[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.05,0:00:02.01,Default,,0000,0000,0000,,Problem 38.
Dialogue: 0,0:00:02.01,0:00:03.23,Default,,0000,0000,0000,,In the drawing below,
Dialogue: 0,0:00:03.23,0:00:05.93,Default,,0000,0000,0000,,the figure formed by the squares with sides
Dialogue: 0,0:00:05.93,0:00:09.26,Default,,0000,0000,0000,,that are labeled x, y, and z is a right triangle.
Dialogue: 0,0:00:09.26,0:00:14.36,Default,,0000,0000,0000,,So the figure, so it's a right triangle.
Dialogue: 0,0:00:14.36,0:00:15.16,Default,,0000,0000,0000,,And then they ask us,
Dialogue: 0,0:00:15.16,0:00:19.03,Default,,0000,0000,0000,,which equation is true for all values of x, y, and z?
Dialogue: 0,0:00:19.03,0:00:21.00,Default,,0000,0000,0000,,So really, they're just trying to see
Dialogue: 0,0:00:21.00,0:00:29.90,Default,,0000,0000,0000,,if you remember the Pythagorean Theorem.
Dialogue: 0,0:00:31.00,0:00:33.89,Default,,0000,0000,0000,,And that just tells us that if we have a right triangle,
Dialogue: 0,0:00:33.89,0:00:39.39,Default,,0000,0000,0000,,that the sum of the squares of the two smaller sides,
Dialogue: 0,0:00:39.39,0:00:42.35,Default,,0000,0000,0000,,so x squared plus y squared,
Dialogue: 0,0:00:42.35,0:00:46.03,Default,,0000,0000,0000,,is going to be equal to the square of the longest side,
Dialogue: 0,0:00:46.03,0:00:49.00,Default,,0000,0000,0000,,or the side that's opposite the right angle.
Dialogue: 0,0:00:49.00,0:00:50.02,Default,,0000,0000,0000,,Or we also call that the hypotenuse.
Dialogue: 0,0:00:53.05,0:00:55.81,Default,,0000,0000,0000,,So that's equal to z squared.
Dialogue: 0,0:00:55.81,0:00:58.04,Default,,0000,0000,0000,,That's what the Pythagorean Theorem tells us.
Dialogue: 0,0:00:58.04,0:01:00.25,Default,,0000,0000,0000,,And so if we look down here,
Dialogue: 0,0:01:00.25,0:01:02.71,Default,,0000,0000,0000,,only one of those match what I just wrote down,
Dialogue: 0,0:01:02.71,0:01:06.00,Default,,0000,0000,0000,,are kind of my restatement of the Pythagorean Theorem.
Dialogue: 0,0:01:06.00,0:01:09.05,Default,,0000,0000,0000,,x squared plus y squared is equal to z squared.
Dialogue: 0,0:01:09.05,0:01:13.03,Default,,0000,0000,0000,,And that's this one right there, choice B.
Dialogue: 0,0:01:13.03,0:01:15.00,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:01:15.00,0:01:18.02,Default,,0000,0000,0000,,Problem 39.
Dialogue: 0,0:01:18.02,0:01:22.03,Default,,0000,0000,0000,,A clothing company created the following diagram for a vest.
Dialogue: 0,0:01:22.03,0:01:24.76,Default,,0000,0000,0000,,So I guess this is somehow a vest.
Dialogue: 0,0:01:24.76,0:01:26.04,Default,,0000,0000,0000,,Maybe it's half of the vest,
Dialogue: 0,0:01:26.04,0:01:28.71,Default,,0000,0000,0000,,because I don't see how I could put that on me.
Dialogue: 0,0:01:28.71,0:01:30.52,Default,,0000,0000,0000,,To show the other side of the vest--
Dialogue: 0,0:01:30.52,0:01:33.97,Default,,0000,0000,0000,,OK, right, so this was half of the vest--
Dialogue: 0,0:01:33.97,0:01:41.06,Default,,0000,0000,0000,,the company will reflect the drawing across the y-axis.
Dialogue: 0,0:01:41.06,0:01:45.02,Default,,0000,0000,0000,,What will be the coordinates of C after the reflection?
Dialogue: 0,0:01:45.02,0:01:46.48,Default,,0000,0000,0000,,So when they say reflection, they mean,
Dialogue: 0,0:01:46.48,0:01:48.56,Default,,0000,0000,0000,,literally, just take the image of this
Dialogue: 0,0:01:48.56,0:01:50.80,Default,,0000,0000,0000,,and you flip it over onto the right-hand side.
Dialogue: 0,0:01:50.80,0:01:53.02,Default,,0000,0000,0000,,So I could draw it out, and draw it in blue.
Dialogue: 0,0:01:53.02,0:01:54.62,Default,,0000,0000,0000,,So if I take the reflection,
Dialogue: 0,0:01:54.62,0:01:57.02,Default,,0000,0000,0000,,this line right here is at negative 1.
Dialogue: 0,0:01:57.02,0:02:00.32,Default,,0000,0000,0000,,It's 1 to the left of the y-axis.
Dialogue: 0,0:02:00.32,0:02:03.95,Default,,0000,0000,0000,,So when I take its reflection, I would draw it right here,
Dialogue: 0,0:02:03.95,0:02:07.05,Default,,0000,0000,0000,,1 to the right of the y-axis.
Dialogue: 0,0:02:07.05,0:02:09.18,Default,,0000,0000,0000,,This line down here,
Dialogue: 0,0:02:09.19,0:02:15.01,Default,,0000,0000,0000,,it goes from 1 to the left all the way to 4 to the left.
Dialogue: 0,0:02:15.01,0:02:16.67,Default,,0000,0000,0000,,On this side, it's going to go from 1 to
Dialogue: 0,0:02:16.67,0:02:20.06,Default,,0000,0000,0000,,the right all the way to 4 to the right.
Dialogue: 0,0:02:20.06,0:02:22.04,Default,,0000,0000,0000,,I could keep doing it.
Dialogue: 0,0:02:22.04,0:02:25.66,Default,,0000,0000,0000,,This segment right here, FE, when I flip it,
Dialogue: 0,0:02:25.66,0:02:28.08,Default,,0000,0000,0000,,will become this segment right here.
Dialogue: 0,0:02:28.08,0:02:32.03,Default,,0000,0000,0000,,This segment, DE, right here,
Dialogue: 0,0:02:32.03,0:02:34.65,Default,,0000,0000,0000,,will become this segment.
Dialogue: 0,0:02:34.65,0:02:38.01,Default,,0000,0000,0000,,It'll just look something like this when I go onto that side
Dialogue: 0,0:02:38.01,0:02:43.02,Default,,0000,0000,0000,,And then C, right here, is 2 to the left of the y-axis.
Dialogue: 0,0:02:43.02,0:02:46.07,Default,,0000,0000,0000,,So C over here will be 2 to the right of the y-axis.
Dialogue: 0,0:02:46.07,0:02:48.41,Default,,0000,0000,0000,,So it's going to look something like this.
Dialogue: 0,0:02:48.41,0:02:52.01,Default,,0000,0000,0000,,So the vest is going to look something like this.
Dialogue: 0,0:02:52.01,0:02:54.00,Default,,0000,0000,0000,,And then of course, it just dips down like that.
Dialogue: 0,0:02:54.00,0:02:56.02,Default,,0000,0000,0000,,So that's the right-hand side of the vest.
Dialogue: 0,0:02:56.02,0:02:58.02,Default,,0000,0000,0000,,But they want to know what are the coordinates of C?
Dialogue: 0,0:02:58.02,0:03:01.24,Default,,0000,0000,0000,,So this is C, and this is the C after the reflection.
Dialogue: 0,0:03:01.24,0:03:03.01,Default,,0000,0000,0000,,Maybe I could call it C prime.
Dialogue: 0,0:03:03.01,0:03:07.04,Default,,0000,0000,0000,,And so its coordinates are-- its x-coordinate is 2.
Dialogue: 0,0:03:07.04,0:03:08.42,Default,,0000,0000,0000,,And we're 2 to the right;
Dialogue: 0,0:03:08.42,0:03:10.69,Default,,0000,0000,0000,,before, we were 2 to the left, at minus 2.
Dialogue: 0,0:03:10.69,0:03:13.26,Default,,0000,0000,0000,,And its y-coordinate is going to be the same,
Dialogue: 0,0:03:13.26,0:03:14.43,Default,,0000,0000,0000,,it's going to be 7.
Dialogue: 0,0:03:14.43,0:03:16.03,Default,,0000,0000,0000,,2, 7.
Dialogue: 0,0:03:16.03,0:03:18.00,Default,,0000,0000,0000,,So that is choice A.
Dialogue: 0,0:03:21.06,0:03:22.92,Default,,0000,0000,0000,,I'll do it in the next video.
Dialogue: 0,0:03:22.92,0:03:24.89,Default,,0000,0000,0000,,Well, there's only two problems in this video.
Dialogue: 0,0:03:24.89,0:03:26.74,Default,,0000,0000,0000,,So let me go to the next page.
Dialogue: 0,0:03:30.06,0:03:31.08,Default,,0000,0000,0000,,Number 40.
Dialogue: 0,0:03:31.08,0:03:34.26,Default,,0000,0000,0000,,What is the area, in square units,
Dialogue: 0,0:03:34.26,0:03:38.88,Default,,0000,0000,0000,,of trapezoid QRST shown below?
Dialogue: 0,0:03:38.88,0:03:40.32,Default,,0000,0000,0000,,So we need to figure out the area of this.
Dialogue: 0,0:03:40.32,0:03:42.01,Default,,0000,0000,0000,,And they actually even give us a formula.
Dialogue: 0,0:03:42.01,0:03:46.00,Default,,0000,0000,0000,,They gave us the formula for this trapezoid.
Dialogue: 0,0:03:46.00,0:03:50.77,Default,,0000,0000,0000,,So they're calling it 1/2 times the height,
Dialogue: 0,0:03:50.78,0:03:54.01,Default,,0000,0000,0000,,times base 1 plus base 2.
Dialogue: 0,0:03:54.01,0:03:55.60,Default,,0000,0000,0000,,So essentially, just to give you an intuition of
Dialogue: 0,0:03:55.60,0:03:57.71,Default,,0000,0000,0000,,where this comes from, you're essentially saying,
Dialogue: 0,0:03:57.71,0:04:00.03,Default,,0000,0000,0000,,what's the average width of this trapezoid?
Dialogue: 0,0:04:00.03,0:04:05.26,Default,,0000,0000,0000,,So you take 1/2 times the sum of this guy and that guy,
Dialogue: 0,0:04:05.26,0:04:06.62,Default,,0000,0000,0000,,and that gives you the average width.
Dialogue: 0,0:04:06.62,0:04:08.79,Default,,0000,0000,0000,,And then you multiply that times the height.
Dialogue: 0,0:04:08.79,0:04:11.61,Default,,0000,0000,0000,,So just applying this formula,
Dialogue: 0,0:04:11.61,0:04:16.43,Default,,0000,0000,0000,,it is 1/2 times my height-- my height is 8--
Dialogue: 0,0:04:16.43,0:04:21.05,Default,,0000,0000,0000,,times base 1, let's call this base 1, 20.
Dialogue: 0,0:04:21.05,0:04:23.03,Default,,0000,0000,0000,,Plus base 2.
Dialogue: 0,0:04:23.03,0:04:25.57,Default,,0000,0000,0000,,Base 2 is this 6 right there.
Dialogue: 0,0:04:25.57,0:04:30.01,Default,,0000,0000,0000,,So I have 1/2 times 8, which is 4, times 26.
Dialogue: 0,0:04:30.01,0:04:36.00,Default,,0000,0000,0000,,And 4 times 26 is equal to 104 square units.
Dialogue: 0,0:04:36.00,0:04:37.23,Default,,0000,0000,0000,,So that's that right there.
Dialogue: 0,0:04:37.23,0:04:38.33,Default,,0000,0000,0000,,So they're really just testing
Dialogue: 0,0:04:38.33,0:04:39.77,Default,,0000,0000,0000,,whether you can apply this formula.
Dialogue: 0,0:04:39.77,0:04:41.37,Default,,0000,0000,0000,,Whether you can recognize what's the height
Dialogue: 0,0:04:41.37,0:04:44.07,Default,,0000,0000,0000,,and what are the two bases.
Dialogue: 0,0:04:44.07,0:04:46.02,Default,,0000,0000,0000,,Problem 41.
Dialogue: 0,0:04:46.02,0:04:47.26,Default,,0000,0000,0000,,One millimeter is.
Dialogue: 0,0:04:47.26,0:04:52.04,Default,,0000,0000,0000,,Well, here they're just seeing if you remember your units.
Dialogue: 0,0:04:52.04,0:04:53.36,Default,,0000,0000,0000,,Let me write it this way.
Dialogue: 0,0:04:53.36,0:04:57.05,Default,,0000,0000,0000,,Deci is equal to 1/10.
Dialogue: 0,0:04:57.05,0:05:01.40,Default,,0000,0000,0000,,Centi is equal to 1/100.
Dialogue: 0,0:05:01.40,0:05:10.00,Default,,0000,0000,0000,,And then milli is equal to 1/1000.
Dialogue: 0,0:05:10.00,0:05:15.01,Default,,0000,0000,0000,,So one millimeter is 1/1000 of a meter.
Dialogue: 0,0:05:15.01,0:05:19.07,Default,,0000,0000,0000,,They're just making sure you remember your metric prefixes.
Dialogue: 0,0:05:19.07,0:05:23.00,Default,,0000,0000,0000,,Problem 42.
Dialogue: 0,0:05:23.00,0:05:30.06,Default,,0000,0000,0000,,In the diagram below, hexagon LMNPQR is
Dialogue: 0,0:05:30.06,0:05:37.63,Default,,0000,0000,0000,,congruent to hexagon STUVWX.
Dialogue: 0,0:05:37.63,0:05:40.50,Default,,0000,0000,0000,,Congruent just means all the sides are equal
Dialogue: 0,0:05:40.50,0:05:43.48,Default,,0000,0000,0000,,and all the measures of their angles are also equal.
Dialogue: 0,0:05:43.48,0:05:50.58,Default,,0000,0000,0000,,So they say, which side is the same length as MN?
Dialogue: 0,0:05:50.58,0:05:52.41,Default,,0000,0000,0000,,So this is MN right there, and we want to know
Dialogue: 0,0:05:52.41,0:05:54.28,Default,,0000,0000,0000,,what side is the same length as that.
Dialogue: 0,0:05:54.28,0:05:58.00,Default,,0000,0000,0000,,So let me make sure that they're not trying to confuse us.
Dialogue: 0,0:05:58.00,0:06:04.26,Default,,0000,0000,0000,,So they start here, they say LMNPQR,
Dialogue: 0,0:06:04.26,0:06:09.00,Default,,0000,0000,0000,,and then they say STUVWX.
Dialogue: 0,0:06:09.00,0:06:10.00,Default,,0000,0000,0000,,So they're not confusing us.
Dialogue: 0,0:06:10.00,0:06:11.52,Default,,0000,0000,0000,,These points do correspond.
Dialogue: 0,0:06:11.52,0:06:13.66,Default,,0000,0000,0000,,S corresponds to L, M corresponds to T,
Dialogue: 0,0:06:13.66,0:06:15.03,Default,,0000,0000,0000,,and so forth and so on.
Dialogue: 0,0:06:15.03,0:06:18.27,Default,,0000,0000,0000,,So this segment is going to be congruent to
Dialogue: 0,0:06:18.27,0:06:19.43,Default,,0000,0000,0000,,that segment right there.
Dialogue: 0,0:06:19.44,0:06:21.57,Default,,0000,0000,0000,,Segment TU.
Dialogue: 0,0:06:21.57,0:06:24.53,Default,,0000,0000,0000,,So MN is the same length as TU.
Dialogue: 0,0:06:25.00,0:06:27.19,Default,,0000,0000,0000,,That is choice B.