Geometry Vocabulary

Hi, welcome back. We are doing a unit three or the unit that is the circles unit. And there are two circles unit, and we're doing part one. So this is the first I have two units, and this is lesson one, and we're going over geometry vocabulary, and then one of our tangent theorems. So here is our note taking guide or the first page because I got two pages here. The first page of our note taking guide, and we're going to kind of fill this out and go over some definitions together. Make sure we're all on the same page. So right here we're going to write the definition, then we're going to draw a picture. Okay, everybody knows what a circle is. But what is actually the definition of a circle? The definition of a circle, it is the set of all points, equidistant from a point. So the set of all points equal and I'm going to distant from a point. Okay, so I don't know if you've ever drawn a circle, but you take attack and you take a piece of string and you circle it around and you put your pencil on that end of the string and you draw all the way around. Well, that distance is constant as you pull the string around your tack to create your circle. So that's the set of all points equals distance from the same point. So of course we know that we have a circle, but we need to designate what point all the points are equidistant to, and that's the center of the circle. And what we name circles we always name them by the center. So if this is circle P, then that point in the center is a P okay, radius. What is a radius? Radius is the distance in a circle. And a circle. From the center to any point on the circle. Okay? So it's the distance from the center to any point on the circle. So if we are drawing with that string, the string is our radius, when we draw with attack, we pull the string around. That string is our equidistance. Okay, what is a chord? A chord on a circle. Has is a line segment, first of all. It's a line segment. Whose end point. Lie on the circle. Lie. On the circle. What do we mean by on the circle? That means if you have a circle, those points that are the end points of a line segment lie on the circle. So here is a chord, it's a line segment, and the endpoints have to be on the circle. So you can't draw one where you have one endpoint on the circle and then one point in the circle or one point on the circle on one point outside, both endpoints have to be on the circle to constitute a chord. Okay, so what is a diameter? Um. A diameter is a chord. So we're gonna say it is a chord whose endpoints lie on the circle, but it has something special on a diameter. It has to go through the center. So a chord that passes through the center. Of a circle. Okay. So you've got a circle. You've got end points. But those endpoints have to pass through that center to create a diameter. And we know that a diameter is two radii. So it's a radius from here to here, and then from here to here. Okay, so that's a diameter. Now let's look at secant. Okay, a secant, it is a line or a line segment. Line or line segment. That contains. Two points on the circle. Okay, so it's similar to a chord only it continues. So a secant goes is a line or a line segment that goes through a circle and it continues. So here's an example of a secant, okay? So it does contain two points, but it doesn't stop at this point. It continues. So it will say it continues out side the circle. Okay, now tangent. Tangent is a very common term that you're going to use, not just here, but a but later in math two. So what is a tangent? It is online or line segment. It can even be a ray. Okay? That. Contains. Only one point on the circle. Okay. Now, how can we draw a line that only contains one point on the circle. So here's our circle and we have to draw a tangent. It's just going to touch it in one place. So there is a tangent. So it doesn't actually contain any points on the interior of the circle. It only can pertains a point on the circle, okay? So that is considered a tangent line. Now let's go down to our picture down here, and we're going to take those terms and try to identify what these are. Let me zoom in just a little bit. Okay, let's start with BH. And notice the symbol on BH. Is array. Okay? So let's look at BH B starts here and goes on forever. Now B is what we call a point of tangency because it's where the tangent line touches the circle. So BH being the rate that it is, it's actually considered a tangent. And you could say just tangent or you could call it a tangent ray, either one, because it doesn't have the other arrow on the end of its symbol. Okay, let's look at E, D E, D it has end points on the circle. While the segment that has endpoints on the circle is a chord, but notice this chord goes through the center a so when you have a cord that goes through the center, it is considered a diameter. But it is also, of course. But more specifically, a diameter. Okay, how about AD? Okay, a is the center of the circle and we do knit call this circle a so AD is a radius. Because it's from the center to the side, CB C to B both of those endpoints are again on the circle. Does it go through the center? Yes, it does. Therefore, it is also a diameter. Just like ED was. How about EF? EF. Okay, EF has endpoints on the circle, but notice it does not go through the center, so it is considered just a cord. And then EG, EG has these little arrows on both ends. That means it's continuous. The line continues in both directions. So that gives us a hint. E, our GF goes through the circle and it contains points on the outside, therefore it is a secant. Okay, so those are the terms, radius core diameter secant tangent, and then of course we call this circle a because a is the center of the circle. So there's our geometry basic vocabulary. I'll scan back over that real quick. And there's all the information on those definitions. Now, we're going to stop for a second and talk about a theorem. Theorem 6.1. I've actually created a little circle here with a tangent on it. Let me zoom back out a little bit for you. Okay, so I printed a circle and I've got a tangent in the center of the circle. And I'm going to demonstrate for you this concept. The theorem is on your second page and it says in a plane, a line is tangent to a circle if and only if it is perpendicular to the radius of the circle at its end point on the circle. Okay, that's a lot of words. So let's just kind of demonstrate. What we're saying is if I draw a radius from the center of the circle to this point up here, point of tangent C and I'll call that T point T