[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.95,0:00:03.46,Default,,0000,0000,0000,,So let's review everything that\Nwe know so far, because it's
Dialogue: 0,0:00:03.46,0:00:05.47,Default,,0000,0000,0000,,good to keep reviewing.
Dialogue: 0,0:00:05.47,0:00:07.36,Default,,0000,0000,0000,,Because these are things\Nyou should never forget
Dialogue: 0,0:00:07.36,0:00:08.87,Default,,0000,0000,0000,,the rest of your life.
Dialogue: 0,0:00:08.87,0:00:14.33,Default,,0000,0000,0000,,So if I have a line and if I\Ndraw an angle that goes--
Dialogue: 0,0:00:14.33,0:00:16.53,Default,,0000,0000,0000,,let's say this is the\Npivot point, right?
Dialogue: 0,0:00:16.53,0:00:19.79,Default,,0000,0000,0000,,If I go all the way around\Nthe line, or in a circle,
Dialogue: 0,0:00:19.79,0:00:20.98,Default,,0000,0000,0000,,that's 360 degrees.
Dialogue: 0,0:00:20.98,0:00:23.97,Default,,0000,0000,0000,,\N11\N00:00:23,97 --> 00:00:27,43\NWe learned that there are\N360 degrees in a circle.
Dialogue: 0,0:00:27.43,0:00:28.75,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:00:28.75,0:00:32.44,Default,,0000,0000,0000,,We also learned that if\NI have lines like this.
Dialogue: 0,0:00:32.44,0:00:41.14,Default,,0000,0000,0000,,If I have two angles-- let\Nme draw it like that.
Dialogue: 0,0:00:41.14,0:00:43.71,Default,,0000,0000,0000,,\N16\N00:00:43,71 --> 00:00:49,49\NAnd this is angle x.
Dialogue: 0,0:00:49.49,0:00:50.62,Default,,0000,0000,0000,,This is angle y.
Dialogue: 0,0:00:50.62,0:00:54.12,Default,,0000,0000,0000,,\N19\N00:00:54,122 --> 00:00:57,825\Nx and y are supplementary.
Dialogue: 0,0:00:57.82,0:01:04.24,Default,,0000,0000,0000,,\N21\N00:01:04,24 --> 00:01:07,63\NAnd that just means that\Nthey add up to 180 degrees.
Dialogue: 0,0:01:07.63,0:01:10.81,Default,,0000,0000,0000,,x plus y is equal\Nto 180 degrees.
Dialogue: 0,0:01:10.81,0:01:11.92,Default,,0000,0000,0000,,And why does that make sense?
Dialogue: 0,0:01:11.92,0:01:16.20,Default,,0000,0000,0000,,Because look, if we add\Nup x plus y we have gone
Dialogue: 0,0:01:16.20,0:01:19.45,Default,,0000,0000,0000,,halfway around the circle.
Dialogue: 0,0:01:19.45,0:01:22.04,Default,,0000,0000,0000,,So that's 180 degrees, right?
Dialogue: 0,0:01:28.62,0:01:31.38,Default,,0000,0000,0000,,So hopefully we\Nhave learned that.
Dialogue: 0,0:01:31.38,0:01:35.32,Default,,0000,0000,0000,,And then let me switch colors\Nfor the sake of variety.
Dialogue: 0,0:01:35.32,0:01:39.08,Default,,0000,0000,0000,,Let me use my line tool.
Dialogue: 0,0:01:39.08,0:01:44.14,Default,,0000,0000,0000,,If I have-- let's see,\NI'm going to draw
Dialogue: 0,0:01:44.14,0:01:46.05,Default,,0000,0000,0000,,perpendicular lines.
Dialogue: 0,0:01:46.05,0:01:50.22,Default,,0000,0000,0000,,If I have that line, and\Nthen I have that line.
Dialogue: 0,0:01:50.22,0:01:52.08,Default,,0000,0000,0000,,And they are perpendicular.
Dialogue: 0,0:01:52.08,0:01:55.27,Default,,0000,0000,0000,,And then I have another line.
Dialogue: 0,0:01:55.27,0:01:56.87,Default,,0000,0000,0000,,Let's say it goes like that.
Dialogue: 0,0:01:56.87,0:01:59.83,Default,,0000,0000,0000,,\N39\N00:01:59,83 --> 00:02:03,73\NAnd then I say that\Nthis is angle x.
Dialogue: 0,0:02:03.73,0:02:05.03,Default,,0000,0000,0000,,Woops.
Dialogue: 0,0:02:05.03,0:02:07.65,Default,,0000,0000,0000,,This is angle x.
Dialogue: 0,0:02:07.65,0:02:09.24,Default,,0000,0000,0000,,And this is angle y.
Dialogue: 0,0:02:09.24,0:02:12.29,Default,,0000,0000,0000,,\N44\N00:02:12,29 --> 00:02:16,04\NWell, I said this line and this\Nline are perpendicular, right?
Dialogue: 0,0:02:16.04,0:02:18.39,Default,,0000,0000,0000,,So that means that they\Nintersect at a 90 degree angle.
Dialogue: 0,0:02:18.39,0:02:20.71,Default,,0000,0000,0000,,So we know that this whole\Nthing is 90 degrees.
Dialogue: 0,0:02:20.71,0:02:24.07,Default,,0000,0000,0000,,\N48\N00:02:24,07 --> 00:02:26,01\NAnd so what do we\Nknow about x plus y?
Dialogue: 0,0:02:26.01,0:02:29.44,Default,,0000,0000,0000,,Well, x plus y is going\Nto equal 90 degrees.
Dialogue: 0,0:02:29.44,0:02:34.13,Default,,0000,0000,0000,,\N51\N00:02:34,13 --> 00:02:41,33\NOr we could say that x\Nand y are complementary.
Dialogue: 0,0:02:41.33,0:02:43.92,Default,,0000,0000,0000,,And I always get confused\Nbetween supplementary
Dialogue: 0,0:02:43.92,0:02:44.67,Default,,0000,0000,0000,,and complementary.
Dialogue: 0,0:02:44.67,0:02:45.91,Default,,0000,0000,0000,,You just got to memorize it.
Dialogue: 0,0:02:45.91,0:02:47.47,Default,,0000,0000,0000,,I don't know if there's\Nany-- let's see, is
Dialogue: 0,0:02:47.47,0:02:48.65,Default,,0000,0000,0000,,there any easy way?
Dialogue: 0,0:02:48.65,0:02:51.95,Default,,0000,0000,0000,,180, supplementary.
Dialogue: 0,0:02:51.95,0:02:56.89,Default,,0000,0000,0000,,You could say that 180-- 100\Nstarts with an O, which
Dialogue: 0,0:02:56.89,0:02:58.95,Default,,0000,0000,0000,,supplementary does\Nnot start with.
Dialogue: 0,0:02:58.95,0:03:00.08,Default,,0000,0000,0000,,So there.
Dialogue: 0,0:03:00.08,0:03:01.50,Default,,0000,0000,0000,,There's your mnemonic.
Dialogue: 0,0:03:01.50,0:03:02.91,Default,,0000,0000,0000,,Complementary.
Dialogue: 0,0:03:02.91,0:03:05.10,Default,,0000,0000,0000,,And 90 starts with an N,\Nand complementary does
Dialogue: 0,0:03:05.10,0:03:05.92,Default,,0000,0000,0000,,not start with an N.
Dialogue: 0,0:03:05.92,0:03:07.45,Default,,0000,0000,0000,,That's your other mnemonic.
Dialogue: 0,0:03:07.45,0:03:07.93,Default,,0000,0000,0000,,Complementary.
Dialogue: 0,0:03:07.93,0:03:15.42,Default,,0000,0000,0000,,\N68\N00:03:15,42 --> 00:03:16,59\NI don't know if I'm\Nspelling it right.
Dialogue: 0,0:03:16.59,0:03:17.59,Default,,0000,0000,0000,,Who cares?
Dialogue: 0,0:03:17.59,0:03:18.75,Default,,0000,0000,0000,,Let's move on.
Dialogue: 0,0:03:18.75,0:03:20.19,Default,,0000,0000,0000,,So let's learn some more\Nstuff about angles.
Dialogue: 0,0:03:20.19,0:03:22.49,Default,,0000,0000,0000,,And what I'm going to do is I'm\Ngoing to give you an arsenal,
Dialogue: 0,0:03:22.49,0:03:25.64,Default,,0000,0000,0000,,and then once you have that\Narsenal you can just tackle
Dialogue: 0,0:03:25.64,0:03:28.28,Default,,0000,0000,0000,,these beastly problems that\NI'm going to throw at you.
Dialogue: 0,0:03:28.28,0:03:31.96,Default,,0000,0000,0000,,So just take these for granted\Nright now, and then in a few
Dialogue: 0,0:03:31.96,0:03:34.63,Default,,0000,0000,0000,,videos, probably, we're\Ngoing to tackle some
Dialogue: 0,0:03:34.63,0:03:35.50,Default,,0000,0000,0000,,beastly problems.
Dialogue: 0,0:03:35.50,0:03:38.22,Default,,0000,0000,0000,,\N79\N00:03:38,22 --> 00:03:40,48\NAnd you know, I'm\Nusing variables here.
Dialogue: 0,0:03:40.48,0:03:41.49,Default,,0000,0000,0000,,And if you're not familiar\Nwith variables you
Dialogue: 0,0:03:41.49,0:03:42.14,Default,,0000,0000,0000,,can put numbers here.
Dialogue: 0,0:03:42.14,0:03:46.05,Default,,0000,0000,0000,,If x was 30 degrees, then y\Nis going to be 60 degrees.
Dialogue: 0,0:03:46.05,0:03:46.67,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:03:46.67,0:03:51.05,Default,,0000,0000,0000,,Or in this case, if x is, I\Ndon't know, 45 degrees, then y
Dialogue: 0,0:03:51.05,0:03:53.96,Default,,0000,0000,0000,,is going to be 135 degrees.
Dialogue: 0,0:03:53.96,0:03:54.56,Default,,0000,0000,0000,,That other way.
Dialogue: 0,0:03:54.56,0:03:59.29,Default,,0000,0000,0000,,Let me draw another property of\Nangles of intersecting lines.
Dialogue: 0,0:03:59.29,0:04:05.89,Default,,0000,0000,0000,,So if I have two angles, two\Nlines that intersect like this.
Dialogue: 0,0:04:05.89,0:04:08.56,Default,,0000,0000,0000,,\N90\N00:04:08,56 --> 00:04:10,76\NSo a couple of\Ninteresting things.
Dialogue: 0,0:04:10.76,0:04:14.70,Default,,0000,0000,0000,,So first, I'm going to teach\Nyou about opposite angles.
Dialogue: 0,0:04:14.70,0:04:17.49,Default,,0000,0000,0000,,\N93\N00:04:17,49 --> 00:04:19,51\NLet me switch colors.
Dialogue: 0,0:04:19.51,0:04:22.86,Default,,0000,0000,0000,,Let me switch to yellow.
Dialogue: 0,0:04:22.86,0:04:30.71,Default,,0000,0000,0000,,So if this is x degrees, then\Nit turns out that the angle
Dialogue: 0,0:04:30.71,0:04:34.11,Default,,0000,0000,0000,,opposite to it is also\Nequal to x degrees.
Dialogue: 0,0:04:34.11,0:04:40.43,Default,,0000,0000,0000,,\N98\N00:04:40,43 --> 00:04:42,18\NAnd you don't believe me?
Dialogue: 0,0:04:42.18,0:04:44.55,Default,,0000,0000,0000,,Well let me prove it to you.
Dialogue: 0,0:04:44.55,0:04:49.90,Default,,0000,0000,0000,,Let's say we call this,\NI don't know, let's
Dialogue: 0,0:04:49.90,0:04:52.80,Default,,0000,0000,0000,,call this y degrees.
Dialogue: 0,0:04:52.80,0:04:53.56,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:04:53.56,0:04:55.52,Default,,0000,0000,0000,,And I'm going to prove\Nto you that the x and
Dialogue: 0,0:04:55.52,0:04:57.02,Default,,0000,0000,0000,,the y are the same.
Dialogue: 0,0:04:57.02,0:04:58.68,Default,,0000,0000,0000,,Well what do we know already?
Dialogue: 0,0:04:58.68,0:05:01.64,Default,,0000,0000,0000,,Let's call this other angle--\Nand I'm doing this to
Dialogue: 0,0:05:01.64,0:05:10.53,Default,,0000,0000,0000,,confuse you-- angle z.
Dialogue: 0,0:05:10.53,0:05:14.94,Default,,0000,0000,0000,,Well what do we know about\Nangle x and angle z?
Dialogue: 0,0:05:14.94,0:05:17.16,Default,,0000,0000,0000,,It may not be obvious to you\Nbecause I've drawn it slightly
Dialogue: 0,0:05:17.16,0:05:21.35,Default,,0000,0000,0000,,different, but I'll give you\Na small hint with
Dialogue: 0,0:05:21.35,0:05:26.31,Default,,0000,0000,0000,,an appropriately\Ninteresting color.
Dialogue: 0,0:05:26.31,0:05:31.87,Default,,0000,0000,0000,,So what angle is this\Nwhole thing right here?
Dialogue: 0,0:05:31.87,0:05:33.55,Default,,0000,0000,0000,,Well I'm just going\Nalong a line, right?
Dialogue: 0,0:05:33.55,0:05:35.60,Default,,0000,0000,0000,,That's halfway around a circle.
Dialogue: 0,0:05:39.19,0:05:41.25,Default,,0000,0000,0000,,So what does x plus z equal?
Dialogue: 0,0:05:41.25,0:05:44.82,Default,,0000,0000,0000,,Well, x plus z is going to\Nequal that larger angle.
Dialogue: 0,0:05:44.82,0:05:54.04,Default,,0000,0000,0000,,x plus purple z is going to\Nequal-- I think I'll switch to
Dialogue: 0,0:05:54.04,0:05:57.03,Default,,0000,0000,0000,,the blue; maybe it's taking too\Nmuch time for me to switch--
Dialogue: 0,0:05:57.03,0:05:58.89,Default,,0000,0000,0000,,is equal to 180 degrees.
Dialogue: 0,0:05:58.89,0:06:03.58,Default,,0000,0000,0000,,Or x and z are supplementary.
Dialogue: 0,0:06:03.58,0:06:09.24,Default,,0000,0000,0000,,\N124\N00:06:09,24 --> 00:06:10,63\NI've run out of space.
Dialogue: 0,0:06:10.63,0:06:12.90,Default,,0000,0000,0000,,So what do we know about z?
Dialogue: 0,0:06:12.90,0:06:20.40,Default,,0000,0000,0000,,Well z is equal to 180 minus x.
Dialogue: 0,0:06:20.40,0:06:20.75,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:20.75,0:06:23.07,Default,,0000,0000,0000,,Because x plus z is 180.
Dialogue: 0,0:06:23.07,0:06:24.54,Default,,0000,0000,0000,,Fine.
Dialogue: 0,0:06:24.54,0:06:27.85,Default,,0000,0000,0000,,Now, what's the relationship\Nbetween z and y?
Dialogue: 0,0:06:27.85,0:06:31.77,Default,,0000,0000,0000,,Well, z and y are\Nalso supplementary.
Dialogue: 0,0:06:31.77,0:06:37.21,Default,,0000,0000,0000,,Because look, if I\Ndrew this angle here.
Dialogue: 0,0:06:37.21,0:06:38.79,Default,,0000,0000,0000,,Look at this big angle.
Dialogue: 0,0:06:38.79,0:06:42.07,Default,,0000,0000,0000,,\N135\N00:06:42,07 --> 00:06:42,69\NWhat angle is that?
Dialogue: 0,0:06:42.69,0:06:45.26,Default,,0000,0000,0000,,Well once again I'm still going\Nhalfway around the circle.
Dialogue: 0,0:06:45.26,0:06:45.99,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:45.99,0:06:48.39,Default,,0000,0000,0000,,But now I'm using this\Nline right here.
Dialogue: 0,0:06:48.39,0:06:51.23,Default,,0000,0000,0000,,So that's 180 degrees.
Dialogue: 0,0:06:51.23,0:06:56.44,Default,,0000,0000,0000,,So we know that angle z\Nplus angle y is also
Dialogue: 0,0:06:56.44,0:06:57.68,Default,,0000,0000,0000,,equal to 180 degrees.
Dialogue: 0,0:06:57.68,0:07:05.54,Default,,0000,0000,0000,,\N143\N00:07:05,54 --> 00:07:06,82\NRight?
Dialogue: 0,0:07:06.82,0:07:08.93,Default,,0000,0000,0000,,Or, I don't want to keep\Nwriting it, but z and y
Dialogue: 0,0:07:08.93,0:07:11.67,Default,,0000,0000,0000,,are also supplementary.
Dialogue: 0,0:07:11.67,0:07:14.50,Default,,0000,0000,0000,,But we just figured out\Nthat z is 180 minus x.
Dialogue: 0,0:07:14.50,0:07:15.14,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:07:15.14,0:07:18.96,Default,,0000,0000,0000,,So let's just substitute\Nthat back in here.
Dialogue: 0,0:07:18.96,0:07:29.42,Default,,0000,0000,0000,,So we get 180 minus x plus\Ny is equal to 180 degrees.
Dialogue: 0,0:07:29.42,0:07:31.69,Default,,0000,0000,0000,,Why don't we subtract 180\Ndegrees from both sides
Dialogue: 0,0:07:31.69,0:07:32.96,Default,,0000,0000,0000,,of this equation.
Dialogue: 0,0:07:32.96,0:07:39.54,Default,,0000,0000,0000,,That cancels out, and we get\Nminus x plus y is equal to 0.
Dialogue: 0,0:07:39.54,0:07:41.73,Default,,0000,0000,0000,,And then add x to both sides\Nof this equation, and
Dialogue: 0,0:07:41.73,0:07:46.03,Default,,0000,0000,0000,,we get y is equal to x.
Dialogue: 0,0:07:52.08,0:07:54.95,Default,,0000,0000,0000,,So x is equal to y.
Dialogue: 0,0:07:54.95,0:07:56.73,Default,,0000,0000,0000,,And if you've played around\Nwith this, if you just drew a
Dialogue: 0,0:07:56.73,0:07:59.16,Default,,0000,0000,0000,,bunch of straight lines and\Nthey intersected at different
Dialogue: 0,0:07:59.16,0:08:02.72,Default,,0000,0000,0000,,angles, I think when you\Neyeball it it would make sense.
Dialogue: 0,0:08:02.72,0:08:06.59,Default,,0000,0000,0000,,And then similarly, if that's z\Nthen the other opposite angle
Dialogue: 0,0:08:06.59,0:08:15.51,Default,,0000,0000,0000,,here is also z degrees.
Dialogue: 0,0:08:15.51,0:08:16.79,Default,,0000,0000,0000,,So what do we know now?
Dialogue: 0,0:08:16.79,0:08:20.87,Default,,0000,0000,0000,,The total angles in a\Ncircle, 360 degrees.
Dialogue: 0,0:08:20.87,0:08:24.38,Default,,0000,0000,0000,,When two angles kind of\Ncombine, go halfway around the
Dialogue: 0,0:08:24.38,0:08:28.52,Default,,0000,0000,0000,,circle-- or they combine,\Nkind of form a line.
Dialogue: 0,0:08:28.52,0:08:30.53,Default,,0000,0000,0000,,There's different ways\Nyou can think about it.
Dialogue: 0,0:08:30.53,0:08:31.37,Default,,0000,0000,0000,,We know they're supplementary.
Dialogue: 0,0:08:31.37,0:08:33.35,Default,,0000,0000,0000,,They add up to 180 degrees.
Dialogue: 0,0:08:33.35,0:08:34.92,Default,,0000,0000,0000,,x plus y is 180 degrees.
Dialogue: 0,0:08:34.92,0:08:38.36,Default,,0000,0000,0000,,If they add up to 90\Nit's complementary.
Dialogue: 0,0:08:38.36,0:08:39.57,Default,,0000,0000,0000,,x plus y is 90.
Dialogue: 0,0:08:39.57,0:08:42.02,Default,,0000,0000,0000,,And then opposite angles\Nare equal to each other.
Dialogue: 0,0:08:42.02,0:08:42.35,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:08:42.35,0:08:46.13,Default,,0000,0000,0000,,This angle is equal\Nto this angle.
Dialogue: 0,0:08:46.13,0:08:49.31,Default,,0000,0000,0000,,And then this angle is going to\Nbe equal to this angle for the
Dialogue: 0,0:08:49.31,0:08:50.99,Default,,0000,0000,0000,,same reason-- because\Nit's opposite.
Dialogue: 0,0:08:50.99,0:08:54.36,Default,,0000,0000,0000,,In the next video I'm going\Nto show you about parallel
Dialogue: 0,0:08:54.36,0:08:55.94,Default,,0000,0000,0000,,lines and transversals.
Dialogue: 0,0:08:55.94,0:08:59.17,Default,,0000,0000,0000,,More fancy words for what\NI think are fairly
Dialogue: 0,0:08:59.17,0:09:00.52,Default,,0000,0000,0000,,straightforward concepts.
Dialogue: 0,0:09:00.52,0:09:03.80,Default,,0000,0000,0000,,I'll see you in the next video.