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00:27

Evan S.

Classify each statement as true or false. Plane $R$ intersects plane $S$ in $\stackrel{\leftrightarrow}{A B}$ .

00:21

Amrita B.

Planes $M$ and $N$ are known to intersect. a. What kind of figure is the intersection of $M$ and $N ?$ lire b. State the postulate that supports your answer to part (a).

01:18

Martha R.

Points $A$ and $B$ are known to lie in a plane. a. What can you say about $\dot{A B}$ ? b. State the postulate that supports your answer to part (a).

00:05

In Exercises $5-11$ you will have to visualize certain lines and planes not shown in the diagram of the box. When you name a plane, name it by using four points, no three of which are collinear. Write the postulate that assures you that $\overrightarrow{A C}$ exists.

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Okay. I'm here to show you a few examples of how you might, uh, work with or see some angle by sector questions. So again, an angle by sector does exactly what it says. It bisects and angle. So look at angle or problem one. If the measure of angle s u t is 34 degrees, find angle one. It's an angle by sector. So half of 34 is gonna be angle one and two is gonna be the same value. So half of 34 and you get 17 degrees. That's the measure of angle one. Okay, Pretty straightforward. Right? Okay. Well, again, if you have two or more angle by sectors, they're going to meet at a point of concurrency, which we call the in center. And I remember that in center is equi distant toe all three sides. So if we know Petey is three, then we automatically know P. U is three. So is s p, for that matter. Okay, now something we didn't talk about but is built into this You have all these right triangles built in. So Pythagorean theorem is all over the place. Yeah. So, for example, if you look like question seven. If we know P Y is to and we know HP right here is three. Then if I draw that picture a little bit better where this is three and this is two and the question is, what's h y? Let's do a little Pythagorean theorem. Let's call this X. We don't know. It would be two squared plus X squared equals three squared. That's four plus X squared equals nine. Or, in other words, X squared equals five. Or, in other words, X equals Route five. So essentially, it's the Pythagorean theorem because of the special relationship, through the points on the instant or on the angle by sectors air all equi distant or perpendicular to that distance to the sides of the triangle. Okay, we can throw some algebra in there so you know, let's say we have exp we know exp is an angle by sector. So we know angles one and two have to be equal. Okay, So guess what that means for X. Plus five has to equal five x minus two, and it's gonna get a seven equals X and look out. They could ask us for what's the angle of angle one. Well, what's the measure of angle one? Well, that means I would just plug seven back in to me. Five times seven is 35 minus 2. 33. So I could say All right, angle one equals 33. This is not being asked up here, but it could have been. That means angle to is equal to 33. And that also means that the whole angle why xz would be equal to 66. So any one of these questions could be asked. Okay, some additional questions that could also be asked would be if you had a triangle like so and I had an angle by sector, and I had a point on the angle by sector. And I had these two distances. Well, we know those two distances have to be the same. So because there equally distant based upon the angle bisect, earthier. Um, So if I knew this was like two x plus 11 and this distance was three x plus five. Well, by default, three x plus five would have to equal two X plus 11. And so we would get his X equal six and again, I could go a little bit further and say All right, what's the length of those segments, then? Well, this plug six. And then do you get 12 plus 11? Okay. Or here you're gonna get 18 plus five. And either way, you're gonna get 23. So those are some examples of some angle by such questions, you could see I'll be back next time to talk about perpendicular by sectors.

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