 In this video, I'm going to talk about corresponding angles postulate, and then I'm also going to talk about alternate, I think it's alternate interior angles theorem. I think that's the one. I'll have to go to the next slide to figure that out. So corresponding angles postulate and also alternate interior angles theorem. So now what we've done is we've taken the vocabulary and we're expanding upon it. So now what we're doing is, now that I am interacting with parallel lines, if I have a transversal that cuts two parallel lines, then the angles that are formed, I actually know something about them. So this is what we have. Corresponding angles theorem. We're going to talk about the corresponding angles. So angles 1 and angle 5, angle 2 and angle 6, angle 4 and angle 8, and angle 3 and angle 7. Those are the different pairs of corresponding angles. Remember, corresponding angles are angles in the same position between two intersections. So here's one intersection. Here's the other. They're in the same position. Those 3 and 7, top right, top right, they're in the same position. So that's a little overview of the vocabulary. All right, now corresponding angles postulate says if a transversal, if a transversal. Basically, we're looking at this picture. We have a transversal and we've got two parallel lines. So if a, if, I've got to put the if in there, if a transversal intersects, intersects two parallel lines, then, so I just stated the hypothesis. Now I've got to have the conclusion, then the, now notice the corresponding angles. Notice the corresponding angles using my abbreviations here, corresponding angles, are congruent. Using my congruency symbol for congruent. If a transversal intersects two parallel lines, then the corresponding angles are congruent. You can actually kind of see that here without really doing a whole lot of math or anything like that. You can notice the angle 1, it's kind of an obtuse angle. It's kind of big over here. And then if you look at the corresponding angle over here, angle 5 is also obtuse. So the corresponding angles are going to, in fact, be congruent. Now what I also want to do is I'm going to list out all of these corresponding angles that are congruent. So that first one, angle 1 is congruent to angle 5. I'm just going to go down the list. Angle 2 and angle 6 are congruent. Angle 2 is congruent to angle 6. Angle 3, angle 7. Angle 3 is congruent to angle 7. And last, we have angle 4 is congruent to angle 8. Angle 4 is congruent to angle 8. All right. So that is all of the corresponding angles that are going to be congruent with this postulate. Now again, you have to have parallel lines first. Parallel line, parallel line. If we have parallel lines, the corresponding angles will be congruent. That's one of our postulates. Now we haven't proven this postulate or anything like that, but that's not the purpose of this video. The purpose of the video is just to relay the information that the postulate has. Moving on to the next one. And did I guess right? Alternate interior angles theorem. I did guess right. So this one, a little bit different, a little bit different. But notice we used kind of the same picture. But it says we're only talking about the alternate interior angles. We're only talking about these angles here in the middle, 3, 4, 5, and 6. So I'm going to start with my hypothesis. If a transversal intersects two parallel lines, then I'm getting to my conclusion. Here's my hypothesis. If a transversal intersects two parallel lines, then, get to my conclusion, then. Now you can kind of guess what's going to happen here. Notice angle 4. Angle 4 is kind of a big angle, kind of a big angle. And if you look, alternate interior over here, angle 5, is also kind of a big angle. Also kind of a big angle. Notice the angle 4 and angle 5 are going to be the same. They're going to be congruent. So then this tells us that alternate interior angles are congruent. Then alternate interior angles are congruent. Notice all the different abbreviations, notation that I'm using. I like to use a lot of abbreviations. It makes the writing go a lot faster. So if a transversal intersects two parallel lines, then alternate interior angles are in fact congruent. So what that does is that says, OK, we'll alternate interior angles. So notice 3, kind of a small angle here. 6, kind of a small angle. Alternate interior angles. Angle 3 is going to be congruent to angle 6. Nice. And then lastly, angle 4 and angle 5. Angle 4 is congruent to angle 5. Now notice there's only four angles on the interior. So that means I only have two pairs of congruent angles. Two pairs of congruent alternate interior angles. All right, that's a very short video on the two postulates in a theorem. The first one was the corresponding angles postulates. And then this one was the alternate interior angles theorem.