[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.69,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.69,0:00:01.81,Default,,0000,0000,0000,,Welcome back.
Dialogue: 0,0:00:01.81,0:00:04.82,Default,,0000,0000,0000,,So where we had left off, we\Nsaid, OK, we have this angle
Dialogue: 0,0:00:04.82,0:00:07.72,Default,,0000,0000,0000,,here, can we figure out if\Nany of these angles
Dialogue: 0,0:00:07.72,0:00:08.93,Default,,0000,0000,0000,,are equal to it?
Dialogue: 0,0:00:08.93,0:00:14.75,Default,,0000,0000,0000,,Well we know that alternate\Ninterior angles on-- this is a
Dialogue: 0,0:00:14.75,0:00:17.78,Default,,0000,0000,0000,,transversal line right here,\Nand these are parallel lines.
Dialogue: 0,0:00:17.78,0:00:18.94,Default,,0000,0000,0000,,So we know alternate interior.
Dialogue: 0,0:00:18.94,0:00:21.32,Default,,0000,0000,0000,,So this is an interior and it's\Nalternate interior is here.
Dialogue: 0,0:00:21.32,0:00:23.34,Default,,0000,0000,0000,,So we know they\Nequal each other.
Dialogue: 0,0:00:23.34,0:00:25.52,Default,,0000,0000,0000,,I'm not going to draw it yet,\Nbecause sometimes if you forget
Dialogue: 0,0:00:25.52,0:00:27.68,Default,,0000,0000,0000,,alternate interior you could\Njust remember, well,
Dialogue: 0,0:00:27.68,0:00:29.46,Default,,0000,0000,0000,,corresponding angles\Nequal each other.
Dialogue: 0,0:00:29.46,0:00:31.41,Default,,0000,0000,0000,,So you could say that\Nthat angle is also
Dialogue: 0,0:00:31.41,0:00:32.88,Default,,0000,0000,0000,,equal to this angle.
Dialogue: 0,0:00:32.88,0:00:35.46,Default,,0000,0000,0000,,And then you can use opposite\Nangles again to kind of get
Dialogue: 0,0:00:35.46,0:00:37.66,Default,,0000,0000,0000,,back to the alternate interior.
Dialogue: 0,0:00:37.66,0:00:38.49,Default,,0000,0000,0000,,I'll show you.
Dialogue: 0,0:00:38.49,0:00:40.90,Default,,0000,0000,0000,,The great thing about math is\Nit's good for people who have
Dialogue: 0,0:00:40.90,0:00:42.52,Default,,0000,0000,0000,,trouble memorizing things,\Nbecause you have to just
Dialogue: 0,0:00:42.52,0:00:45.53,Default,,0000,0000,0000,,memorize a few things and\Nthen everything else just
Dialogue: 0,0:00:45.53,0:00:46.52,Default,,0000,0000,0000,,kind of falls out of it.
Dialogue: 0,0:00:46.52,0:00:47.22,Default,,0000,0000,0000,,But anyway.
Dialogue: 0,0:00:47.22,0:00:51.02,Default,,0000,0000,0000,,So we figured out that\Nthis angle is the
Dialogue: 0,0:00:51.02,0:00:52.44,Default,,0000,0000,0000,,same as this angle.
Dialogue: 0,0:00:52.44,0:00:52.65,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:00:52.65,0:00:55.55,Default,,0000,0000,0000,,Because they're alternate\Ninterior angles.
Dialogue: 0,0:00:55.55,0:01:00.32,Default,,0000,0000,0000,,And this is its\Ncorresponding side.
Dialogue: 0,0:01:00.32,0:01:03.03,Default,,0000,0000,0000,,And then finally, what\Nabout this angle here?
Dialogue: 0,0:01:03.03,0:01:05.27,Default,,0000,0000,0000,,I'm going to draw\Na triple angle.
Dialogue: 0,0:01:05.27,0:01:08.64,Default,,0000,0000,0000,,One, two, three.
Dialogue: 0,0:01:08.64,0:01:11.40,Default,,0000,0000,0000,,What is that one equal\Nto on this triangle?
Dialogue: 0,0:01:11.40,0:01:13.23,Default,,0000,0000,0000,,Well, same reason.
Dialogue: 0,0:01:13.23,0:01:15.99,Default,,0000,0000,0000,,Alternate interior angles of\Ntwo parallel lines-- and
Dialogue: 0,0:01:15.99,0:01:18.42,Default,,0000,0000,0000,,remember, the only reason we\Ncan kind of make this claim is
Dialogue: 0,0:01:18.42,0:01:21.81,Default,,0000,0000,0000,,because I told you at the\Nbeginning that this line right
Dialogue: 0,0:01:21.81,0:01:25.03,Default,,0000,0000,0000,,here and this line right\Nhere are parallel.
Dialogue: 0,0:01:25.03,0:01:25.31,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:01:25.31,0:01:27.33,Default,,0000,0000,0000,,Otherwise, you couldn't\Nmake this claim.
Dialogue: 0,0:01:27.33,0:01:29.01,Default,,0000,0000,0000,,But since they are alternate\Ninterior we know that
Dialogue: 0,0:01:29.01,0:01:34.57,Default,,0000,0000,0000,,this is the same angle.
Dialogue: 0,0:01:34.57,0:01:35.56,Default,,0000,0000,0000,,All right.
Dialogue: 0,0:01:35.56,0:01:39.08,Default,,0000,0000,0000,,So we now have shown that\Nthese are similar triangles.
Dialogue: 0,0:01:39.08,0:01:40.63,Default,,0000,0000,0000,,And I didn't have to\Ndo all three angles.
Dialogue: 0,0:01:40.63,0:01:42.96,Default,,0000,0000,0000,,I could have just done two, and\Nthat should have been good
Dialogue: 0,0:01:42.96,0:01:44.38,Default,,0000,0000,0000,,enough for you to know\Nthat they're similar.
Dialogue: 0,0:01:44.38,0:01:46.18,Default,,0000,0000,0000,,Because if two are the\Nsame then the third also
Dialogue: 0,0:01:46.18,0:01:47.37,Default,,0000,0000,0000,,has to be the same.
Dialogue: 0,0:01:47.37,0:01:49.74,Default,,0000,0000,0000,,And now let's see if we can\Nuse this information to
Dialogue: 0,0:01:49.74,0:01:51.98,Default,,0000,0000,0000,,figure out our ratios.
Dialogue: 0,0:01:51.98,0:01:53.56,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:01:53.56,0:01:58.04,Default,,0000,0000,0000,,Let's color the sides the\Nsame side as the angle so
Dialogue: 0,0:01:58.04,0:01:58.98,Default,,0000,0000,0000,,we don't get confused.
Dialogue: 0,0:01:58.98,0:02:02.97,Default,,0000,0000,0000,,So this side is\Nthe orange side.
Dialogue: 0,0:02:02.97,0:02:04.80,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:02:04.80,0:02:05.81,Default,,0000,0000,0000,,This side is the blue.
Dialogue: 0,0:02:05.81,0:02:06.39,Default,,0000,0000,0000,,This side is the red.
Dialogue: 0,0:02:06.39,0:02:06.65,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:02:06.65,0:02:08.81,Default,,0000,0000,0000,,So we have everything\Ncolor coded.
Dialogue: 0,0:02:08.81,0:02:13.32,Default,,0000,0000,0000,,And it might be confusing you\Nbut it's useful, because, as
Dialogue: 0,0:02:13.32,0:02:16.22,Default,,0000,0000,0000,,we'll see, these triangles are\Nactually kind of flipped.
Dialogue: 0,0:02:16.22,0:02:17.29,Default,,0000,0000,0000,,So let's see what we can do.
Dialogue: 0,0:02:17.29,0:02:21.47,Default,,0000,0000,0000,,So we need to figure out\Nthis orange side here.
Dialogue: 0,0:02:21.47,0:02:24.98,Default,,0000,0000,0000,,So this orange side\Nhere, let's call it x.
Dialogue: 0,0:02:24.98,0:02:28.85,Default,,0000,0000,0000,,So x equals question mark.
Dialogue: 0,0:02:28.85,0:02:31.82,Default,,0000,0000,0000,,This orange side here\Ncorresponds to this side here.
Dialogue: 0,0:02:31.82,0:02:32.00,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:02:32.00,0:02:34.73,Default,,0000,0000,0000,,Because it's opposite\Nthis angle, which is
Dialogue: 0,0:02:34.73,0:02:36.09,Default,,0000,0000,0000,,equal to this angle.
Dialogue: 0,0:02:36.09,0:02:38.76,Default,,0000,0000,0000,,So they're opposite\Nto the same angle.
Dialogue: 0,0:02:38.76,0:02:40.94,Default,,0000,0000,0000,,So that's how we know they\Ncorrespond to each other.
Dialogue: 0,0:02:40.94,0:02:47.96,Default,,0000,0000,0000,,So we could say x\Nover 6 is equal to.
Dialogue: 0,0:02:47.96,0:02:50.26,Default,,0000,0000,0000,,And now, what other\Nsides do we know?
Dialogue: 0,0:02:50.26,0:02:53.41,Default,,0000,0000,0000,,Well we know this side\Nhere-- we know this 4 side.
Dialogue: 0,0:02:53.41,0:02:55.24,Default,,0000,0000,0000,,Let me do it in that color.
Dialogue: 0,0:02:55.24,0:02:57.31,Default,,0000,0000,0000,,We know this side is 4.
Dialogue: 0,0:02:57.31,0:02:59.57,Default,,0000,0000,0000,,And since we've put x in the\Nnumerator on the left-hand
Dialogue: 0,0:02:59.57,0:03:03.07,Default,,0000,0000,0000,,side, and 4 is in the same\Ntriangle as this x we're trying
Dialogue: 0,0:03:03.07,0:03:04.90,Default,,0000,0000,0000,,to figure out, we'll put 4 in\Nthe numerator on the
Dialogue: 0,0:03:04.90,0:03:06.59,Default,,0000,0000,0000,,right-hand side.
Dialogue: 0,0:03:06.59,0:03:09.25,Default,,0000,0000,0000,,4 over what?
Dialogue: 0,0:03:09.25,0:03:10.88,Default,,0000,0000,0000,,Well what side\Ncorresponds to 4?
Dialogue: 0,0:03:10.88,0:03:14.29,Default,,0000,0000,0000,,What is opposite this\Nangle right here?
Dialogue: 0,0:03:14.29,0:03:15.00,Default,,0000,0000,0000,,Well it's this angle.
Dialogue: 0,0:03:15.00,0:03:17.72,Default,,0000,0000,0000,,
Dialogue: 0,0:03:17.72,0:03:19.05,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:03:19.05,0:03:24.69,Default,,0000,0000,0000,,So the corresponding side of\Nthis side is this side-- is 5.
Dialogue: 0,0:03:24.69,0:03:26.31,Default,,0000,0000,0000,,And now we can solve.
Dialogue: 0,0:03:26.31,0:03:29.01,Default,,0000,0000,0000,,x is equal-- we just\Nmultiply both sides by 6.
Dialogue: 0,0:03:29.01,0:03:31.31,Default,,0000,0000,0000,,So you get 24 over 5.
Dialogue: 0,0:03:31.31,0:03:35.74,Default,,0000,0000,0000,,x is equal to 24 over 5.
Dialogue: 0,0:03:35.74,0:03:38.76,Default,,0000,0000,0000,,
Dialogue: 0,0:03:38.76,0:03:40.04,Default,,0000,0000,0000,,Not too bad.
Dialogue: 0,0:03:40.04,0:03:41.65,Default,,0000,0000,0000,,And then we could\Neven go further.
Dialogue: 0,0:03:41.65,0:03:44.17,Default,,0000,0000,0000,,We can now figure out what\Nthis side is right here.
Dialogue: 0,0:03:44.17,0:03:45.77,Default,,0000,0000,0000,,This magenta side.
Dialogue: 0,0:03:45.77,0:03:48.34,Default,,0000,0000,0000,,Let's call that,\NI don't know, y.
Dialogue: 0,0:03:48.34,0:03:50.00,Default,,0000,0000,0000,,Not too creative here.
Dialogue: 0,0:03:50.00,0:03:53.25,Default,,0000,0000,0000,,Well y corresponds\Nto this angle.
Dialogue: 0,0:03:53.25,0:03:55.55,Default,,0000,0000,0000,,So y corresponds\Nto this 8 side.
Dialogue: 0,0:03:55.55,0:03:57.06,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:03:57.06,0:04:03.12,Default,,0000,0000,0000,,So we could do y over 8 is\Nequal to-- oh, we could
Dialogue: 0,0:04:03.12,0:04:03.68,Default,,0000,0000,0000,,do a bunch of things.
Dialogue: 0,0:04:03.68,0:04:07.09,Default,,0000,0000,0000,,We could say 4 over 5 or we\Ncould do-- let's do 4 over 5,
Dialogue: 0,0:04:07.09,0:04:09.87,Default,,0000,0000,0000,,because we could do 24 over\N5 over 6 and that's
Dialogue: 0,0:04:09.87,0:04:10.52,Default,,0000,0000,0000,,kind of confusing.
Dialogue: 0,0:04:10.52,0:04:11.98,Default,,0000,0000,0000,,So we could also do\Nthat [UNINTELLIGIBLE]
Dialogue: 0,0:04:11.98,0:04:15.38,Default,,0000,0000,0000,,over 4 over 5.
Dialogue: 0,0:04:15.38,0:04:17.00,Default,,0000,0000,0000,,Multiply both sides by 8.
Dialogue: 0,0:04:17.00,0:04:24.77,Default,,0000,0000,0000,,And you get y is equal\Nto 8 times 4, is what?
Dialogue: 0,0:04:24.77,0:04:27.16,Default,,0000,0000,0000,,32 over 5.
Dialogue: 0,0:04:27.16,0:04:31.98,Default,,0000,0000,0000,,
Dialogue: 0,0:04:31.98,0:04:33.82,Default,,0000,0000,0000,,And the reason why I did this\Nexample is because I want
Dialogue: 0,0:04:33.82,0:04:37.17,Default,,0000,0000,0000,,to show you that you\Ncan't just eyeball.
Dialogue: 0,0:04:37.17,0:04:39.86,Default,,0000,0000,0000,,Sometimes you can, if you get\Ngood at it, but it's not always
Dialogue: 0,0:04:39.86,0:04:42.71,Default,,0000,0000,0000,,completely obvious which sides\Ncorrespond to which sides.
Dialogue: 0,0:04:42.71,0:04:45.61,Default,,0000,0000,0000,,It might have been tempting to\Nsay that, I don't know, this
Dialogue: 0,0:04:45.61,0:04:48.27,Default,,0000,0000,0000,,side corresponds to this\Nside or that this side
Dialogue: 0,0:04:48.27,0:04:49.50,Default,,0000,0000,0000,,corresponds to this side.
Dialogue: 0,0:04:49.50,0:04:53.15,Default,,0000,0000,0000,,But you really have to pay\Nattention to which side kind of
Dialogue: 0,0:04:53.15,0:04:55.00,Default,,0000,0000,0000,,matches up with which angles.
Dialogue: 0,0:04:55.00,0:04:58.18,Default,,0000,0000,0000,,So any side that matches up\Nwith a certain angle, that same
Dialogue: 0,0:04:58.18,0:05:02.61,Default,,0000,0000,0000,,angle in the other triangle,\Nwhatever side is opposite that,
Dialogue: 0,0:05:02.61,0:05:04.30,Default,,0000,0000,0000,,that's its corresponding side.
Dialogue: 0,0:05:04.30,0:05:07.80,Default,,0000,0000,0000,,I use a lot of words, but\Nhopefully you have a
Dialogue: 0,0:05:07.80,0:05:09.67,Default,,0000,0000,0000,,bit of an intuition.
Dialogue: 0,0:05:09.67,0:05:12.23,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:05:12.23,0:05:16.97,Default,,0000,0000,0000,,First, let's take a triangle\Nand prove to ourselves that the
Dialogue: 0,0:05:16.97,0:05:18.16,Default,,0000,0000,0000,,two triangles are similar.
Dialogue: 0,0:05:18.16,0:05:20.71,Default,,0000,0000,0000,,
Dialogue: 0,0:05:20.71,0:05:21.80,Default,,0000,0000,0000,,I like these parallel lines.
Dialogue: 0,0:05:21.80,0:05:25.83,Default,,0000,0000,0000,,Let me do two parallel\Nlines again.
Dialogue: 0,0:05:25.83,0:05:28.52,Default,,0000,0000,0000,,And then this time\Naround-- let's see.
Dialogue: 0,0:05:28.52,0:05:31.48,Default,,0000,0000,0000,,I'm going to draw.
Dialogue: 0,0:05:31.48,0:05:34.45,Default,,0000,0000,0000,,There's a line.
Dialogue: 0,0:05:34.45,0:05:35.30,Default,,0000,0000,0000,,There we go.
Dialogue: 0,0:05:35.30,0:05:39.14,Default,,0000,0000,0000,,
Dialogue: 0,0:05:39.14,0:05:41.24,Default,,0000,0000,0000,,First, I said these\Nare parallel lines.
Dialogue: 0,0:05:41.24,0:05:45.11,Default,,0000,0000,0000,,So let me mark them as such.
Dialogue: 0,0:05:45.11,0:05:46.22,Default,,0000,0000,0000,,Parallel lines.
Dialogue: 0,0:05:46.22,0:05:49.99,Default,,0000,0000,0000,,So what we want to do is we\Nwant to prove that this
Dialogue: 0,0:05:49.99,0:05:58.30,Default,,0000,0000,0000,,triangle right here is similar\Nto the bigger triangle-- is
Dialogue: 0,0:05:58.30,0:06:00.31,Default,,0000,0000,0000,,similar to this triangle.
Dialogue: 0,0:06:00.31,0:06:01.19,Default,,0000,0000,0000,,This is pretty interesting.
Dialogue: 0,0:06:01.19,0:06:02.49,Default,,0000,0000,0000,,They actually overlap.
Dialogue: 0,0:06:02.49,0:06:02.83,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:02.83,0:06:08.07,Default,,0000,0000,0000,,
Dialogue: 0,0:06:08.07,0:06:10.97,Default,,0000,0000,0000,,So first of all, do we know any\Nangles of the two triangles
Dialogue: 0,0:06:10.97,0:06:12.42,Default,,0000,0000,0000,,that equal each other?
Dialogue: 0,0:06:12.42,0:06:13.01,Default,,0000,0000,0000,,Well, sure.
Dialogue: 0,0:06:13.01,0:06:13.88,Default,,0000,0000,0000,,They have this angle.
Dialogue: 0,0:06:13.88,0:06:16.73,Default,,0000,0000,0000,,They actually both share the\Nsame exact angle in common.
Dialogue: 0,0:06:16.73,0:06:17.23,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:17.23,0:06:20.25,Default,,0000,0000,0000,,Because the two triangles\Noverlap at that point.
Dialogue: 0,0:06:20.25,0:06:22.00,Default,,0000,0000,0000,,So what else can we figure out?
Dialogue: 0,0:06:22.00,0:06:23.95,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:06:23.95,0:06:25.53,Default,,0000,0000,0000,,I mean, I don't to be\Ntacky without any
Dialogue: 0,0:06:25.53,0:06:26.93,Default,,0000,0000,0000,,colors, but let's see.
Dialogue: 0,0:06:26.93,0:06:31.55,Default,,0000,0000,0000,,We have this angle here.
Dialogue: 0,0:06:31.55,0:06:33.47,Default,,0000,0000,0000,,And what other angles are\Nequal to this angle?
Dialogue: 0,0:06:33.47,0:06:37.32,Default,,0000,0000,0000,,Well, we can use our parallel\Nlines and transversal of
Dialogue: 0,0:06:37.32,0:06:42.35,Default,,0000,0000,0000,,angle rules, or theorems or\Nwhatever, and figure it out.
Dialogue: 0,0:06:42.35,0:06:44.86,Default,,0000,0000,0000,,Well this angle\Ncorresponds to what?
Dialogue: 0,0:06:44.86,0:06:46.62,Default,,0000,0000,0000,,Well, it corresponds\Nto this angle.
Dialogue: 0,0:06:46.62,0:06:48.32,Default,,0000,0000,0000,,So it's equivalent.
Dialogue: 0,0:06:48.32,0:06:49.75,Default,,0000,0000,0000,,And you got that from\Nyour parallel lines.
Dialogue: 0,0:06:49.75,0:06:50.09,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:50.09,0:06:52.00,Default,,0000,0000,0000,,So these two are the same.
Dialogue: 0,0:06:52.00,0:06:57.15,Default,,0000,0000,0000,,And then, finally, if I have--\Nlet me pick a good color-- if I
Dialogue: 0,0:06:57.15,0:06:59.55,Default,,0000,0000,0000,,have this angle, draw\Na triple angle here.
Dialogue: 0,0:06:59.55,0:07:00.11,Default,,0000,0000,0000,,Same thing.
Dialogue: 0,0:07:00.11,0:07:02.61,Default,,0000,0000,0000,,This corresponding angle is\Ngoing to be right here.
Dialogue: 0,0:07:02.61,0:07:05.25,Default,,0000,0000,0000,,
Dialogue: 0,0:07:05.25,0:07:05.83,Default,,0000,0000,0000,,So there.
Dialogue: 0,0:07:05.83,0:07:10.45,Default,,0000,0000,0000,,We know all of the three angles\Nof this triangle are the same.
Dialogue: 0,0:07:10.45,0:07:11.76,Default,,0000,0000,0000,,So this is a similar triangle.
Dialogue: 0,0:07:11.76,0:07:16.54,Default,,0000,0000,0000,,
Dialogue: 0,0:07:16.54,0:07:18.78,Default,,0000,0000,0000,,Let's say we know that this\Nside right here-- I'll give
Dialogue: 0,0:07:18.78,0:07:19.92,Default,,0000,0000,0000,,you a little trick question.
Dialogue: 0,0:07:19.92,0:07:24.43,Default,,0000,0000,0000,,From here to here is 5.
Dialogue: 0,0:07:24.43,0:07:29.53,Default,,0000,0000,0000,,And from here to here is 7.
Dialogue: 0,0:07:29.53,0:07:41.25,Default,,0000,0000,0000,,
Dialogue: 0,0:07:41.25,0:07:46.82,Default,,0000,0000,0000,,From here to here is-- I\Ndon't know; make up a
Dialogue: 0,0:07:46.82,0:07:49.82,Default,,0000,0000,0000,,good number-- is 12.
Dialogue: 0,0:07:49.82,0:08:01.43,Default,,0000,0000,0000,,And from here to here\Nis, let me say, 6.
Dialogue: 0,0:08:01.43,0:08:04.92,Default,,0000,0000,0000,,And I wanted to figure\Nout what this is.
Dialogue: 0,0:08:04.92,0:08:06.08,Default,,0000,0000,0000,,How do we do that?
Dialogue: 0,0:08:06.08,0:08:08.72,Default,,0000,0000,0000,,And I've further made it more\Nconfusing by adding all
Dialogue: 0,0:08:08.72,0:08:10.05,Default,,0000,0000,0000,,these squiggly lines.
Dialogue: 0,0:08:10.05,0:08:11.46,Default,,0000,0000,0000,,Well, we already know\Nthat these are two
Dialogue: 0,0:08:11.46,0:08:12.46,Default,,0000,0000,0000,,similar triangles.
Dialogue: 0,0:08:12.46,0:08:14.91,Default,,0000,0000,0000,,So we can use that information\Nto do our ratios.
Dialogue: 0,0:08:14.91,0:08:20.11,Default,,0000,0000,0000,,So if we call this\Nis equal to x.
Dialogue: 0,0:08:20.11,0:08:21.70,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:08:21.70,0:08:23.32,Default,,0000,0000,0000,,So what do we know?
Dialogue: 0,0:08:23.32,0:08:31.35,Default,,0000,0000,0000,,We know that this whole side\Ncorresponds to what side
Dialogue: 0,0:08:31.35,0:08:33.25,Default,,0000,0000,0000,,on the smaller triangle?
Dialogue: 0,0:08:33.25,0:08:34.58,Default,,0000,0000,0000,,Well, it corresponds\Nto this side.
Dialogue: 0,0:08:34.58,0:08:34.82,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:08:34.82,0:08:37.08,Default,,0000,0000,0000,,It corresponds to here.
Dialogue: 0,0:08:37.08,0:08:39.22,Default,,0000,0000,0000,,So let me draw it in\Nthe correct color.
Dialogue: 0,0:08:39.22,0:08:42.78,Default,,0000,0000,0000,,So if we do the orange, this\Norange corresponds to this.
Dialogue: 0,0:08:42.78,0:08:44.03,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:08:44.03,0:08:47.19,Default,,0000,0000,0000,,Well this orange corresponds\Nto the whole thing.
Dialogue: 0,0:08:47.19,0:08:49.90,Default,,0000,0000,0000,,It corresponds to\Nthis whole line.
Dialogue: 0,0:08:49.90,0:08:52.77,Default,,0000,0000,0000,,So if we take the big\Ntriangle, the big triangle
Dialogue: 0,0:08:52.77,0:08:54.21,Default,,0000,0000,0000,,side is not just x.
Dialogue: 0,0:08:54.21,0:08:54.49,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:08:54.49,0:08:55.88,Default,,0000,0000,0000,,Because that's not the whole\Nside of the triangle.
Dialogue: 0,0:08:55.88,0:08:56.93,Default,,0000,0000,0000,,It's x plus 5.
Dialogue: 0,0:08:56.93,0:09:00.85,Default,,0000,0000,0000,,
Dialogue: 0,0:09:00.85,0:09:02.06,Default,,0000,0000,0000,,That's this whole side.
Dialogue: 0,0:09:02.06,0:09:02.45,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:09:02.45,0:09:06.12,Default,,0000,0000,0000,,
Dialogue: 0,0:09:06.12,0:09:11.34,Default,,0000,0000,0000,,x plus 5 over the corresponding\Nside on the smaller triangle.
Dialogue: 0,0:09:11.34,0:09:12.66,Default,,0000,0000,0000,,Well, on the corresponding\Nside of the smaller
Dialogue: 0,0:09:12.66,0:09:14.63,Default,,0000,0000,0000,,triangle it's just this.
Dialogue: 0,0:09:14.63,0:09:16.61,Default,,0000,0000,0000,,It's over 5.
Dialogue: 0,0:09:16.61,0:09:17.87,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:09:17.87,0:09:22.18,Default,,0000,0000,0000,,Is equal to-- and then\Nwe could say, well, 12.
Dialogue: 0,0:09:22.18,0:09:25.74,Default,,0000,0000,0000,,Is equal to 12, because this\Ncorresponds to this angle
Dialogue: 0,0:09:25.74,0:09:27.33,Default,,0000,0000,0000,,on the big triangle.
Dialogue: 0,0:09:27.33,0:09:30.54,Default,,0000,0000,0000,,Is equal to 12 over what?
Dialogue: 0,0:09:30.54,0:09:33.98,Default,,0000,0000,0000,,Over 6, because this is\Nthe smaller triangle.
Dialogue: 0,0:09:33.98,0:09:34.93,Default,,0000,0000,0000,,And then we could\Nsolve for that.
Dialogue: 0,0:09:34.93,0:09:35.90,Default,,0000,0000,0000,,This becomes 2.
Dialogue: 0,0:09:35.90,0:09:36.86,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:09:36.86,0:09:40.94,Default,,0000,0000,0000,,You get x plus 5\Nis equal to 10.
Dialogue: 0,0:09:40.94,0:09:43.53,Default,,0000,0000,0000,,x is equal to 5.
Dialogue: 0,0:09:43.53,0:09:46.30,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:09:46.30,0:09:48.56,Default,,0000,0000,0000,,That's all the time\NI have for now.
Dialogue: 0,0:09:48.56,0:09:51.54,Default,,0000,0000,0000,,I hope I helped you\Nunderstand similar triangles
Dialogue: 0,0:09:51.54,0:09:52.58,Default,,0000,0000,0000,,just a little bit.
Dialogue: 0,0:09:52.58,0:09:54.72,Default,,0000,0000,0000,,I'll see you soon.