Topic B: Foundations
In this video, I really just want to introduce you to some terminology for some basic angle types. And the terminology I want to introduce you to are acute angles, right angles, and obtuse angles. And I think when we just go through these, they'll be pretty self-explanatory. An acute angle is an angle-- well, let me just draw them first. Then it might start to make sense. So an acute angle will look something like that. I draw two rays that are coming from a common point. So the acute angle will be this angle right over here. I could also draw an acute angle, maybe an angle that's formed from the intersection of two lines. This angle will be acute, and so will this angle. They're both acute angles. And we're going to see is acute angles are ones that are-- since I haven't defined right angles yet-- they're narrower. And what we're going to see is that they're smaller than right angles. Right angles are when the rays or the lines are going, I guess, in the-- I don't want to use the word, right, in my definition-- but if one is going horizontal, the other one will be going vertical. So let me draw it with the rays first. So the right angle, this one's going from the left to the right. Then the other ray is going from the bottom to the top. This angle right over here is a right angle. And I could label it like that, as a traditional angle. But the general convention for labeling right angles is to put a little, kind of a half of a box right over there. And that means that is a right angle. Or that if this is going left to right, this is going perfectly top to bottom, that this is in no way kind of-- I guess the best way to think about it and why it's called right is that this ray is completely upright, compared to this ray over here. And let me draw it with some lines. So if I have one line like this and then I have another line like that, a right angle over here-- actually all of these would have to be right angles-- it would mean that this line is completely-- if this was the ground, this line is completely upright, relative to this line over here. So either of these, that's what a right angle means. And now that we've defined right angle, I can give you another definition for an acute angle. An acute angle has a measure, or it's smaller, than a right angle. When you learn about radians and degrees, which are different ways to measure angles, you'll see that a right angle can be measured as 90 degrees. This over here is less than 90 degrees. So this is less than 90 degrees. And one way to conceptualize this is that this angle, its opening is smaller, it's more narrow, the lines are-- you would have to rotate one line less to get to the other line than you would over here. Here, you'd have to move it all the way over there. Here, you'd only have to move it a little bit. So the acute angle is less than a right angle. And so you might imagine already what an obtuse angle is. It is greater than a right angle. So let me draw a couple of examples of obtuse angles. So an obtuse angle might look like-- let me make it a little bit clearer. It might look like that. If this was a right angle, this line over here would look something like that. It would be completely upright relative to this if this were the ground. But we don't see that. This orange ray over here is actually opened out wider. It's opened up wider. So it is obtuse. And this kind of comes from the actual everyday meaning. Acute means very sharp or very sensitive. Obtuse means not very sharp or not very sensitive. So you could imagine this looks like a sharp point or it's not opening up much, so maybe it's more sensitive relative to other things, or I don't know. I'm just trying to make connections. This is less sensitive. It's all big and open. It won't be able to notice things that are small because I don't know. Maybe that's not an appropriate analogy. But one way to think about it, it's kind of open up wider, or it's bigger than a right angle. It's larger than 90 degrees if you measure it. You would have to rotate this ray more to get to this other ray than you would if they were right angles, and definitely a lot more than if they were acute angles. If I were to draw this with lines, which of the angles are obtuse and which are acute? Well, the way I've drawn them right over here, these two over here are acute, and then these over here are going to be obtuse. This one and this one, these are both obtuse angles. And I actually drew it up here, as well. This one and this one are going to be obtuse. So very simple idea. If one line or one ray relative to the other one is straight up and down, versus to left and right, or is completely upright, then we're talking about a right angle. If they're closer to each other, if you have to rotate them less, you're talking about an acute angle. If you have to rotate them more, you're talking about an obtuse angle. And I think when you just look at them visually, it's pretty easy to pick out.