[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.49,0:00:02.32,Default,,0000,0000,0000,,In this video we're going to\Nthink a little bit about
Dialogue: 0,0:00:02.32,0:00:11.58,Default,,0000,0000,0000,,parallel lines, and other lines\Nthat intersect the parallel
Dialogue: 0,0:00:11.58,0:00:13.78,Default,,0000,0000,0000,,lines, and we call\Nthose transversals.
Dialogue: 0,0:00:13.78,0:00:16.81,Default,,0000,0000,0000,,So first let's think about\Nwhat a parallel or what
Dialogue: 0,0:00:16.81,0:00:18.49,Default,,0000,0000,0000,,parallel lines are.
Dialogue: 0,0:00:18.49,0:00:21.70,Default,,0000,0000,0000,,So one definition we could use,\Nand I think that'll work well
Dialogue: 0,0:00:21.70,0:00:24.22,Default,,0000,0000,0000,,for the purposes of this video,\Nare they're two lines that
Dialogue: 0,0:00:24.22,0:00:25.66,Default,,0000,0000,0000,,sit in the same plane.
Dialogue: 0,0:00:25.66,0:00:29.09,Default,,0000,0000,0000,,And when I talk about a plane,\NI'm talking about a, you can
Dialogue: 0,0:00:29.09,0:00:32.49,Default,,0000,0000,0000,,imagine a flat two-dimensional\Nsurface like this screen --
Dialogue: 0,0:00:32.49,0:00:33.91,Default,,0000,0000,0000,,this screen is a plane.
Dialogue: 0,0:00:33.91,0:00:37.73,Default,,0000,0000,0000,,So two lines that sit in a\Nplane that never intersect.
Dialogue: 0,0:00:37.73,0:00:41.57,Default,,0000,0000,0000,,So this line -- I'll try my\Nbest to draw it -- and imagine
Dialogue: 0,0:00:41.57,0:00:43.75,Default,,0000,0000,0000,,the line just keeps going in\Nthat direction and that
Dialogue: 0,0:00:43.75,0:00:47.28,Default,,0000,0000,0000,,direction -- let me do another\None in a different color --
Dialogue: 0,0:00:47.28,0:00:52.05,Default,,0000,0000,0000,,and this line right\Nhere are parallel.
Dialogue: 0,0:00:52.05,0:00:53.69,Default,,0000,0000,0000,,They will never intersect.
Dialogue: 0,0:00:53.69,0:00:55.66,Default,,0000,0000,0000,,If you assume that I drew it\Nstraight enough and that
Dialogue: 0,0:00:55.66,0:00:58.00,Default,,0000,0000,0000,,they're going in the exact\Nsame direction, they
Dialogue: 0,0:00:58.00,0:00:59.84,Default,,0000,0000,0000,,will never intersect.
Dialogue: 0,0:00:59.84,0:01:02.07,Default,,0000,0000,0000,,And so if you think about what\Ntypes of lines are not
Dialogue: 0,0:01:02.07,0:01:07.84,Default,,0000,0000,0000,,parallel, well, this green line\Nand this pink line
Dialogue: 0,0:01:07.84,0:01:08.94,Default,,0000,0000,0000,,are not parallel.
Dialogue: 0,0:01:08.94,0:01:11.94,Default,,0000,0000,0000,,They clearly intersect\Nat some point.
Dialogue: 0,0:01:11.94,0:01:15.35,Default,,0000,0000,0000,,So these two guys are parallel\Nright over here, and sometimes
Dialogue: 0,0:01:15.35,0:01:18.69,Default,,0000,0000,0000,,it's specified, sometimes\Npeople will draw an arrow going
Dialogue: 0,0:01:18.69,0:01:20.90,Default,,0000,0000,0000,,in the same direction to show\Nthat those two lines
Dialogue: 0,0:01:20.90,0:01:21.84,Default,,0000,0000,0000,,are parallel.
Dialogue: 0,0:01:21.84,0:01:24.40,Default,,0000,0000,0000,,If there are multiple parallel\Nlines, they might do two arrows
Dialogue: 0,0:01:24.40,0:01:25.76,Default,,0000,0000,0000,,and two arrows or whatever.
Dialogue: 0,0:01:25.76,0:01:27.27,Default,,0000,0000,0000,,But you just have to say\NOK, these lines will
Dialogue: 0,0:01:27.27,0:01:28.55,Default,,0000,0000,0000,,never intersect.
Dialogue: 0,0:01:28.55,0:01:31.06,Default,,0000,0000,0000,,What we want to think about\Nis what happens when
Dialogue: 0,0:01:31.06,0:01:36.20,Default,,0000,0000,0000,,these parallel lines are\Nintersected by a third line.
Dialogue: 0,0:01:36.20,0:01:37.82,Default,,0000,0000,0000,,Let me draw the\Nthird line here.
Dialogue: 0,0:01:37.82,0:01:41.69,Default,,0000,0000,0000,,So third line like this.
Dialogue: 0,0:01:41.69,0:01:45.97,Default,,0000,0000,0000,,And we call that, right there,\Nthe third line that intersects
Dialogue: 0,0:01:45.97,0:01:52.17,Default,,0000,0000,0000,,the parallel lines we\Ncall a transversal line.
Dialogue: 0,0:01:52.17,0:01:56.15,Default,,0000,0000,0000,,Because it tranverses\Nthe two parallel lines.
Dialogue: 0,0:01:56.15,0:01:59.23,Default,,0000,0000,0000,,Now whenever you have a\Ntransversal crossing parallel
Dialogue: 0,0:01:59.23,0:02:02.19,Default,,0000,0000,0000,,lines, you have an interesting\Nrelationship between
Dialogue: 0,0:02:02.19,0:02:03.32,Default,,0000,0000,0000,,the angles form.
Dialogue: 0,0:02:03.32,0:02:05.66,Default,,0000,0000,0000,,Now this shows up on a lot\Nof standardized tests.
Dialogue: 0,0:02:05.66,0:02:09.20,Default,,0000,0000,0000,,It's kind of a core type\Nof a geometry problem.
Dialogue: 0,0:02:09.20,0:02:12.45,Default,,0000,0000,0000,,So it's a good thing to really\Nget clear in our heads.
Dialogue: 0,0:02:12.45,0:02:15.62,Default,,0000,0000,0000,,So the first thing to realize\Nis if these lines are parallel,
Dialogue: 0,0:02:15.62,0:02:18.35,Default,,0000,0000,0000,,we're going to assume these\Nlines are parallel, then we
Dialogue: 0,0:02:18.35,0:02:21.76,Default,,0000,0000,0000,,have corresponding angles\Nare going to be the same.
Dialogue: 0,0:02:21.76,0:02:25.82,Default,,0000,0000,0000,,What I mean by corresponding\Nangles are I guess you could
Dialogue: 0,0:02:25.82,0:02:28.84,Default,,0000,0000,0000,,think there are four angles\Nthat get formed when this
Dialogue: 0,0:02:28.84,0:02:31.20,Default,,0000,0000,0000,,purple line or this\Nmagenta line intersects
Dialogue: 0,0:02:31.20,0:02:32.35,Default,,0000,0000,0000,,this yellow line.
Dialogue: 0,0:02:32.35,0:02:38.07,Default,,0000,0000,0000,,You have this angle up here\Nthat I've specified in green,
Dialogue: 0,0:02:38.07,0:02:42.97,Default,,0000,0000,0000,,you have -- let me do another\None in orange -- you have this
Dialogue: 0,0:02:42.97,0:02:48.28,Default,,0000,0000,0000,,angle right here in orange, you\Nhave this angle right here in
Dialogue: 0,0:02:48.28,0:02:52.60,Default,,0000,0000,0000,,this other shade of green, and\Nthen you have this angle
Dialogue: 0,0:02:52.60,0:02:55.29,Default,,0000,0000,0000,,right here -- right there\Nthat I've made in that
Dialogue: 0,0:02:55.29,0:02:56.93,Default,,0000,0000,0000,,bluish-purplish color.
Dialogue: 0,0:02:56.93,0:02:58.79,Default,,0000,0000,0000,,So those are the four angles.
Dialogue: 0,0:02:58.79,0:03:01.68,Default,,0000,0000,0000,,So when we talk about\Ncorresponding angles, we're
Dialogue: 0,0:03:01.68,0:03:04.77,Default,,0000,0000,0000,,talking about, for example,\Nthis top right angle in green
Dialogue: 0,0:03:04.77,0:03:08.93,Default,,0000,0000,0000,,up here, that corresponds to\Nthis top right angle in, what
Dialogue: 0,0:03:08.93,0:03:12.04,Default,,0000,0000,0000,,I can draw it in that same\Ngreen, right over here.
Dialogue: 0,0:03:12.04,0:03:14.57,Default,,0000,0000,0000,,These two angles\Nare corresponding.
Dialogue: 0,0:03:14.57,0:03:17.99,Default,,0000,0000,0000,,These two are corresponding\Nangles and they're
Dialogue: 0,0:03:17.99,0:03:19.52,Default,,0000,0000,0000,,going to be equal.
Dialogue: 0,0:03:19.52,0:03:20.82,Default,,0000,0000,0000,,These are equal angles.
Dialogue: 0,0:03:20.82,0:03:24.41,Default,,0000,0000,0000,,If this is -- I'll make up\Na number -- if this is 70
Dialogue: 0,0:03:24.41,0:03:27.88,Default,,0000,0000,0000,,degrees, then this angle\Nright here is also
Dialogue: 0,0:03:27.88,0:03:29.41,Default,,0000,0000,0000,,going to be 70 degrees.
Dialogue: 0,0:03:29.41,0:03:32.00,Default,,0000,0000,0000,,And if you just think about it,\Nor if you even play with
Dialogue: 0,0:03:32.00,0:03:35.15,Default,,0000,0000,0000,,toothpicks or something, and\Nyou keep changing the direction
Dialogue: 0,0:03:35.15,0:03:38.14,Default,,0000,0000,0000,,of this transversal line,\Nyou'll see that it actually
Dialogue: 0,0:03:38.14,0:03:40.75,Default,,0000,0000,0000,,looks like they should\Nalways be equal.
Dialogue: 0,0:03:40.75,0:03:43.20,Default,,0000,0000,0000,,If I were to take -- let me\Ndraw two other parallel
Dialogue: 0,0:03:43.20,0:03:45.98,Default,,0000,0000,0000,,lines, let me show maybe\Na more extreme example.
Dialogue: 0,0:03:45.98,0:03:50.35,Default,,0000,0000,0000,,So if I have two other parallel\Nlines like that, and then let
Dialogue: 0,0:03:50.35,0:03:57.34,Default,,0000,0000,0000,,me make a transversal that\Nforms a smaller -- it's even a
Dialogue: 0,0:03:57.34,0:03:59.93,Default,,0000,0000,0000,,smaller angle here -- you see\Nthat this angle right here
Dialogue: 0,0:03:59.93,0:04:02.07,Default,,0000,0000,0000,,looks the same as that angle.
Dialogue: 0,0:04:02.07,0:04:05.34,Default,,0000,0000,0000,,Those are corresponding angles\Nand they will be equivalent.
Dialogue: 0,0:04:05.34,0:04:08.33,Default,,0000,0000,0000,,From this perspective it's kind\Nof the top right angle and each
Dialogue: 0,0:04:08.33,0:04:10.43,Default,,0000,0000,0000,,intersection is the same.
Dialogue: 0,0:04:10.43,0:04:13.60,Default,,0000,0000,0000,,Now the same is true of the\Nother corresponding angles.
Dialogue: 0,0:04:13.60,0:04:16.66,Default,,0000,0000,0000,,This angle right here in this\Nexample, it's the top left
Dialogue: 0,0:04:16.66,0:04:21.12,Default,,0000,0000,0000,,angle will be the same as the\Ntop left angle right over here.
Dialogue: 0,0:04:21.12,0:04:27.08,Default,,0000,0000,0000,,This bottom left angle will\Nbe the same down here.
Dialogue: 0,0:04:27.08,0:04:30.00,Default,,0000,0000,0000,,If this right here is 70\Ndegrees, then this down here
Dialogue: 0,0:04:30.00,0:04:32.04,Default,,0000,0000,0000,,will also be 70 degrees.
Dialogue: 0,0:04:32.04,0:04:36.04,Default,,0000,0000,0000,,And then finally, of course,\Nthis angle and this angle
Dialogue: 0,0:04:36.04,0:04:37.99,Default,,0000,0000,0000,,will also be the same.
Dialogue: 0,0:04:37.99,0:04:41.52,Default,,0000,0000,0000,,So corresponding angles -- let\Nme write these -- these are
Dialogue: 0,0:04:41.52,0:04:43.17,Default,,0000,0000,0000,,corresponding angles\Nare congruent.
Dialogue: 0,0:04:46.64,0:04:55.18,Default,,0000,0000,0000,,Corresponding angles are equal.
Dialogue: 0,0:04:55.18,0:04:57.05,Default,,0000,0000,0000,,And that and that are\Ncorresponding, that and
Dialogue: 0,0:04:57.05,0:04:59.40,Default,,0000,0000,0000,,that, that and that,\Nand that and that.
Dialogue: 0,0:04:59.40,0:05:04.60,Default,,0000,0000,0000,,Now, the next set of equal\Nangles to realize are sometimes
Dialogue: 0,0:05:04.60,0:05:06.61,Default,,0000,0000,0000,,they're called vertical angles,\Nsometimes they're called
Dialogue: 0,0:05:06.61,0:05:08.44,Default,,0000,0000,0000,,opposite angles.
Dialogue: 0,0:05:08.44,0:05:11.70,Default,,0000,0000,0000,,But if you take this angle\Nright here, the angle that is
Dialogue: 0,0:05:11.70,0:05:15.06,Default,,0000,0000,0000,,vertical to it or is opposite\Nas you go right across the
Dialogue: 0,0:05:15.06,0:05:18.65,Default,,0000,0000,0000,,point of intersection is this\Nangle right here, and that is
Dialogue: 0,0:05:18.65,0:05:20.58,Default,,0000,0000,0000,,going to be the same thing.
Dialogue: 0,0:05:20.58,0:05:23.86,Default,,0000,0000,0000,,So we could say opposite -- I\Nlike opposite because it's not
Dialogue: 0,0:05:23.86,0:05:25.72,Default,,0000,0000,0000,,always in the vertical\Ndirection, sometimes it's in
Dialogue: 0,0:05:25.72,0:05:27.65,Default,,0000,0000,0000,,the horizontal direction, but\Nsometimes they're referred
Dialogue: 0,0:05:27.65,0:05:29.40,Default,,0000,0000,0000,,to as vertical angles.
Dialogue: 0,0:05:29.40,0:05:37.37,Default,,0000,0000,0000,,Opposite or vertical\Nangles are also equal.
Dialogue: 0,0:05:37.37,0:05:40.94,Default,,0000,0000,0000,,So if that's 70 degrees, then\Nthis is also 70 degrees.
Dialogue: 0,0:05:40.94,0:05:43.98,Default,,0000,0000,0000,,And if this is 70 degrees,\Nthen this right here
Dialogue: 0,0:05:43.98,0:05:46.71,Default,,0000,0000,0000,,is also 70 degrees.
Dialogue: 0,0:05:46.71,0:05:49.24,Default,,0000,0000,0000,,So it's interesting, if that's\N70 degrees and that's 70
Dialogue: 0,0:05:49.24,0:05:52.23,Default,,0000,0000,0000,,degrees, and if this is 70\Ndegrees and that is also 70
Dialogue: 0,0:05:52.23,0:05:55.75,Default,,0000,0000,0000,,degrees, so no matter what this\Nis, this will also be the same
Dialogue: 0,0:05:55.75,0:05:58.06,Default,,0000,0000,0000,,thing because this is\Nthe same as that, that
Dialogue: 0,0:05:58.06,0:05:59.77,Default,,0000,0000,0000,,is the same as that.
Dialogue: 0,0:05:59.77,0:06:07.18,Default,,0000,0000,0000,,Now, the last one that you need\Nto I guess kind of realize are
Dialogue: 0,0:06:07.18,0:06:09.87,Default,,0000,0000,0000,,the relationship between\Nthis orange angle and this
Dialogue: 0,0:06:09.87,0:06:11.86,Default,,0000,0000,0000,,green angle right there.
Dialogue: 0,0:06:11.86,0:06:17.89,Default,,0000,0000,0000,,You can see that when you add\Nup the angles, you go halfway
Dialogue: 0,0:06:17.89,0:06:19.71,Default,,0000,0000,0000,,around a circle, right?
Dialogue: 0,0:06:19.71,0:06:22.23,Default,,0000,0000,0000,,If you start here you do\Nthe green angle, then
Dialogue: 0,0:06:22.23,0:06:23.57,Default,,0000,0000,0000,,you do the orange angle.
Dialogue: 0,0:06:23.57,0:06:26.60,Default,,0000,0000,0000,,You go halfway around the\Ncircle, and that'll give you,
Dialogue: 0,0:06:26.60,0:06:28.72,Default,,0000,0000,0000,,it'll get you to 180 degrees.
Dialogue: 0,0:06:28.72,0:06:32.87,Default,,0000,0000,0000,,So this green and orange angle\Nhave to add up to 180 degrees
Dialogue: 0,0:06:32.87,0:06:34.71,Default,,0000,0000,0000,,or they are supplementary.
Dialogue: 0,0:06:34.71,0:06:37.12,Default,,0000,0000,0000,,And we've done other videos on\Nsupplementary, but you just
Dialogue: 0,0:06:37.12,0:06:40.72,Default,,0000,0000,0000,,have to realize they form the\Nsame line or a half circle.
Dialogue: 0,0:06:40.72,0:06:43.99,Default,,0000,0000,0000,,So if this right here is 70\Ndegrees, then this orange angle
Dialogue: 0,0:06:43.99,0:06:50.72,Default,,0000,0000,0000,,right here is 110 degrees,\Nbecause they add up to 180.
Dialogue: 0,0:06:50.72,0:06:54.32,Default,,0000,0000,0000,,Now, if this character right\Nhere is 110 degrees, what
Dialogue: 0,0:06:54.32,0:06:56.66,Default,,0000,0000,0000,,do we know about this\Ncharacter right here?
Dialogue: 0,0:06:56.66,0:06:59.37,Default,,0000,0000,0000,,Well, this character is\Nopposite or vertical
Dialogue: 0,0:06:59.37,0:07:02.45,Default,,0000,0000,0000,,to the 110 degrees so\Nit's also 110 degrees.
Dialogue: 0,0:07:02.45,0:07:06.37,Default,,0000,0000,0000,,We also know since this angle\Ncorresponds with this angle,
Dialogue: 0,0:07:06.37,0:07:09.36,Default,,0000,0000,0000,,this angle will also\Nbe 110 degrees.
Dialogue: 0,0:07:09.36,0:07:11.83,Default,,0000,0000,0000,,Or we could have said that\Nlook, because this is 70 and
Dialogue: 0,0:07:11.83,0:07:14.18,Default,,0000,0000,0000,,this guy is supplementary,\Nthese guys have to add up to
Dialogue: 0,0:07:14.18,0:07:16.18,Default,,0000,0000,0000,,180 so you could have\Ngotten it that way.
Dialogue: 0,0:07:16.18,0:07:19.27,Default,,0000,0000,0000,,And you could also figure out\Nthat since this is 110, this
Dialogue: 0,0:07:19.27,0:07:22.30,Default,,0000,0000,0000,,is a corresponding angle,\Nit is also going to be 110.
Dialogue: 0,0:07:22.30,0:07:25.19,Default,,0000,0000,0000,,Or you could have said\Nthis is opposite to
Dialogue: 0,0:07:25.19,0:07:26.43,Default,,0000,0000,0000,,that so they're equal.
Dialogue: 0,0:07:26.43,0:07:30.80,Default,,0000,0000,0000,,Or you could have said that\Nthis is supplementary with
Dialogue: 0,0:07:30.80,0:07:34.15,Default,,0000,0000,0000,,that angle, so 70 plus\N110 have to be 180.
Dialogue: 0,0:07:34.15,0:07:38.60,Default,,0000,0000,0000,,Or you could have said 70\Nplus this angle are 180.
Dialogue: 0,0:07:38.60,0:07:41.81,Default,,0000,0000,0000,,So there's a bunch of ways\Nto come to figure out
Dialogue: 0,0:07:41.81,0:07:43.74,Default,,0000,0000,0000,,which angle is which.
Dialogue: 0,0:07:43.74,0:07:46.00,Default,,0000,0000,0000,,In the next video I'm just\Ngoing to do a bunch of examples
Dialogue: 0,0:07:46.00,0:07:48.99,Default,,0000,0000,0000,,just to show that if you know\None of these angles, you
Dialogue: 0,0:07:48.99,0:07:51.88,Default,,0000,0000,0000,,can really figure out\Nall of the angles.