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Evan S.

The numbers given are the coordinates of two points on a number line. State the distance between the points. $$-3 \text { and }-17$$

00:29

The numbers given are the coordinates of two points on a number line. State the distance between the points. $$-1.2 \text { and }-5.7$$

00:23

Classify each statement as true or false. $h$ is in $S$.

00:27

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

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all right, we're here with just a few more examples of how to prove to triangles can grow. Um and you know, there's a ton of givens Utkan be presented with, all of which had, like, their own little set of reasons. So I'm gonna try to do, uh, tomb or examples and noticing these particular problems. Nothing's marked up. Yes, you have some right angles that air Britain in there, but it's not as marked a Z. Other proofs were eso. What I like to do with any given proof is go through my givens, mark up my drawing accordingly, mark up also what's indirectly implied, like something that's reflexive or vertical angle, and then proceed. So if you can see what we have here being dear right angles, so yes, clearly they are. They're marked now. If they weren't, I would have put the little right angle symbol in there. It also says e bisects BD what does that mean? Well, that means it cuts it in half if e cuts b d in half on, here's what I know that segment and that segment are equal. And then indirectly, I know that this angle here in this angle here congruent because the vertical angles. And now do you see I have angle, side angle. I'm ready to go. So before I even jump into writing anything, I want to mark up my picture, get a game plan, see where it's going, and then go ahead and start. So first I'm gonna say it right angle B An angle d are right angles that's given. Okay, then I'm gonna say angle B is congruent to angle D. Well, why? What's true? But all right, angles. All right. Angles, Right. That over with You got a small space here. All right? Angles. Arkan growing. Okay, that's one thing. Three e by sex PD. That's given what does that tell us? That tells us option four that B c is congruent to D. C. Why would that be the case? Well, what happens when you buy sex something It cuts it in half. So the reason would be definition of a by sector. Okay, at this point, I'm gonna throw in that option five angle B C A is congruent thio angle D c E. Notice. My order is very important. We've seen this before. The reason is you just say vertical angles. Okay, Running out of room here. But my six statement is going to be because now I have my one, 23 pieces I need for my angle side angle. I could now say that Triangle A B C is congruent to triangle e d. C. And the reason angle, side angle. So normally this, by the way, would be my sixth statement and reason. And so that is another proof. So oftentimes you're gonna be given some information like, Hey, these air right angles or this is perpendicular. I think about it. Perpendicular means you have right angles and right angles. Means you have can grew it or I have a midpoint. What is the midpoint? Do it by sex and therefore by sex means you have congruent segments. So if you just follow the chain of logic and their reasons should be very intuitive what does the midpoint do? It cuts a segment in half. Well, the segments cut in half. What do we have to congruent segments? So you could say like definition in mid point. Definition of by sector, definition of angle by sector, reflexive property. All right. Angles are equal definition of vertical angles. So based upon what you know, it's either going to be definition of or one thing implies the other. So, for example, if you're giving parallel lines, well, what do you know? What parallel lines they tell you information about angle. So you might say, Well, we have parallel lines. Therefore we have, you know, corresponding angles that are congruent. Oh, we have parallel alliance. Oh, we have, you know, uh, ultimate interior angles, something like that. And so take what you know. That becomes a reason. Take something that we've already proven or have already learned about. That becomes either definition or something you can use as a reason. Okay, So if we go to questions, let's see here this last question I'm gonna go ahead and erase some of this from above. You don't mind? So I can Oops. So we can kind of see what's going on here. Okay. Again, What's the first thing I love to do? Mark up my picture? It says J M by sex angle J. I don't like that technically because there's technically three angle Jay's this Jay this j and this J that's me being picky, but we get the picture. What they're saying is is that this angle and this angle are equal. We also have J am is perpendicular to K l. That means both of these are right angles. And then if you haven't noticed by now, we have a side that shared So hopefully you can see we have an angle aside in an angle in that order. So you know your last statements, reason is gonna be angle side angle. I was attacked this in the appropriate order. Okay, so my first given, by the way, is that J m by sex angle J that's clearly given. But that's not one of my three pieces. It's not a side or an angle statement, but it does Give us that angle. K J M is congruent to angle. L J M. Guess what? Definition of angle by sector. Cool. Three j. M is perpendicular to K l Here's what we're gonna get little picky. First of all, this is given okay. From here, you would say that angle l m J and Angles K m J are right angles. And the definition would be the reason would be definition of perpendicular. Yeah. Okay, then you would say, and I'm running out of room here. But then you would say for option five if they're both right, well, then they're both equals. I'm gonna say there can grow it. And the reason is gonna be all right. Angles. I'll use this symbol. So we're getting smashed here. All my gosh. Okay. All right. Angles are congruent, and the more times you do proofs like this, the more like you're gonna, like, be using abbreviations. Okay, So I'm gonna take out some of this so that we can actually fill in the rest of the steps, because if I had more paper, I would use that. Okay. What? So so far, we have an angle now and an angle now, of the three pieces we knew the third, and that is going to be option six. So I'm going up here. J m is congruent to itself as we have seen. That's reflective. So now, last but not least, I can say that one triangle is can grow into the other. I'm cutting. I'm cutting edges here so that we can kind of be done and save some space. But the reason for it, as we said earlier. Angle, side angle and then order. Okay, so again, too. Comment on the process. Here you're given a bunch of things. They're called givens for a reason. You're gonna mark up your picture accordingly to those givens. You're then gonna mark up what is implied. That might be a shared side, a shared angle or vertical angles or something like that. Then what you're gonna do is we're gonna start with your givens. And if they're very direct, like two sides congruent or two angles congruent great. If it's about a midpoint or an angle by sector or perpendicular or something like that, and you're gonna probably have to do two or three steps to get to showing that another angle or side Perry's can grow it. Then once you get three things either side side, side, side angle, side angle, side angle or angle, angle side, Then you can put the three pieces together to say that the triangles grew by one of those terms. And then if it's asking you to prove that some remaining side or angle Arkan growing, then you're gonna use you're gonna make that statement in your final reasons. Either gonna be C p C T. C. Which dance for congruent parts of congruent triangles are congruent. I'll say that again. C p c T c or you can say in instead definition of concurrency. So I hope these videos helped. This is just the tip of the iceberg in terms of proving triangles congruent polygons can group, for that matter. Hopefully does a good enough job of kind of getting your feet wet a little bit and well, I'll talk to you later. Thanks.

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