[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.37,Default,,0000,0000,0000,,I thought I would do some more example problems involving triangles. And so in this first one it says the
Dialogue: 0,0:00:05.37,0:00:13.23,Default,,0000,0000,0000,,measure of the largest angle in a triangle is four times the measure of the second largest angle. The
Dialogue: 0,0:00:13.23,0:00:20.28,Default,,0000,0000,0000,,smallest angle is ten degrees. What are the measures of all the angles? Well we know one of them, we
Dialogue: 0,0:00:20.28,0:00:22.17,Default,,0000,0000,0000,,know it's ten degrees.
Dialogue: 0,0:00:22.17,0:00:25.50,Default,,0000,0000,0000,,Let's draw an arbitrary triangle right over here. now let's say that is our triangle.
Dialogue: 0,0:00:25.50,0:00:30.26,Default,,0000,0000,0000,,We know the the smallest angle is going to be ten degrees and I'll just say let's just assume that this
Dialogue: 0,0:00:30.26,0:00:36.38,Default,,0000,0000,0000,,right over here is the measure of the smallest angle. It's ten degrees. Now let's call the second largest
Dialogue: 0,0:00:36.38,0:00:46.35,Default,,0000,0000,0000,,angle, let's call that x. So this is going to be x. And then the first sentence, they say the measure
Dialogue: 0,0:00:46.35,0:00:51.41,Default,,0000,0000,0000,,of the largest angle in the triangle is four times, four times the measure of the second largest angle.
Dialogue: 0,0:00:51.41,0:00:59.04,Default,,0000,0000,0000,,So if the second largest angle is x, four times that measure is going to be 4x. So the largest angle
Dialogue: 0,0:00:59.04,0:01:05.87,Default,,0000,0000,0000,,is going to be 4x. And so, the one thing we know about the measures of the angles inside a triangle is
Dialogue: 0,0:01:05.87,0:01:20.64,Default,,0000,0000,0000,,they add up to 180 degrees. So we know that 4x + x + 10 degrees is going to be equal to 180 degrees.
Dialogue: 0,0:01:20.64,0:01:30.99,Default,,0000,0000,0000,,And 4x + x, that just gives us 5x. And then we have 5x + 10 is equal to 180 degrees. Subtract 10 from
Dialogue: 0,0:01:30.99,0:01:44.54,Default,,0000,0000,0000,,both sides, you get 5x = 170. And so, x = 170 / 5. Let's see, it will go into it 34 times? Let me verify
Dialogue: 0,0:01:44.54,0:01:50.50,Default,,0000,0000,0000,,this. So 5 goes into, yeah, it should be 34 times. It's going to go into it twice as many times as 10
Dialogue: 0,0:01:50.50,0:01:56.10,Default,,0000,0000,0000,,would go into it. 10 would go into 170 17 times, 5 would go into 170 34 times.
Dialogue: 0,0:01:56.10,0:02:05.10,Default,,0000,0000,0000,,So we can verify it. 3 times 5 is 15. Subtract, we get 2. Bring down the 0.
Dialogue: 0,0:02:05.10,0:02:09.82,Default,,0000,0000,0000,,5 goes into 20 four times. And then you can have the remainder. 4 times 5 is 20.
Dialogue: 0,0:02:09.82,0:02:13.92,Default,,0000,0000,0000,,No remainder. So it's 34 times. X is equal to 34.
Dialogue: 0,0:02:13.92,0:02:21.70,Default,,0000,0000,0000,,So the second largest angle has the measure of 34 degrees. This angle up here is going to be 4 times that.
Dialogue: 0,0:02:21.70,0:02:28.03,Default,,0000,0000,0000,,So 4 times 34, it's gonna be 120 degrees plus 16 degrees. This is going to be...
Dialogue: 0,0:02:28.03,0:02:34.81,Default,,0000,0000,0000,,136 degrees. Is that right? 4 times 4 is 16. 4 times 30 is 120.
Dialogue: 0,0:02:34.81,0:02:37.86,Default,,0000,0000,0000,,16 plus 120 is 136 degrees. So we're done.
Dialogue: 0,0:02:37.86,0:02:45.86,Default,,0000,0000,0000,,The three measures or the sizes of the three angles are 10 degrees, 34 degrees and 136 degrees.
Dialogue: 0,0:02:45.86,0:02:47.62,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:02:47.62,0:02:50.74,Default,,0000,0000,0000,,So let's see. We have a little bit of a drawing here.
Dialogue: 0,0:02:50.74,0:02:54.11,Default,,0000,0000,0000,,And what I want to do is, and we could think about different things.
Dialogue: 0,0:02:54.11,0:02:59.31,Default,,0000,0000,0000,,We could say, let's solve for x. I'm assuming that 4x is the measure of this angle.
Dialogue: 0,0:02:59.31,0:03:02.37,Default,,0000,0000,0000,,2x is the measure of that angle right over there.
Dialogue: 0,0:03:02.37,0:03:08.50,Default,,0000,0000,0000,,We can solve for x and if we know x we can figure out what the actual measures of these angles are. Assuming that we can figure out x.
Dialogue: 0,0:03:08.50,0:03:13.76,Default,,0000,0000,0000,,And the other thing that they tell us is that this line over here is parallel to this line over here.
Dialogue: 0,0:03:13.76,0:03:19.02,Default,,0000,0000,0000,,And it's craftily drawn because it's parallel but one stops here and one sparks up there.
Dialogue: 0,0:03:19.02,0:03:22.62,Default,,0000,0000,0000,,So the first thing I want to do, if they're telling us these two lines are parallel,
Dialogue: 0,0:03:22.62,0:03:25.85,Default,,0000,0000,0000,,it's probably going to be something involving transversals or something.
Dialogue: 0,0:03:25.85,0:03:29.02,Default,,0000,0000,0000,,It might be something involving, the other option is something involving triangles.
Dialogue: 0,0:03:29.02,0:03:32.97,Default,,0000,0000,0000,,And at first you might say, wait, is this angle and that angle vertical angle?
Dialogue: 0,0:03:32.97,0:03:35.94,Default,,0000,0000,0000,,But we have to be very careful. They are not. These are not the same lines.
Dialogue: 0,0:03:35.94,0:03:42.52,Default,,0000,0000,0000,,This line is parallel to that line. This line it's bending right over there.
Dialogue: 0,0:03:42.52,0:03:44.26,Default,,0000,0000,0000,,So we can't make any attempt of assumption like that.
Dialogue: 0,0:03:44.26,0:03:48.80,Default,,0000,0000,0000,,So the interesting thing, and I'm not sure if this will lead us in the right direction,
Dialogue: 0,0:03:48.80,0:03:52.60,Default,,0000,0000,0000,,is to just make it clear that these two are part of parallel lines.
Dialogue: 0,0:03:52.60,0:03:57.74,Default,,0000,0000,0000,,So I could continue this line down like this. And I can continue this line up like that.
Dialogue: 0,0:03:57.74,0:04:02.13,Default,,0000,0000,0000,,And then that starts to look a little bit more like we're used to when we're dealing with parallel lines.
Dialogue: 0,0:04:02.13,0:04:07.56,Default,,0000,0000,0000,,And then this line segment BC or we could even say line BC if we were to continue it on,
Dialogue: 0,0:04:07.56,0:04:11.84,Default,,0000,0000,0000,,if we were to continue it on and on even pass D.
Dialogue: 0,0:04:11.84,0:04:16.90,Default,,0000,0000,0000,,Then this is clearly a transversal of those two parallel lines. This is clearly a trasnversal.
Dialogue: 0,0:04:16.90,0:04:22.47,Default,,0000,0000,0000,,And so if this angle right over here, if this angle right over here is 4x,
Dialogue: 0,0:04:22.47,0:04:27.84,Default,,0000,0000,0000,,it has a corresponding angle. Half of the..or maybe most of the work on all these
Dialogue: 0,0:04:27.84,0:04:34.79,Default,,0000,0000,0000,,is to try to see the parallel lines and see the transversal and see the things that might be useful for you.
Dialogue: 0,0:04:34.79,0:04:36.75,Default,,0000,0000,0000,,So that right there is the transversal.
Dialogue: 0,0:04:36.75,0:04:41.44,Default,,0000,0000,0000,,These are the parallel lines, that's one parallel line, that's the other parallel line.
Dialogue: 0,0:04:41.44,0:04:43.93,Default,,0000,0000,0000,,You can almost try to zone out all the other stuff in the diagram.
Dialogue: 0,0:04:43.93,0:04:52.29,Default,,0000,0000,0000,,And so if this angle right over here is 4x, it has a corresponding angle where the transversal intersects the other parallel line.
Dialogue: 0,0:04:52.29,0:04:55.82,Default,,0000,0000,0000,,This right here is its corresponding angle.
Dialogue: 0,0:04:55.82,0:04:58.30,Default,,0000,0000,0000,,So let me draw it in the same yellow.
Dialogue: 0,0:04:58.30,0:05:00.45,Default,,0000,0000,0000,,So this right here is the corresponding angle.
Dialogue: 0,0:05:00.45,0:05:04.32,Default,,0000,0000,0000,,So this will also be, this will also be 4x.
Dialogue: 0,0:05:04.32,0:05:09.86,Default,,0000,0000,0000,,And we see that this angle and this angle, this angle has a measure of 4x,
Dialogue: 0,0:05:09.86,0:05:13.79,Default,,0000,0000,0000,,this angle has a measure of 2x. We can see that they're supplementary.
Dialogue: 0,0:05:13.79,0:05:18.61,Default,,0000,0000,0000,,They're adjacent to each other. The outer sides form a straight angle.
Dialogue: 0,0:05:18.61,0:05:21.76,Default,,0000,0000,0000,,So they're supplementary which means that their measure add up to 180 degrees.
Dialogue: 0,0:05:21.76,0:05:26.90,Default,,0000,0000,0000,,They go all the way around like that, if you add the two adjacent angles together.
Dialogue: 0,0:05:26.90,0:05:33.15,Default,,0000,0000,0000,,So we know that 4x plus 2x needs to be equal to 180 degrees.
Dialogue: 0,0:05:33.15,0:05:36.42,Default,,0000,0000,0000,,Or we get 6x is equal to 180 degrees.
Dialogue: 0,0:05:36.42,0:05:40.63,Default,,0000,0000,0000,,Divide both sides by 6, you get x is equal to 30.
Dialogue: 0,0:05:40.63,0:05:48.96,Default,,0000,0000,0000,,And this angle right over here is 2 times x, so it's going to be 60 degrees.
Dialogue: 0,0:05:48.96,0:05:52.91,Default,,0000,0000,0000,,So this angle right over here is going to be 60 degrees.
Dialogue: 0,0:05:52.91,0:06:02.81,Default,,0000,0000,0000,,And this angle right over here is 4 times x. So it is 120 degrees.
Dialogue: 0,0:06:02.81,0:06:05.00,Default,,0000,0000,0000,,And we're done.