Circle angles I (Parallel chords intercept congruent arcs)

Hey, it's mister Estrada here and in this video we're going to learn how to find the measurement of arcs intercepted by parallel lines. So let's talk about what is an arc. An arc is a portion of the circumference of a circle. So circumference is, of course, the we could say circumference is the measurement around the circle. And in arc is just a portion of that circumference. So here's an example of an arc. Right over here. This portion of the circumference, and in arc can be measured in degrees relative to the central angle, of course, you can also measure an arc in radians, centimeters, et cetera, et cetera, but in our course, we are going to use degrees to measure the art and that's degrees relative to the central angle. So if we want to know the measurement of this arc, it would simply be the measurement of the central angle that intercepts the arc. And by intercept, I mean the central angle here is connecting with the endpoints, so to speak of this arc. So the measurement of this arc here would be 90° as you can see the central angle is 90° here. Also, you recall that the whole circle is 360°, so the whole thing is 360°. And, you know, this is one fourth of 360° and one fourth of 360 is 90. So that's another way to get the 90. And I'll show you an example of another arc. So we see this here is also an arc, then no, don't do that. Stay as an arc. So this here is also an example of another arc. And obviously the measurement would have to be less than 90°, right? Because the central angle is a cube. So that's a little bit about arcs there. Let's look at the theorem for today. So the theorem says in a circle parallel chords intercept congruent arcs. So here we are given that chord AB is parallel to chord CD. We're given that here. These symbol means parallel. So once you're told that automatically, this arc, excuse me, this arc AC will be congruent to this arc BD. So that's what the theorem says in a circle of parallel chords intercept congruent arts. So let's work out an example. Example one, there it is. In the diagram of circle all below chords AB and CD are parallel. So we know that this chord is parallel to this chord D.C.. And it says BD is a diameter of the circle. What is the measurement of RBC? So you just learn from our theorem that if you have two parallel chords, this arc over here will be equal to this arc, right? The arcs intercepted by the chords are congruent. So arc BC, and by the way, you'll notice the symbol, the symbology for an arc is basically an arc on top of these two letters. So arc BC is equal to 60°. Let's look at another example. Example two in the diagram of circle or below chord CD is parallel to diameter AOB and the measure of arc AC is 40°. So arc AC is 40°. Automatically, you know that arc DB is also 40°. But they want us to give the measurement of arc CD. They want us to give the measurement of this arc. And how would we find that? Well, since we're told here that chord CD is parallel to diameter AOB, we are implicitly told that AOB is a diameter. And what a diameter does is that it cuts the circle in half. And what that means is that this whole arc AC DB, so this whole thing a, C, D, B, is equal to a 180°, right? So I'm talking about this whole arc over here, AC DB rack is half the circle would be a 180°. So if the whole thing is one 80, what should be the measurement of CD? Well, we know that 40 plus 40. Plus our missing arc CD must equal a 180. So that means that arc CD is equal to a 100°. And that's our final answer. Okay, so I hope this video helps take care.