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# Angles formed between transversals and parallel lines

## Video transcript

in this video we're going to think a little bit about parallel lines parallel parallel lines and other lines that intersect the parallel lines and we call those transversal so first let's think about what a parallel or what parallel lines are so one definition we could use and I think that'll work well for the purposes of this video are there are two lines that sit in the same plane when I talk about a plane I'm talking about a you can imagine a flat two-dimensional surface like this screen the screen is a plane so two lines that sit in a plane that never intersect so this line I'll try my best to draw it and imagine the line just keeps going in that direction in that direction and let me do an another one in a different color and this line right here are parallel they will never intersect if you assume that I drew it straight enough and that they're going in the exact same direction they will never intersect and so if you think about what types of lines are not parallel well this green line and this pink line are not parallel they clearly intersect at some point so these two guys are parallel right over here and sometimes it's specified sometimes people will draw an arrow going in the same direction to show that those two lines are parallel if there are multiple parallel lines they might do two arrows and two arrows or whatever but you just have to say okay these lines will never intersect and what we want to think about is what happens when these parallel lines are intersected by a third line by a third line let me draw the third line here so a third line like this a third line like that and we call that right there this third line that intersects the parallel lines we call a transversal transversal line because it transverses the two parallel lines now whenever you have a transversal crossing parallel lines you have an interesting relationship between the angles form now this shows up on a lot of standardized tests it's kind of a core type of geometry problem so it's a good thing to really get clear on our heads so the first thing to realize is if these lines are parallel we're going to assume these lines are parallel then we have corresponding angles are going to be the same what I mean about by corresponding angles are I guess you could think there's four angles that get formed when this purple line or this magenta line intersects this yellow line you have this angle up here you have this angle up here that I've specified in green you have let me do another one in orange you have this angle right here in orange you have this angle right here in this other shade of green and then you have this angle right here right there that I've made in that bluish purplish color so those are the four angles so we talked about corresponding angles that's we're talking about for example this top right angle in green up here that corresponds to this top right angle in what I could drew it in that same green right over here these two angles are corresponding these two are corresponding angles and they're going to be equal these are equal angles if this is how may make up a number if this is 70 degrees then this angle right here is also going to be 70 degrees and if you just think about it or if you even play with toothpicks or something and you keep changing the direction of this transversal line you look it you'll see that it actually looks like they should always be equal if I were to take let me draw two other parallel lines let me show maybe a more extreme example so if I have two other parallel lines like that and then let me make a transversal that goes that forms a smaller say it goes even it's kind of even a smaller angle here you see that this angle right here looks the same as that angle those are corresponding angles and they will be equivalent from this perspective is kind of the top right angle and each intersection is the same now the same is true of the other corresponding angles this angle right here in this example it's the top left angle will be the same as the top left angle right over here this bottom left angle this bottom left angle will be the same down here if this right here 70 degrees then this down here will also be 70 degrees and then finally of course this angle and this angle will also be the same so corresponding angles let me write these these are corresponding angles are congruent corresponding corresponding angles angles are equal and that and that are corresponding that and that that and that and that and that now the next set of equal angles to realize are the sometimes they're called vertical angles sometimes they're called opposite angles but if you take this angle right here the angle that is vertical to it or is opposite is you go right across the point of intersection is this angle right here and that is going to be the same thing so we could say opposite I like opposite because it's not always in the vertical direction sometimes it's in the horizontal direction but sometimes referred to as vertical angles opposite or vertical angles are also equal so that's 70 degrees then this is also 70 degrees and if this is 70 degrees then this right here is also 70 degrees so it's interesting if that 70 degrees and that's 70 degrees and if this is 70 degrees and that is also 70 degrees so no matter what this is this will also be the same thing because this is the same as that that is the same as that now the last one that you need a I guess kind of realize are this the relationship between this orange angle and this green angle right there and you can see you can see that when you take when you add up the angles you go halfway around the circle right if you if you start here you do the green angle then you do the orange angle you go halfway around the circle and that'll give you get you to 180 degrees so these this green and orange angle have to add up to 180 degrees or they are supplementary and we've done other videos on supplementary but you just have to realize they form the same line or a half circle so right here 70 degrees then this orange angle right here is 110 degrees because they add up to 180 now if this character right here is 110 degrees what do we know about this character right here well this character is opposite or vertical to the 110 degrees so it's also 110 degrees we also know since this angle corresponds with this angle this angle will also be 110 degrees or we could have said that look because this is 70 and this guy is supplementary these guys have to add up to 180 so you could have gotten it that way and you could also figure out that since this is 110 this is the corresponding angle it is also going to be 110 or you could have said this is opposite to that so they're equal or you could have said you could have said that this is supplementary with that angle so 70 plus 110 have to be 180 or you could have said 70 Plus this angle are 180 so you could there's a bunch of ways to come to to figure out which angle is which in the next video I'm just going to do a bunch of examples just to show that if you know one of these angles you can really figure out all of the angles