 In this video, I'm going to talk about the alternate exterior angles theorem, and then I'm also going to talk about on my next slide here, I'm going to talk about the same side interior angles theorem. And just to start off with it, now this one we're talking about alternate exterior angles. So if we talk about the exterior angles, that's going to be angles one and two, and it's going to be the angles seven and eight. So notice that we have two parallel lines here, and a transversal T. So what I'm going to talk about is the relationship between the alternate exterior angles. So start with my hypothesis. If a transversal intersects two parallel lines, then, my conclusion, then, okay, so now one thing you can actually probably see from this is, okay, so if I actually look at the alternate exterior angles, here's angle one, angle one, there's an exterior angle, and if I go alternate, so I cross over the transversal, and I go to the other exterior angle that's over here at eight, notice that eight is kind of a big angle also, notice angle one is big, angle eight is big, so therefore, one and eight, kind of, you can look at this, you can look at this to kind of see this, angle one and angle eight are in fact going to be congruent. Same thing over here, angle two, cross over here to go to seven, angle seven is kind of small here, angle two is kind of small here, so those two are going to be congruent. So that's kind of the theorem there. Now again, we're not proving this theorem, we're just writing it down trying to understand it. If a transversal intersects two parallel lines, then the alternate exterior angles are congruent, okay, using again my abbreviations, my notation, my shorthand here, to say alternate exterior angles are congruent, okay. So that is what the theorem states, now what I'm also going to do is I'm going to write down the actual angles that are congruent. So one, two, seven and eight are the exterior angles, so one and eight is one pair, angle one is congruent to angle eight and then also angle two and angle seven is the next one, angle two is congruent to angle seven, okay, angle two is congruent to angle seven, that's kind of a bad eight there, apologies about that. All right, so those are the congruent exterior angles, now again this only happens if a transversal basically intersects two parallel lines, a transversal goes through two parallel lines. Okay, so the next one we're going to talk about is the same side interior theorem, same side interior kind of goes over the same thing that the previous one did, we're going to look at the same side interior angles. So notice here on my diagram, three and five are same side, four and six are same side interior. Okay, so let's start with the hypothesis, always got to start with what we know. If a transversal intersects two parallel lines then, then, now let's take a look at these, now again you can kind of just see it, angle three and I got, wait a minute, now all the last ones that I've looked at, all the other videos that I've done on these, all these theorems have said that everything is congruent, but hold on a minute, angle three and angle five, angle three is small, angle five is big, they're not congruent, there's no way they can be congruent, look at them, I mean three is small, five is big, they can't be congruent, they can't be the same. So it's something else, okay, now that's quite obvious, this is the only one that differs from the other theorems and the other postulate that we have. This one is going to be different, this one is the hardest one to remember, everything else is congruent, this one is, angle three and angle five, then the same side interior angles are, wait for it, supplementary, which means angle three and angle five are going to add up to 180 degrees, they're not going to be congruent, I mean just look at them, they can't be congruent, three is small, five is big, I mean they can't be congruent, there's no way. So it has to be something else, in this case, same side interior angles theorem tells us that same side interior angles are supplementary, this is the only one that's different from the rest of them, everything else that was congruent, this one is different, this was the one you've really got to remember, okay, a lot of students will misinterpret this one and think that everything is congruent, same side interior angles, that's the different one, those ones are going to be supplementary, okay, so that means angle three and angle five are supplementary, okay, which also means, you can also write it down a little bit differently, the measure of angle three is plus, sorry, the measure of angle five equals 180 degrees, you can also write it that way, you can also write it that way, okay, and now the other pair of same side interior, angle four and angle six, same deal, angle four and angle six are going to be supplementary, using my abbreviations here, using supplementary, also we can write it a little bit differently, the measure of angle four plus the measure of angle six is going to be equal to 180 degrees, okay, the measure of angle four plus the measure of angle six is equal to 180 degrees, okay, now that right there, again, that one's a little bit different, I can't stress that enough, this one is different from all the rest, everything that you've watched so far has been congruent, but these ones are going to be supplementary, now when you just look, just take a look at everything, angle three and angle five they're obviously different, so when you take a look at the picture, please pay attention to what the angles look like and that gives you a hint, again gives you a hint on what they're supposed to be, either congruent or supplementary, three and five are obviously not the same, so they're going to be supplementary, all right, so those are the other two theorems, those last two, that was the alternate exterior angles theorem and then this one here, the same side interior angles theorem.