\N60 degrees is equal
Dialogue: 0,0:01:50.46,0:01:54.30,Default,,0000,0000,0000,,to 180 degrees.
Dialogue: 0,0:01:54.30,0:01:57.76,Default,,0000,0000,0000,,And if you subtract 60 from\Nboth sides of this equation you
Dialogue: 0,0:01:57.76,0:02:03.52,Default,,0000,0000,0000,,get x is equal to 120 degrees.
Dialogue: 0,0:02:03.52,0:02:06.97,Default,,0000,0000,0000,,
Dialogue: 0,0:02:06.97,0:02:08.03,Default,,0000,0000,0000,,And you could keep going.
Dialogue: 0,0:02:08.03,0:02:11.08,Default,,0000,0000,0000,,You could actually figure out\Nevery angle formed between
Dialogue: 0,0:02:11.08,0:02:13.14,Default,,0000,0000,0000,,the transversals and\Nthe parallel lines.
Dialogue: 0,0:02:13.14,0:02:16.39,Default,,0000,0000,0000,,If this is 120 degrees,\Nthen the angle opposite to
Dialogue: 0,0:02:16.39,0:02:19.27,Default,,0000,0000,0000,,it is also 120 degrees.
Dialogue: 0,0:02:19.27,0:02:22.58,Default,,0000,0000,0000,,If this angle is 60 degrees,\Nthen this one right here
Dialogue: 0,0:02:22.58,0:02:24.60,Default,,0000,0000,0000,,is also 60 degrees.
Dialogue: 0,0:02:24.60,0:02:28.19,Default,,0000,0000,0000,,If this is 60, then its\Nopposite angle is 60 degrees.
Dialogue: 0,0:02:28.19,0:02:30.38,Default,,0000,0000,0000,,And then you could either say\Nthat, hey, this has to be
Dialogue: 0,0:02:30.38,0:02:33.80,Default,,0000,0000,0000,,supplementary to either this\N60 degree or this 60 degree.
Dialogue: 0,0:02:33.80,0:02:37.03,Default,,0000,0000,0000,,Or you could say that this\Nangle corresponds to this 120
Dialogue: 0,0:02:37.03,0:02:41.35,Default,,0000,0000,0000,,degrees, so it is also 120, and\Nmake the same exact argument.
Dialogue: 0,0:02:41.35,0:02:43.79,Default,,0000,0000,0000,,This angle is the same\Nas this angle, so it
Dialogue: 0,0:02:43.79,0:02:45.95,Default,,0000,0000,0000,,is also 120 degrees.
Dialogue: 0,0:02:45.95,0:02:47.46,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:02:47.46,0:02:48.66,Default,,0000,0000,0000,,Let's say I have two lines.
Dialogue: 0,0:02:48.66,0:02:51.55,Default,,0000,0000,0000,,
Dialogue: 0,0:02:51.55,0:02:52.79,Default,,0000,0000,0000,,So that's one line.
Dialogue: 0,0:02:52.79,0:02:56.27,Default,,0000,0000,0000,,Let me do that in purple and\Nlet me do the other line in a
Dialogue: 0,0:02:56.27,0:02:57.66,Default,,0000,0000,0000,,different shade of purple.
Dialogue: 0,0:02:57.66,0:03:00.59,Default,,0000,0000,0000,,Let me darken that other\None a little bit more.
Dialogue: 0,0:03:00.59,0:03:02.03,Default,,0000,0000,0000,,So you have that purple\Nline and the other one
Dialogue: 0,0:03:02.03,0:03:02.86,Default,,0000,0000,0000,,that's another line.
Dialogue: 0,0:03:02.86,0:03:04.66,Default,,0000,0000,0000,,That's blue or\Nsomething like that.
Dialogue: 0,0:03:04.66,0:03:08.20,Default,,0000,0000,0000,,And then I have a line that\Nintersects both of them; we
Dialogue: 0,0:03:08.20,0:03:09.30,Default,,0000,0000,0000,,draw that a little\Nbit straighter.
Dialogue: 0,0:03:09.30,0:03:16.59,Default,,0000,0000,0000,,
Dialogue: 0,0:03:16.59,0:03:25.08,Default,,0000,0000,0000,,And let's say that this angle\Nright here is 50 degrees.
Dialogue: 0,0:03:25.08,0:03:29.73,Default,,0000,0000,0000,,And let's say that I were also\Nto tell you that this angle
Dialogue: 0,0:03:29.73,0:03:34.23,Default,,0000,0000,0000,,right here is 120 degrees.
Dialogue: 0,0:03:34.23,0:03:38.45,Default,,0000,0000,0000,,Now the question I want to\Nask here is, are these
Dialogue: 0,0:03:38.45,0:03:40.22,Default,,0000,0000,0000,,two lines parallel?
Dialogue: 0,0:03:40.22,0:03:44.23,Default,,0000,0000,0000,,Is this magenta line and\Nthis blue line parallel?
Dialogue: 0,0:03:44.23,0:03:46.42,Default,,0000,0000,0000,,So the way to think about is\Nwhat would have happened
Dialogue: 0,0:03:46.42,0:03:47.96,Default,,0000,0000,0000,,if they were parallel?
Dialogue: 0,0:03:47.96,0:03:51.84,Default,,0000,0000,0000,,If they were parallel, then\Nthis and this would be
Dialogue: 0,0:03:51.84,0:03:59.07,Default,,0000,0000,0000,,corresponding angles, and so\Nthen this would be 50 degrees.
Dialogue: 0,0:03:59.07,0:04:00.53,Default,,0000,0000,0000,,This would have to\Nbe 50 degrees.
Dialogue: 0,0:04:00.53,0:04:03.39,Default,,0000,0000,0000,,We don't know, so maybe I\Nshould put a little asterisk
Dialogue: 0,0:04:03.39,0:04:05.49,Default,,0000,0000,0000,,there to say, we're not sure\Nwhether that's 50 degrees.
Dialogue: 0,0:04:05.49,0:04:07.09,Default,,0000,0000,0000,,Maybe put a question mark.
Dialogue: 0,0:04:07.09,0:04:10.81,Default,,0000,0000,0000,,This would be 50 degrees if\Nthey were parallel, but this
Dialogue: 0,0:04:10.81,0:04:16.02,Default,,0000,0000,0000,,and this would have to be\Nsupplementary; they would have
Dialogue: 0,0:04:16.02,0:04:17.79,Default,,0000,0000,0000,,to add up to 180 degrees.
Dialogue: 0,0:04:17.79,0:04:19.90,Default,,0000,0000,0000,,Actually, regardless of whether\Nthe lines are parallel, if I
Dialogue: 0,0:04:19.90,0:04:24.38,Default,,0000,0000,0000,,just take any line and I have\Nsomething intersecting, if this
Dialogue: 0,0:04:24.38,0:04:28.89,Default,,0000,0000,0000,,angle is 50 and whatever this\Nangle would be, they would have
Dialogue: 0,0:04:28.89,0:04:31.23,Default,,0000,0000,0000,,to add up to 180 degrees.
Dialogue: 0,0:04:31.23,0:04:35.20,Default,,0000,0000,0000,,But we see right here that this\Nwill not add up to 180 degrees.
Dialogue: 0,0:04:35.20,0:04:38.00,Default,,0000,0000,0000,,50 plus 120 adds up to 170.
Dialogue: 0,0:04:38.00,0:04:39.91,Default,,0000,0000,0000,,So these lines aren't parallel.
Dialogue: 0,0:04:39.91,0:04:42.76,Default,,0000,0000,0000,,Another way you could have\Nthought about it-- I guess this
Dialogue: 0,0:04:42.76,0:04:45.80,Default,,0000,0000,0000,,would have maybe been a more\Nexact way to think about it
Dialogue: 0,0:04:45.80,0:04:50.49,Default,,0000,0000,0000,,--is if this is 120 degrees,\Nthis angle right here has to be
Dialogue: 0,0:04:50.49,0:04:53.42,Default,,0000,0000,0000,,supplementary to that; it\Nhas to add up to 180.
Dialogue: 0,0:04:53.42,0:04:57.29,Default,,0000,0000,0000,,So this angle-- do it in this\Nscreen --this angle right
Dialogue: 0,0:04:57.29,0:04:59.94,Default,,0000,0000,0000,,here has to be 60 degrees.
Dialogue: 0,0:04:59.94,0:05:03.01,Default,,0000,0000,0000,,Now this angle corresponds\Nto that angle, but
Dialogue: 0,0:05:03.01,0:05:03.93,Default,,0000,0000,0000,,they're not equal.
Dialogue: 0,0:05:03.93,0:05:06.53,Default,,0000,0000,0000,,The corresponding angles\Nare not equal, so these
Dialogue: 0,0:05:06.53,0:05:13.81,Default,,0000,0000,0000,,lines are not parallel.
Dialogue: 0,0:05:13.81,0:05:14.18,Default,,0000,0000,0000,,