G 1 TOPIC 4 1 Parallel Lines Transversals 16 32 min

Topic 4-1 parallel lines and transversals. You can reference this with our HOL textbook chapter 3 section 1 on page 146 through 151. Another site I'll mention it again www.mmathis is also going I'm going to show some things during this lesson that you can use look at some animation. Okay, let's start with definitions. Parallel lines in the same plane. line that's in the same plane that does not intersect. They have the same slope and are equal distant. When they talk about equal distance, they mean the distance here to here all the way continuing in this direction and that direction denoted by the arrows. Sometimes they're filled in arrows and sometimes they'll just be an open arrow that denotes parallel lines. So the and if we labeled it would be parallel to each other. skew lines, lines not in the same plane and they're not parallel and they do not intersect. So drawing the diagram three-dimensional. Now it's already drawn. sometimes teach kids how to draw rectangular prism. If you'll draw rectangle and then draw another rectangle similar in shape slightly higher and off to the right, connect the top to the top and the bottom lines to the bottom lines. You can actually make three three-dimensional figure. Okay. When they talk about skew lines, you have to be careful. They're not parallel and they would not intersect. So they're drawing line on one that's on this plane. When you're thinking about the plane, it would be line that takes the place of this plane here. Well, line that would not be parallel and would never intersect that line could be, and I'll draw mine little bit different than that one. That would be one like this one. We could draw them dotted, kind of dotted look. So that this hits this plane, but it's never going to intersect and it's not parallel. So it's too skew. If you want to see that threedimensionally, I've got it in the figure. You've got plane like this. We turn it up. That would be like this line here, which is at the top. And then one of these lines at the bottom. So again, one that would not be parallel and they would never cross each other. Guess could show it. Two pencils like this one and that one. I'm going try to hold this up. That one where the green line goes and then this one along that plane there. Notice how they would never intersect each other. It's easiest to see it that way. Skew lines, parallel lines, planes that do not intersect. So again, if you draw rectangular prism, you can shade the top and the bottom of your picture that you've done. This would have two parallel planes. Highlighted little bit darker. So these are parallel to each other. That would be the same as taking couple of playing cards if had two playing cards and line them up like that. Parallel lines. These could be parallel planes that don't intersect and they are parallel. Trying to make parallel as best can. Parallel to one another. Okay, here's an example using this figure below to answer the questions that follow. What lines in the plane AB? I'm sorry, parallel to AB. Well, if this is AB, lines that would be parallel to it would be and Those lie these two lie in the same plane and that share FAB. But this one shares the plane So that one's also parallel. So you got to make sure you use symbols when they ask for lines. If they say lines, you show it with an arrows on going both directions. What are other sets of parallel lines? Well, is parallel to CF. There's several more. DA is parallel to CB. and line EA is parallel to FB. So take minute and put showing this is the symbol for parallel. Two lines without any arrows just straight up and down. lot of times stress that the name parallel has the two L's on the inside of the actual word. So denote it with two lines going straight down. Name pair of skew lines. Sometimes this is little harder to do, but look it closely. would be here and AB would be here. On flat surface, yes, they would appear to cross. But if it's threedimensional, think I've got prism. Just turn. You can look at it. Here's 3D figure that if you're going along the back side, it would be like showing this one. And that would never cross or intersect or be parallel to that one. Kind of hard to see these. That one and that one. They're never going to cross. Move it around. Those are skew lines, but you're often only going to see it in flat piece of paper that shows three dimensions. Name pair of parallel planes. Very different than lines. It's the parallel planes. And so in plane, you have to denote it by three letters. We could actually go back to our shading could be this whole plane right here and it is parallel to CF. And none of the other planes are parallel. They all connect to one another. So there's not another plane that's actually parallel. You would have had to have prism to be able to do that. Okay, let's move on to transversals. transversal is line that intersects two or more lines in plane at different points. We're not talking about parallel lines yet. That'll be the next section. This one, however, is considered the is the transversal of line and because it cuts through both of those lines. So when two lines are cut by transversal, several types of angle pairs are formed. All right, we're going to talk about the interior and exterior before we go any further. Let's get rid of that plane. Interior. The inside would be like all of these on the inside. So I'm going to shade that inside plane. So this would be the inside interior. The exterior would be the ones on the outside. So, we'll shade those blue. This is the outside and this is the outside. Sorry, this paper seems to shake. Hope that's easy enough to see the difference in color. Make this little darker. There's your green. The green is the interior. The exterior is the blue. Okay, alternate interior angles are two non-adjacent interior angles on opposite sides of the transversal. You can always denote the transversal with highlighter if you'd like. So that is your transversal. So if you are going to alternate, that means you're going to take one on the inside two hop over the transversal and go to the other side. So two and seven are alternate interior angles as well as three and six. The transversal that those two are denoting is transversal line That's why we put the there also. All right. Alternate exterior angles are two nonadjacent exterior angles on the opposite sides of the transversal. So again the highlighted yellow line. Or now in the blue section for exterior, we hop over 1 and 8 and five and four. So those are both going to be denoting each of the exterior same side interior and exterior. You got to be careful interior and exterior angles on the same side of the transversal. First, let's name the exterior ones. Well, guess I'll leave that down. One and four are on the same side. They didn't flip over. They're same side of that yellow line. Those are exterior, though. They're in that blue area. Hop over and look at five and eight. Those are Oops. Those are also exterior. The interiors would be two and three on the same side inside the green area. And six and seven would be the interior on that side. same side again. The I'm not sure exactly what that is. Let's move on. corresponding angles, two angles that are in similar position relative to the lines and the transversal. So again, this one's sometimes the hardest one to denote, but we're not talking about parallel lines, so we're not talking about congruency yet. But corresponding in the same similar position relative to the transversal would be 1 and 3, 5 and 7, 2 and 4, and 6 and 8. And those are your corresponding angles. Okay, let's go on to the last example in this section and that is using the figure below to classify the angle pairs and determine the transversal that forms them. Okay, this can be transversal for and can also be transversal for and But then you could also have being the transversal for and and being the transversal for and So let's look at the different angle pairs. left some blanks on your notes topic pages. So we're going to fill them in. The first one the corresponding ones filled in for you. One and five. one and five are on the same side of the ex the transversal. Which transversal denotes that correspondence? That would be transversal All right, looking at four and six. Let me try to do this with two pencils. If you've got four and six, I'm not going to highlight it because it changes all the time. But if you look at the transversal, the transversal is the line that includes both these two lines. It cuts them in two. Well, cuts through them. And that would be transversal but it's alternate. What are they on the inside or the outside? They're on the inside. So we'll denote that abbreviation interior cut by the transversal And the transversal you think made note on yours too that this is line in common. You've got the line in common to both of the lines that they're talking about. So four and 10. There's four and there's 10. Now, if you look closely, the transversal that includes both of these is transversal And again, look closely. Are these on the outside of that transversal or the inside? Exterior would be the outside. Abbreviate that XT exterior 2 and 9. Again, I've helped you out here, but we want to know which one. Is it same side interior or same side exterior? So two and nine. Here's two and here's nine. They're both two in the inside of the transversal So they would be considered same side interior with the transversal crossing them. gave this one to you again. 4 and 12. They're not parallel this time, although they appear to be parallel, but we're just not. We're just looking at transversals in their angle pairs. 4 and 12 would be corresponding with the transversal 3 and 9. three and 9 with which line cutting in between both of them would be transversal and they are on the alternate interior period 2 and 7 2 and 7 these are on the outside cut by the transversal so that's alternate exterior with transversal in common with both of them. Two more. Three and 12. 3 and 12. They're both on the inside. They didn't cross over. So, they're same side, but are they on the inside of this or are they on the outside? They're on the inside. So that's transversal interior one and seven. Here's one. Here's seven. You've got they're both on the same side. They didn't cross over the transversal. They're on the same side with this one cutting them in half. So they're on the same side, but they're to the out exterior. So this is exterior with transversal to show you the different things on the math. Let me get to it real quick. It talks about pairing interior and exterior angles. See if can get to it. already had it. internet problem. Just minute. Let's see. Well, math isf fun.com. You can actually I'll just show Let's see if I'll get to it. It's still trying to find it. Autotune. It's the first time I've actually referenced with the computer. Bear with me. Okay. Interior angles and exterior angles. This is just too bright. Now, come see me and will show you exactly where that is on your computer to be able to let you move lines around and figure out differences of complimentaries and supplementary angles. We'll get to that, too.