[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.43,0:00:02.07,Default,,0000,0000,0000,,In this video, I really wanted to introduce
Dialogue: 0,0:00:02.07,0:00:06.40,Default,,0000,0000,0000,,you to some terminology for some basic angle types
Dialogue: 0,0:00:06.40,0:00:09.67,Default,,0000,0000,0000,,and terminology. I wanted to introduce you to are
Dialogue: 0,0:00:09.67,0:00:20.87,Default,,0000,0000,0000,,acute angles, right angles, and obtuse angles.
Dialogue: 0,0:00:20.87,0:00:22.45,Default,,0000,0000,0000,,I think when we go through these,
Dialogue: 0,0:00:22.45,0:00:24.87,Default,,0000,0000,0000,,it will be pretty self-explanatory.
Dialogue: 0,0:00:24.87,0:00:27.19,Default,,0000,0000,0000,,And an acute angle is an angle --
Dialogue: 0,0:00:27.19,0:00:29.36,Default,,0000,0000,0000,,let me just draw them first
Dialogue: 0,0:00:29.36,0:00:30.40,Default,,0000,0000,0000,,then you might,
Dialogue: 0,0:00:30.40,0:00:31.33,Default,,0000,0000,0000,,you might,
Dialogue: 0,0:00:31.33,0:00:32.86,Default,,0000,0000,0000,,it might start to make sense.
Dialogue: 0,0:00:32.86,0:00:33.78,Default,,0000,0000,0000,,So an acute angle
Dialogue: 0,0:00:33.78,0:00:35.04,Default,,0000,0000,0000,,will look something like that.
Dialogue: 0,0:00:35.04,0:00:35.80,Default,,0000,0000,0000,,I draw two rays
Dialogue: 0,0:00:35.80,0:00:37.78,Default,,0000,0000,0000,,coming from a common point.
Dialogue: 0,0:00:37.78,0:00:38.71,Default,,0000,0000,0000,,I could also --
Dialogue: 0,0:00:38.71,0:00:41.87,Default,,0000,0000,0000,,so the acute angle could be this angle right over here.
Dialogue: 0,0:00:41.87,0:00:43.96,Default,,0000,0000,0000,,I could also draw an acute angle;
Dialogue: 0,0:00:43.96,0:00:47.16,Default,,0000,0000,0000,,maybe an angle that is formed from an intersection of two lines,
Dialogue: 0,0:00:47.16,0:00:49.85,Default,,0000,0000,0000,,so this angle would be acute,
Dialogue: 0,0:00:49.85,0:00:51.43,Default,,0000,0000,0000,,and so will this angle.
Dialogue: 0,0:00:51.43,0:00:52.53,Default,,0000,0000,0000,,They're both acute angles.
Dialogue: 0,0:00:52.53,0:00:54.53,Default,,0000,0000,0000,,We are going to see acute angles as ones
Dialogue: 0,0:00:54.53,0:00:55.70,Default,,0000,0000,0000,,that are --
Dialogue: 0,0:00:55.70,0:00:58.03,Default,,0000,0000,0000,,that since I haven't defined right angles yet.
Dialogue: 0,0:00:58.03,0:00:59.19,Default,,0000,0000,0000,,They are narrower,
Dialogue: 0,0:00:59.19,0:01:00.60,Default,,0000,0000,0000,,so we are going to see that they are
Dialogue: 0,0:01:00.60,0:01:01.93,Default,,0000,0000,0000,,smaller than right angles.
Dialogue: 0,0:01:01.93,0:01:04.11,Default,,0000,0000,0000,,Right angles are when the rays
Dialogue: 0,0:01:04.11,0:01:07.20,Default,,0000,0000,0000,,or the lines are going, oh
Dialogue: 0,0:01:07.20,0:01:11.53,Default,,0000,0000,0000,,I guess, I don't want to use the word "right"
Dialogue: 0,0:01:11.53,0:01:12.61,Default,,0000,0000,0000,,in my definition.
Dialogue: 0,0:01:12.61,0:01:13.80,Default,,0000,0000,0000,,They are kind of
Dialogue: 0,0:01:13.80,0:01:15.58,Default,,0000,0000,0000,,if one is going horizontal
Dialogue: 0,0:01:15.58,0:01:17.58,Default,,0000,0000,0000,,then the other one will be going vertical.
Dialogue: 0,0:01:17.58,0:01:18.87,Default,,0000,0000,0000,,so let me draw with rays first
Dialogue: 0,0:01:18.87,0:01:20.04,Default,,0000,0000,0000,,so the right angle
Dialogue: 0,0:01:20.04,0:01:21.80,Default,,0000,0000,0000,,this one is going from the left to the right
Dialogue: 0,0:01:21.80,0:01:24.17,Default,,0000,0000,0000,,and the other ray is going from the bottom
Dialogue: 0,0:01:24.17,0:01:25.43,Default,,0000,0000,0000,,to the top
Dialogue: 0,0:01:25.43,0:01:27.20,Default,,0000,0000,0000,,this angle right over here
Dialogue: 0,0:01:27.20,0:01:28.86,Default,,0000,0000,0000,,is a right angle
Dialogue: 0,0:01:28.86,0:01:30.54,Default,,0000,0000,0000,,and I could label it like that
Dialogue: 0,0:01:30.54,0:01:31.60,Default,,0000,0000,0000,,but as a traditional angle
Dialogue: 0,0:01:31.60,0:01:32.86,Default,,0000,0000,0000,,but the general,
Dialogue: 0,0:01:32.86,0:01:35.50,Default,,0000,0000,0000,,the general convention for labeling right angles
Dialogue: 0,0:01:35.50,0:01:36.52,Default,,0000,0000,0000,,is to put a little,
Dialogue: 0,0:01:36.52,0:01:39.36,Default,,0000,0000,0000,,a kind of a half of a box over there.
Dialogue: 0,0:01:39.36,0:01:44.19,Default,,0000,0000,0000,,That tells me that this is a right angle
Dialogue: 0,0:01:44.19,0:01:47.90,Default,,0000,0000,0000,,or, that if this is going left to right
Dialogue: 0,0:01:47.90,0:01:50.18,Default,,0000,0000,0000,,this is going perfectly top to bottom
Dialogue: 0,0:01:50.18,0:01:52.60,Default,,0000,0000,0000,,that this is a no way kind of
Dialogue: 0,0:01:52.60,0:01:53.85,Default,,0000,0000,0000,,that this is a completely,
Dialogue: 0,0:01:53.85,0:01:54.92,Default,,0000,0000,0000,,I guess the best way to think about it
Dialogue: 0,0:01:54.92,0:01:56.26,Default,,0000,0000,0000,,why it's called right
Dialogue: 0,0:01:56.26,0:01:58.91,Default,,0000,0000,0000,,is that this ray is completely upright
Dialogue: 0,0:01:58.91,0:02:01.93,Default,,0000,0000,0000,,compared to this ray over here
Dialogue: 0,0:02:01.93,0:02:03.67,Default,,0000,0000,0000,,let me draw with some lines
Dialogue: 0,0:02:03.67,0:02:05.92,Default,,0000,0000,0000,,if I have one line like this
Dialogue: 0,0:02:05.92,0:02:08.52,Default,,0000,0000,0000,,and I have another line like that
Dialogue: 0,0:02:08.52,0:02:11.36,Default,,0000,0000,0000,,a right angle over here
Dialogue: 0,0:02:11.36,0:02:12.84,Default,,0000,0000,0000,,actually all of these would have to be
Dialogue: 0,0:02:12.84,0:02:13.77,Default,,0000,0000,0000,,right angles
Dialogue: 0,0:02:13.77,0:02:15.16,Default,,0000,0000,0000,,it would mean that this line
Dialogue: 0,0:02:15.16,0:02:15.91,Default,,0000,0000,0000,,is completely,
Dialogue: 0,0:02:15.91,0:02:16.93,Default,,0000,0000,0000,,if this line were the ground,
Dialogue: 0,0:02:16.93,0:02:18.60,Default,,0000,0000,0000,,this line is completely upright
Dialogue: 0,0:02:18.60,0:02:21.25,Default,,0000,0000,0000,,relative to this line over here.
Dialogue: 0,0:02:21.25,0:02:22.50,Default,,0000,0000,0000,,so either these,
Dialogue: 0,0:02:22.50,0:02:24.33,Default,,0000,0000,0000,,so that is what a right angle means
Dialogue: 0,0:02:24.33,0:02:25.84,Default,,0000,0000,0000,,so now that we defined right angle
Dialogue: 0,0:02:25.84,0:02:28.17,Default,,0000,0000,0000,,I can give you another definition for acute angle
Dialogue: 0,0:02:28.17,0:02:31.09,Default,,0000,0000,0000,,so an acute angle has a measure
Dialogue: 0,0:02:31.09,0:02:33.93,Default,,0000,0000,0000,,or it's smaller than a right angle
Dialogue: 0,0:02:33.93,0:02:36.62,Default,,0000,0000,0000,,so you learn about radients and degrees
Dialogue: 0,0:02:36.62,0:02:38.67,Default,,0000,0000,0000,,which are different ways to measure angles
Dialogue: 0,0:02:38.67,0:02:39.92,Default,,0000,0000,0000,,so you'll see that a right angle
Dialogue: 0,0:02:39.92,0:02:42.52,Default,,0000,0000,0000,,can be measured as 90 degrees
Dialogue: 0,0:02:42.52,0:02:45.54,Default,,0000,0000,0000,,this over here is less than 90 degrees
Dialogue: 0,0:02:45.54,0:02:48.93,Default,,0000,0000,0000,,so this is less than 90 degrees.
Dialogue: 0,0:02:48.93,0:02:51.11,Default,,0000,0000,0000,,and one way to conceptualize this is
Dialogue: 0,0:02:51.11,0:02:52.36,Default,,0000,0000,0000,,that this angle,
Dialogue: 0,0:02:52.36,0:02:54.36,Default,,0000,0000,0000,,it's opening is smaller
Dialogue: 0,0:02:54.36,0:02:55.84,Default,,0000,0000,0000,,it's more narrow,
Dialogue: 0,0:02:55.84,0:02:58.77,Default,,0000,0000,0000,,it's lines are,
Dialogue: 0,0:02:58.77,0:03:01.28,Default,,0000,0000,0000,,you would have to rotate one line
Dialogue: 0,0:03:01.28,0:03:03.00,Default,,0000,0000,0000,,less to get to the other line
Dialogue: 0,0:03:03.00,0:03:04.11,Default,,0000,0000,0000,,then you would over here.
Dialogue: 0,0:03:04.11,0:03:05.00,Default,,0000,0000,0000,,here, you would have to move
Dialogue: 0,0:03:05.00,0:03:06.25,Default,,0000,0000,0000,,all the way over there
Dialogue: 0,0:03:06.25,0:03:07.59,Default,,0000,0000,0000,,here you only have to move it a little bit
Dialogue: 0,0:03:07.59,0:03:10.47,Default,,0000,0000,0000,,so the acute angle is less than a right angle
Dialogue: 0,0:03:10.47,0:03:12.53,Default,,0000,0000,0000,,so you might imagine already
Dialogue: 0,0:03:12.53,0:03:14.10,Default,,0000,0000,0000,,what an obtuse angle is
Dialogue: 0,0:03:14.10,0:03:16.51,Default,,0000,0000,0000,,it is greater than a right angle
Dialogue: 0,0:03:16.51,0:03:18.18,Default,,0000,0000,0000,,so let me draw a couple of examples
Dialogue: 0,0:03:18.18,0:03:19.00,Default,,0000,0000,0000,,of obtuse angles
Dialogue: 0,0:03:19.00,0:03:20.92,Default,,0000,0000,0000,,so an obtuse angle might look like
Dialogue: 0,0:03:20.92,0:03:25.57,Default,,0000,0000,0000,,let me get it a little clearer
Dialogue: 0,0:03:25.57,0:03:27.84,Default,,0000,0000,0000,,might look like that
Dialogue: 0,0:03:27.84,0:03:30.44,Default,,0000,0000,0000,,if it was a right angle,
Dialogue: 0,0:03:30.44,0:03:32.44,Default,,0000,0000,0000,,then this line over here
Dialogue: 0,0:03:32.44,0:03:33.28,Default,,0000,0000,0000,,would be,
Dialogue: 0,0:03:33.28,0:03:33.92,Default,,0000,0000,0000,,would look something like that
Dialogue: 0,0:03:33.92,0:03:35.36,Default,,0000,0000,0000,,it would be completely upright
Dialogue: 0,0:03:35.36,0:03:36.57,Default,,0000,0000,0000,,relative to this, if this were the ground.
Dialogue: 0,0:03:36.57,0:03:38.24,Default,,0000,0000,0000,,but we don't see that
Dialogue: 0,0:03:38.24,0:03:41.45,Default,,0000,0000,0000,,this orange ray over here is actually
Dialogue: 0,0:03:41.45,0:03:42.94,Default,,0000,0000,0000,,opened out wider
Dialogue: 0,0:03:42.94,0:03:44.93,Default,,0000,0000,0000,,it's opened up wider
Dialogue: 0,0:03:44.93,0:03:47.44,Default,,0000,0000,0000,,so it is obtuse.
Dialogue: 0,0:03:47.44,0:03:49.25,Default,,0000,0000,0000,,it is obtuse
Dialogue: 0,0:03:49.25,0:03:50.60,Default,,0000,0000,0000,,so this kind of comes from the actual
Dialogue: 0,0:03:50.60,0:03:51.67,Default,,0000,0000,0000,,everyday meaning
Dialogue: 0,0:03:51.67,0:03:54.82,Default,,0000,0000,0000,,acute means very sharp or very sensitive
Dialogue: 0,0:03:54.82,0:03:58.00,Default,,0000,0000,0000,,obtuse means not very sharp or not very sensitive.
Dialogue: 0,0:03:58.00,0:04:00.86,Default,,0000,0000,0000,,you could imagine this looks like a sharp point
Dialogue: 0,0:04:00.86,0:04:02.90,Default,,0000,0000,0000,,or it's, it's not opening up much.
Dialogue: 0,0:04:02.90,0:04:04.95,Default,,0000,0000,0000,,so maybe it's more sensitive to
Dialogue: 0,0:04:04.95,0:04:06.16,Default,,0000,0000,0000,,you know, relative to other things
Dialogue: 0,0:04:06.16,0:04:08.24,Default,,0000,0000,0000,,I don't know, just trying to make connections
Dialogue: 0,0:04:08.24,0:04:10.10,Default,,0000,0000,0000,,This is less sensitive
Dialogue: 0,0:04:10.10,0:04:11.50,Default,,0000,0000,0000,,It's all big and open
Dialogue: 0,0:04:11.50,0:04:13.58,Default,,0000,0000,0000,,It won't be able to notice things that are small
Dialogue: 0,0:04:13.58,0:04:17.76,Default,,0000,0000,0000,,or maybe that is not an appropriate analogy
Dialogue: 0,0:04:17.76,0:04:19.44,Default,,0000,0000,0000,,but one way to think about it
Dialogue: 0,0:04:19.44,0:04:20.67,Default,,0000,0000,0000,,it's kind of open up wider,
Dialogue: 0,0:04:20.67,0:04:23.10,Default,,0000,0000,0000,,or it's bigger than a right angle
Dialogue: 0,0:04:23.10,0:04:24.92,Default,,0000,0000,0000,,it's larger than 90 degrees
Dialogue: 0,0:04:24.92,0:04:27.24,Default,,0000,0000,0000,,larger than 90 degrees
Dialogue: 0,0:04:27.24,0:04:28.17,Default,,0000,0000,0000,,if you measure it
Dialogue: 0,0:04:28.17,0:04:30.40,Default,,0000,0000,0000,,you would have to rotate this ray more to
Dialogue: 0,0:04:30.40,0:04:33.60,Default,,0000,0000,0000,,get to this other ray
Dialogue: 0,0:04:33.60,0:04:34.95,Default,,0000,0000,0000,,than you would if you had right angles
Dialogue: 0,0:04:34.95,0:04:37.33,Default,,0000,0000,0000,,and definitively a lot more if they were acute angles.
Dialogue: 0,0:04:37.33,0:04:39.50,Default,,0000,0000,0000,,If I were to draw this with lines,
Dialogue: 0,0:04:39.50,0:04:44.19,Default,,0000,0000,0000,,which of the angles are obtuse and
Dialogue: 0,0:04:44.19,0:04:45.20,Default,,0000,0000,0000,,which are acute?
Dialogue: 0,0:04:45.20,0:04:47.44,Default,,0000,0000,0000,,Well the way I drawn them right over here,
Dialogue: 0,0:04:47.44,0:04:49.25,Default,,0000,0000,0000,,these two over here are acute
Dialogue: 0,0:04:49.25,0:04:51.85,Default,,0000,0000,0000,,are acute
Dialogue: 0,0:04:51.85,0:04:54.27,Default,,0000,0000,0000,,and then these over here are going to be
Dialogue: 0,0:04:54.27,0:04:55.57,Default,,0000,0000,0000,,obtuse
Dialogue: 0,0:04:55.57,0:04:56.50,Default,,0000,0000,0000,,so this one
Dialogue: 0,0:04:56.50,0:04:57.28,Default,,0000,0000,0000,,and this one
Dialogue: 0,0:04:57.28,0:05:00.91,Default,,0000,0000,0000,,these are both obtuse angles
Dialogue: 0,0:05:00.91,0:05:02.44,Default,,0000,0000,0000,,and I actually drew them up here as well.
Dialogue: 0,0:05:02.44,0:05:05.50,Default,,0000,0000,0000,,This one and this one are going to be
Dialogue: 0,0:05:05.50,0:05:08.52,Default,,0000,0000,0000,,obtuse
Dialogue: 0,0:05:08.52,0:05:09.59,Default,,0000,0000,0000,,so very simple idea
Dialogue: 0,0:05:09.59,0:05:12.56,Default,,0000,0000,0000,,if one line
Dialogue: 0,0:05:12.56,0:05:14.51,Default,,0000,0000,0000,,or if one ray is relative to the other one
Dialogue: 0,0:05:14.51,0:05:15.58,Default,,0000,0000,0000,,is straight up and down
Dialogue: 0,0:05:15.58,0:05:16.67,Default,,0000,0000,0000,,versus left to the right
Dialogue: 0,0:05:16.67,0:05:17.87,Default,,0000,0000,0000,,or is completely upright
Dialogue: 0,0:05:17.87,0:05:19.95,Default,,0000,0000,0000,,then we're talking about a right angle
Dialogue: 0,0:05:19.95,0:05:21.94,Default,,0000,0000,0000,,if they are closer to each other
Dialogue: 0,0:05:21.94,0:05:23.24,Default,,0000,0000,0000,,if you had to rotate them less
Dialogue: 0,0:05:23.24,0:05:24.27,Default,,0000,0000,0000,,you're talking about a acute angle
Dialogue: 0,0:05:24.27,0:05:25.94,Default,,0000,0000,0000,,if you had to rotate them more
Dialogue: 0,0:05:25.94,0:05:27.94,Default,,0000,0000,0000,,you are talking about an obtuse angle
Dialogue: 0,0:05:27.94,0:05:29.10,Default,,0000,0000,0000,,and I think if you look at them visually
Dialogue: 0,0:05:29.10,0:05:31.28,Default,,0000,0000,0000,,it's pretty easy to pick out