G7 Geometry: Sec 8.3

Added: 2026-05-19

[00:00:01]Hello everyone. Today I'm going to be doing math uh math geometry course practice chapter 8.1 I mean 8.3.

[00:00:11]8.3 here.

[00:00:15]It's about alternate interior corresponding angles. That's it. So we'll just um go through alternate interiors and corresponding. So we have alternate interiors means that both of them will be interiors. So two interiors and they'll be on different sides of transversal.

[00:00:56]I'll tell you what I mean by this later.

[00:01:01]Then we have um corresponding.

[00:01:08]Corresponding on the other hand means you have one interior and one exterior on the same side of transversal.

[00:01:40]Okay? So that's the difference.

[00:01:42]Alternate interiors are two interiors on different sides of transversal. So example this is the transversal and these are two uh lines and this is two this is one this is three okay?

[00:01:57]So one and two I mean this is three. We don't need this.

[00:02:03]So one and three would be alternate interiors because you can see they're on different sides. One is on this side and one is on this side. Corresponding on the other hand is one interior so one is an interior. They're between the two lines and two is the exterior. It's outside the two lines. They both are the both they both are on this side of the transversal. Got that?

[00:02:29]So if T is the transversal, so what's the transversal? T.

[00:02:34]Two lines M and N.

[00:02:36]Which of the following is a pair of corresponding angles? So we'll do one and one five and two six. We'll just write it down. One and five and two and six.

[00:02:52]So one and this is five.

[00:02:57]This is the transversal, right? So are they on the same side of the transversal or on the different? They are on the same.

[00:03:05]So they are first they are on the same.

[00:03:12]Same side of the transversal which is T.

[00:03:15]And are is one of them is interior, right? They're between the two lines M and N. And one of them is outside the two lines. So this is the interior and the rest is exterior. So what do we have? We have one interior and one exterior.

[00:03:34]So what does that description fit? It's corresponding, right? Because it means it has to be on the same side of the transversal and one interior one exterior. So one and five are corresponding.

[00:03:48]Then we have two and six.

[00:03:51]We know that.

[00:03:55]Okay, so this is two and this is six.

[00:03:59]First thing.

[00:04:01]And this is T, right? The transversal.

[00:04:03]Are they on different sides of the transversal or same?

[00:04:07]Different, right? One is on this side, one is on this side.

[00:04:12]So, different.

[00:04:17]Then the second thing about this is that one of them is interior and the other one is also interior. See, they're in between N and M.

[00:04:28]So, two interior.

[00:04:31]So, what does that tell you? The description that they both are alternate interior. Both interiors and they're on the different sides of the transversal.

[00:04:40]But, we're not looking for interior, we're looking about we're looking for corresponding.

[00:04:45]Then the next one, angle three and angle five.

[00:04:50]Angle three and angle five.

[00:04:55]Angle three, angle five.

[00:04:58]Number one, what do you see?

[00:05:00]This is the transversal. They're on different sides.

[00:05:05]Right? And number two, what do you see?

[00:05:08]One of them both of them are interior, right? They both are between N and M.

[00:05:13]So, again, both interior, two interiors.

[00:05:19]So, that means they are alternate interior.

[00:05:21]Then the last one, seven and three.

[00:05:27]Seven and three.

[00:05:30]What can you say about them? Number one, is that they both are on the same side of the transversal, which is this.

[00:05:38]Second thing, is that one of them is the interior, which is between N and M.

[00:05:44]And the other one is exterior. So, this is the interior and this is the exterior.

[00:05:50]So, one is interior and one is ex- um one is exterior.

[00:05:58]So, what does that fit? It's corresponding angles.

[00:06:03]So, that means the only corresponding pair of angles are I and uh I mean first the first one and the fourth one.

[00:06:12]Number four.

[00:06:15]Question number 22. I mean sorry, two.

[00:06:19]If T is a transversal to line M and N, which of the following is a pair of alternate interior angles? So, instead of looking for corresponding, we're looking for alternate interior angles.

[00:06:30]We'll look for one and five first. So, this is T.

[00:06:34]This is one and this is five. Number one.

[00:06:37]One of them is an interior and one of them is a exterior.

[00:06:41]Now, some people would like to stop here because it's we're looking for alternate interior angles. The first thing we need is that both of them should be interior.

[00:06:52]So, this is wrong. We don't have to look for the second thing.

[00:06:56]Two and six.

[00:07:00]Two and six.

[00:07:03]And this is the transversal. Number one.

[00:07:06]Both of them have to be interior. This is interior and this is interior. Both of them are in between N and M. In here.

[00:07:13]Right?

[00:07:14]So, two interiors.

[00:07:18]Number two.

[00:07:20]They both have to be on different sides of the transversal. Yes, it's correct.

[00:07:26]Both of them are on different sides of the transversal. One is over here, one is over here. So, two and six are a pair of alternate interior. But, we have to check all of them.

[00:07:37]Three and five.

[00:07:40]It's three, five.

[00:07:42]One thing is that they both are in different sides. That's true.

[00:07:49]Oh, this three is an interior and this is also interior. So, two interiors.

[00:07:58]So, that means it is also alternate interior.

[00:08:02]Then we have seven and three.

[00:08:07]Seven and three.

[00:08:09]They're on the same side.

[00:08:15]They're same side of the transversal and one of them is an interior and one of them is an exterior. So, what does that mean? It's the corresponding.

[00:08:25]But, we're looking for alternate interior. So, that means it's only one five and three five.

[00:08:34]Then wait.

[00:08:35]Um, one Sorry, two second one and the third one.

[00:08:42]Yeah.

[00:08:45]Question three.

[00:08:47]If T is the transversal to the lines M and L, then a pair of corresponding angles is So, this is line T.

[00:08:58]Let's look at eight and two first.

[00:09:00]Line T.

[00:09:01]Eight and two. They're looking for um, corresponding.

[00:09:09]Eight, two.

[00:09:12]First thing, are they on different sides? Yes, they are on different sides.

[00:09:17]That means they are not um, corresponding. Because corresponding means the two angles on are on the same um, side of the transversal. So, before even checking the second thing, we won't um, think about it. One and eight.

[00:09:37]One.

[00:09:38]Sorry.

[00:09:39]Um, 1 8 Are they on the same side? Yes, they are on the same side.

[00:09:46]Uh the second thing, is one of them an exterior and one of them is an interior?

[00:09:51]No, both of them are exterior. This is one exterior, this is one exterior exterior. None of them are inside this part.

[00:09:59]So, no.

[00:10:01]3 and 5 3 and 5 Um are they both on the same side?

[00:10:13]No. They both are on different. So, before even thinking about it, we're going to go to the next.

[00:10:20]4 and 5 4 and 5 Are they on the same side? Yes, they are on the same side.

[00:10:28]Number 2 Is one of them an interior and one of them exterior? No, instead of this, there are two interiors.

[00:10:37]Two interiors That's wrong. We need one exterior and one interior.

[00:10:43]Then we have um 1 and 5.

[00:10:48]1 and 5 Are they on the same side? Yes, they are on the same side. One of is one of them exterior and one interior? Yes. 5 is an interior, that means inside here, and 1 is an exterior, that means outside.

[00:11:03]So, yes, this is a corresponding pair of angles.

[00:11:10]Number 4, given the figure be- above, which of the following is true?

[00:11:15]So, 1 and 9 are alternate interior angles.

[00:11:19]So, this is 1 and this is 9.

[00:11:22]Um and this is T, of course.

[00:11:25]So, are they and this is 1, this is interior and this one is exterior.

[00:11:31]Okay? This one is inside N and M. Look, they're inside N and M.

[00:11:37]And this one?

[00:11:39]No.

[00:11:40]So, it's not alternate interior.

[00:11:44]Some people might uh say that how do you know what the transversal is?

[00:11:48]So, example, if I have seven and 10 are corresponding, we go to seven and 10. It matters on the um uh the angles. So, we think what's the common line between seven and 10?

[00:12:03]It can be angle T because angle T is only has T, I mean 10.

[00:12:09]M only has seven.

[00:12:11]So, it's N. N is the transversal. That's how you find out what the transversal is. But, it really isn't important because we don't need to think about it too much.

[00:12:23]Like here, examp- uh example, we know this is transversal.

[00:12:28]This is a interior because look, this is inside this part.

[00:12:32]And this is a exterior.

[00:12:35]This one is outside.

[00:12:38]So, one exterior and one interior.

[00:12:42]Are they correct? No, since I'm actually 10 and seven.

[00:12:52]Yes, they are correct. One of them is a exterior, one of them is a interior, and they are on the same side of the transversal. So, that means see um sorry, this is correct.

[00:13:03]So, next, if L is the transversal to the lines N and M, then a pair of alternate interior angles is So, we know in this part, L is the transversal.

[00:13:16]Then a proper alternate interior, I guess, a pair of alternate interior angles. So, we'll do one and five first.

[00:13:24]One, five. Um first thing, are they on the same side or different sides? Different.

[00:13:31]So that means yes, it could be the alternate interior angles.

[00:13:36]Number two, are they both interior angles? Yes, they both are interior angles. They're two interior angles. So yes, one and five are the correct answer. I won't go through all of them because it's the same concept. What are alternate interiors and what is corresponding? To find the answers you always check what side the it's on and how many interior or exterior there is.

[00:14:03]Okay? So if T is the transversal to the lines L and M, then the pair of corresponding angles is So T is the transversal here and this is L and M. So that means 4, 3, 5, 6 are interior.

[00:14:19]Then a pair of corresponding. So we're looking for corresponding now.

[00:14:25]Corresponding. So we're looking 8 and 2 is the first thing. So number one, are they This is T, the transversal.

[00:14:33]Number one, are they on the same side of the transversal? No, they're on different sides.

[00:14:41]So that means no, this is 100% not correct corresponding cuz corresponding means same side. Then we do 4 and 5.

[00:14:51]4 and 5. Number one, are they on the same side? Yes, they are on the same side so it might be corresponding.

[00:14:56]Number two, are they one exterior and one interior? No, there's two interiors.

[00:15:03]So that means this is wrong.

[00:15:07]Then we have 3 and 5.

[00:15:11]3 and 5.

[00:15:13]First question, are they on different sides or the same side? Because remember T is the transversal. Is 3 and 5 on the different sides of the transversal? Yes.

[00:15:23]So that means it it is 100% wrong because um corresponding means same side.

[00:15:30]Uh so we were doing Now we have to do one and five.

[00:15:38]One and five.

[00:15:39]Are they on the same side? Yes, they are on the same side. So that means it might be corresponding. Number two, are they Is there one exterior and one interior?

[00:15:49]Yes, there is one interior and one exterior.

[00:15:53]The five is a interior while the one is a exterior.

[00:15:58]Cuz it's not inside these two.

[00:16:01]So one and five is your correct answer.

[00:16:03]Then I'll just do the last one.

[00:16:05]Um one and eight.

[00:16:09]Are they on the same side? Yes, they are on the same side. Is one of them an interior and one of them exterior? No, they are two exteriors.

[00:16:21]Okay.

[00:16:22]See what Both of them are not inside these this part.

[00:16:27]Then we have question number seven.

[00:16:30]Given the figure below, which of the following is true? Seven and 10 are corresponding. We will check.

[00:16:37]Seven, 10.

[00:16:39]Corresponding.

[00:16:41]So which line do they share?

[00:16:44]N, right? They short They share the line N.

[00:16:48]So are they corre- uh First thing, are they on the same side or different side?

[00:16:54]Many people think the same side, but look. This is on this side and this seven is on the other side. So that means different. And we're looking And it said corresponding. So is it correct?

[00:17:05]No. It has to be on same side to be corresponding. Two and five are altern- alternate interior angles.

[00:17:13]Two and five. First thing, what's uh what are they sharing? It can Mhm, this side, right?

[00:17:22]Sorry, this side.

[00:17:25]Two and five.

[00:17:26]So, two and five. Is one of them interior and one of them exterior? I mean, um are they on the same side or different side? Different side. So, it might be correct.

[00:17:38]Okay, different. Number two.

[00:17:41]Um Sorry.

[00:17:45]Number two, uh are they both interiors? Yes. But, you see alternate interior means it cannot be two and five or three or six or four or nine and one and 10. No, they can't be next to each other. If they're next to each other, they're called co- I mean, um we won't we didn't learn it yet, but it's not it doesn't mean alternate interior.

[00:18:15]Interior, just normal interior or co-interior, means one and five or two and 10 or 10 and yeah, like that.

[00:18:27]Okay? So, this is wrong because they're next to each other. Alternate interiors can never ever be uh like close to each other, next to each other, like two and five.

[00:18:38]Next one, five and 10 are corresponding.

[00:18:41]So, we have five and 10. Number one, are they on the different side or same side?

[00:18:46]Different side, right? Because they share M.

[00:18:50]They share M. So, this is five, which is on this side, and 10 on this side. So, it's wrong without even checking the second one because the corresponding means same side.

[00:19:00]Five and eight are corresponding.

[00:19:04]So, this is five, this is eight. First thing, are they on the same side? T is the transversal here. Five and eight, are they are they on the same side? Yes, they are same side so they might be corresponding.

[00:19:17]Two is one of them interior and one of them exterior. So N and M, so this is the interior part, right? Because this is um N M and this is N. So this is the part that uh that is inside.

[00:19:30]So eight, so there's one interior and one exterior.

[00:19:37]Five is the exterior, eight is the interior. So yes, that they are corresponding. The last one, one and nine are alternate interiors. Again, you can't have two in um whether it's this with this is that uh transversal. See, two and five two and five, they can either be on T or M, right? So it's confusing. Or one and nine, they can be either on N and or M.

[00:20:02]That's And that must be a reason why they are not alternate interior, but we still didn't learn what they are called yet, okay?

[00:20:11]So number eight, relative to lines F and D with transversal J.

[00:20:16]So we have lines F and D with um This is uh J, the transversal, and F and D.

[00:20:25]Angle six and something. So we have angle six and something make a pair of alternate interior. So the first thing we need to do is make them have different sides.

[00:20:37]Right? Different sides from the transversal. So that means it can't be five. Okay?

[00:20:43]It can't be three because remember we can't we said it can't be and two or one because this is outside. We're not using E.

[00:20:51]And two, it's exterior. We need interior. That means inside here.

[00:20:56]And we also need it to be interior. Yes, I just said that. Interior.

[00:21:01]So it's four. Angle four and six make it um make it alternate interior.

[00:21:10]Then here we have E and D with transversal J.

[00:21:16]E and D, D E.

[00:21:19]And we have angle one and something make a pair of corresponding. So this one is the interior because they're inside D and E.

[00:21:28]So we uh we need them to have the same side on the transversal. Same side, okay? And we also need an exterior because since we already have an interior, we need one exterior. So it's not two 100% has to be on the same side so it's not three, so it's six. Some people might ask why it's not five because we're not talking about F. It said specifically D and E. So six is ba- is on D. So yes, so it's one and six make up corresponding angles.

[00:22:05]Then question number nine.

[00:22:08]Relative to lines M and N with transversal R, angle three and something make up a pair of alternate interior. So M and N and this is R, transversal R.

[00:22:21]Angle three angle three and something make a pair of alternate interior. So the first thing it needs to be interior so we remove one we remove five so we have four or two.

[00:22:36]Second thing, they have to be on different sides of the transversal. So it can't be four, it has to be two because four is on the same side as three.

[00:22:45]So it's three and angle two make a pair of alternate interior. Then the next one again, M and N and transversal R.

[00:22:57]Okay.

[00:22:58]Angle um four and something make a pair of co-interior. Co-interior means it's not alternate interior, but they're just two interiors on the same side. So, first thing they have to be on the same side.

[00:23:14]Second thing, they have to be interior.

[00:23:17]So, five is not interior, one is not interior, and it has to be on the same side. Two is not in in the same on the same side. So, it's three. So, four and three make a pair of co-interior.

[00:23:30]Then we have L and N.

[00:23:33]L and N. So, we remove five. We don't even I mean M. We don't look at three and one.

[00:23:40]And R is your um transversal.

[00:23:45]Five and something make a pair of corresponding. So, five is in between N and L, right? So, that means this is the interior part. We need to find the exterior. So, it has to be a exterior, which is four and two.

[00:23:59]And then the second thing also for corresponding, it has to be on the same side of the transversal. So, is it two or four? Four. They're on the same side.

[00:24:07]So, five and four make a pair of corresponding angles.

[00:24:11]So, this was chapter 8.3. It was all about corresponding and alternate interiors. And in the last part, they also asked for um co-interior. Whatever.

[00:24:22]And um I good luck for exam. And bye.