 Hi, this video is called Vocabulary. It is the first video for section 11.3 called Areas of Regular Polygons and Circles. I think I would it would be safe to say that Section 11.3 is very important to take good notes on pay attention and make sure you ask your teacher questions in the future tomorrow in class if you have any. The vocabulary that you're going to learn in this video is very important to introduce and kind of help you have success in this lesson, which will be important for success in the chapter. So take good notes pay attention here we go. If you look at this picture, I see a circle. I also see a pentagon. It has five sides. So looking this we've got a pentagon inscribed inside of a circle and when I look at this, the first vocab word is basically called the center of the polygon. That's exactly what it sounds like. It's a point that's equidistant from each vertex. So each vertex being P, E, N, T, and A. So the center of the polygon is G. You can write that in your notes. And please notice it also would be considered the center of the circle. One thing that's worth noting that I should have mentioned at the very beginning is that this lesson is called Area of Regular Polygons. Please remember that regular means that all your side lengths and all your angle measures are the same. So in this pentagon, all of these segments would be the same and all of these angle measures would be the same. The formula that you're going to be learning and using today only works for regular polygons. So it only works when all the side lengths are equal, congruent, and all the angles are congruent as well. All right, the next vocab word talks about the radius of the polygon. And you're used to hearing about the radius of a circle. So please remember radius of a circle goes from the center of your circle out to touching the circle. Well, the radius of the polygon is kind of the same idea. It's a segment whose endpoints are the center and the vertex of the polygon. So it's important that where a radius of a circle can go from the center to anywhere on the circle, the radius of a polygon goes from the center to the vertex. So we would have a radius ga, we would have a radius segment gp, we would have another one at gE, another radius would be segment gn, and I'd have a fifth one at gt. So those segments are all considered a radius of the polygon or radii of the polygon. Since the pentagon has five sides, it's going to have five radii. All right, our next vocab word is called the central angle. You've already been exposed to this a little bit. You're going to start using it a lot and become very comfortable with it. The definition of a central angle says it's an angle formed by two adjacent radii. So remember adjacent means next to. So if you look at this picture, I've got a radius ga because it goes from the center out to a vertex, and I've got the radius gp. So you have a central angle right here. It would be called angle pga. What do you know? All right, because this pentagon has five sides, that means it's also going to have five central angles. So if I went and drew out all the radii, these would all be my central angles, and they will all be congruent to each other. So we'd also have one at eGp. We'd have one at eGn. Angle eGn would be a central angle, and gt would be a central angle, and finally tga. So just some things to consider. Since it's a pentagon has five sides, it's going to have five central angles that are all congruent. Stop from it and think about what would those five angles add up to? Hopefully you're thinking 360 degrees because they make a circle. We'll get to that later though. I'm just throwing that out there to see what you think. All right, and then the last vocab word for the day. This is the one that is truly new. You've probably never heard it before, and it is so special. There's actually kind of two different ways that people tend to pronounce it. You could either pronounce it as the apathem or the apathem. To be honest, I am not sure which one is is correct. I would answer to both if you if you used either of them. So you choose what you like better or ask your teacher what they prefer, apathem or apathem. And what it is, it's a very important segment in this section. It says that it's a segment whose end points are the center and the midpoint of the side of the polygon. That's kind of a lot. That's a mouthful. We'll look at the picture to really make sure you understand it. One important thing to note is that it's perpendicular to the side of the polygon. So to back up a little bit, GA is considered a radius because it goes from the center to the edge of your to the vertex of your pentagon or you know the edge of the circle. The apathem goes from the center, but instead of going to a vertex, it goes in the middle of a side. So we put this point here. We called it C. So we would have an apathem segment GC. We're told it's perpendicular to the side of the polygon. So that's why the 90 degree angle is there. And please notice we've just created a right triangle GCa. That will end up helping us out a lot. We're going to use that a lot. So I think what I'm going to do just to illustrate, I'd have an apathem right here because it goes from the center to the middle of that side. I'd have an apathem here. I'd have one here and I'd have one here. They all make 90 degree angles with the side of my pentagon because they're perpendicular. And then it also says that it goes to the midpoint of the side of the polygon. So it creates congruent segments all the way around your pentagon. Again, we'll get into more detail with that. You'll get much more comfortable with that soon. It's just important to remember what your apathem is. It goes from the center of your circle or center of the pentagon, I should say, to the middle of one of the end points. Where do your radii went from the center to the vertex? So lots of segments. You just have to remember a radius goes to the vertex and apathem or an apathem goes to the middle of the edges.