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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).

00:06

State Theorem $1-2$ using the phrase one and only one.

01:05

Suzanne W.

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.

00:48

Evan S.

A plane can be named by three or more noncollinear points it contains. In Chapter 12 you will study pyramids like the one shown at the right below. Name five planes that contain sides of the pyramid shown.

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Okay, So we're here just to do a couple of problems for us to practice whether or not we can recognize if two triangles congruent, and if so, by what fear? Um, which of the four side side, side side angle, side angle, side angle or angle. Angle side. So we're going to a few of these, Okay. You have two triangles here. Well, you have to keep in mind is that they actually share aside, they actually share this side. So by default, that side's congruent to itself. So if you look at, let's say this bottom triangle, do this in blue. What do we know about that triangle compared to the other one? Well, we know we have two sides, so we have this side and this side that's could grow into each other. And we have the high pot news. Unfortunately, though the order is going to be side side. I'll do this in a different color as well. The order is side side angle s s a which you said is not a congruence there. Question one here would be inconclusive. It's not that they're not congruent is that we don't have any one of the four congruence teams met because the order is very important. Really? Good question to once again, these two triangles share aside. Okay, they share this site. Don't you notice something? They have an angle. Then aside than an angle uncommon, this would be angle, side angle, congruence. And yes, these two triangles are congruent. Take a look at this third question again. They have a third side in common. And hopefully you can see clearly by side, side side congruence. These three trying or these two triangles are congruent to each other. Pardon me? Let's do a couple more. Okay. So what if we had questions? Six. Like the previous examples where we shared aside, these triangles actually have an angle in common because we have vertical angles here. So that's something to keep in mind from something we talked about before. So now look, we have an angle aside and an angle on that order an angle aside and then order. We have angle side angle, congruence. Let's do a couple more clearly. Eight. A side side side, clearly Tennis side, side side. Because pardon me, we have that shite that side in common. Let's see here, seven. Do we have anything? Well, it looks like on this triangle we have an angle, are part of a side that an angle on a side. This would be a side angle side. However, on this one, the angle is not where it needs to be. So we don't have side angle side. These triangles are inconclusive. So you can see the order is super important here, whether or not we have a side that an angle that aside back to back to back those particular pieces have to match up number nine here. Notice again. We have vertical angles. So we now have a side angle, side situation, side angle, side situation. And there you go. We have congruent triangles. So this is this a couple of problems for you to be ableto quickly? Identify? Yes. Do we have congruent triangles? And if so, by which of the four therms and you're gonna notice that sometimes they either share sides, they share angles or have vertical angles, which is kind of like sharing angles. And so it's basically a extra piece of info that might not be labeled directly. All right, more examples improves coming at you soon

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