Parallel Lines and Transversals Simplifying Math

hello this is Mr Buffington we're going to look at parallel lines and transversals today what is parallel line parallel line are two lines on single plane that do not intersect they look like this typically they'll Run next to each other and never touch no matter how far you extend them into Infinity they're not going to cross each other all right and they are on the same plane we often call that c-pl ler lines that do not intersect all right so that's what parallel lines look like transversal is any line that intersects two other lines on same plane specifically what we're going to look at is transversal that intersects parallel lines so it's going to look like this all right so we're going to set up two parallel lines and then we're going to draw transversal across them and talk about all the different things that are created by all these angles that we see here so how many angles are there when we look at the transversal and where it crossed these two parallel lines when transversal crosses two lines you get one 2 3 four angles there and then one two three four more angles here so you'll get eight different angles we're going to talk about the relationships between these eight different angles because there are some really neat things that happen with parallel lines and transversals so let's go ahead and just get right into it alternate angles when we talk about alternate angles we're talking about angles on different sides of the transversal so here's an example 2 and seven remember our transversal is this line that crosses over the two parallel lines so our transversal anything on opposite sides of the transversal are called alternate angles all right so you could also have this like two and five are alternate angles because they're on opposite sides of the transversal all right we'll also talk about exterior and interior angles exterior angles are angles that are on the outside of the parallel lines all right I've represented that with these light blue shaded sections all right anything on the outside of the parallel lines are going to be called exterior angles anything on the inside of the parallel lines will be called interior angles it seems pretty straightforward but just want to be clear of where the exterior interior and then also the alternate that we talked about so the next part then of course is to put these two ideas together an alternate exterior angle are the two angles that are on different sides of the transversal like 2 and 7 and they're on the outside of the parallel lines the exterior of the parallel lines those are alternate exterior angles the other example of alternate exterior angles is angle one and angle 8 they are on the different sides of the transversal exterior the outside of the parallel lines the ne thing property of alternate exterior angles is that they're congruent they're the same measurement and they look the same look the measurement of angle one here it's definitely an acute angle and you see measurement of angle 8 it looks the same and they are the same alternate exterior angles are congruent all right so that's one property in one way that essentially if you know one of these eight angles you can tell what all the other eight ones angles measurements are and that's neat and one of the ways you know that is because alternate exterior angles are congruent all right now that we've talked about alternate exterior where do you think the alternate interior angles might be you see the word Alternate which means they have to be on different sides of this transversal one will be on this side and one will be on this side and we see the word interior which means they'll be on the inside of the parallel lines so one example of alternate interior angles is four and five angle four and angle five the other example is angle three and angle six and just like alternate exterior angles we know that alternate interior angles are also congruent so angle three is equal to angle six angle four is equal to angle five because they are alternate interior angles corresponding angles for me what like to do when I'm thinking about corresponding angles is like to look at just one set of four angles at time so look at this set of angles and you could put circle around it or square around it or something just to say I'm looking at just this section separate from the other ones and then put similar circle around that and basically what corresponding angles means is if you're only looking at this circle and this circle they're in the same exact place all right so corresponding angles are angles 2 and six can you see another set of corresponding angles perhaps you notice that one and five are corresponding angles three and seven are corresponding angles and angle four and eight are the last set of corresponding angles so I'm going to represent them by color coding them here to show that these are the corresponding angles again for me it's easiest to just put circle around that you can also color code it if that helps and identify which angles are corresponding now one property about corresponding angles you may have already guessed is that the corresponding angles are congruent all right angle two is the same measurement as angle six angle one is the same measurement as angle five so corresponding angles are congruent they have the same measurement all right the next set of angles are called adjacent angles and adjacent just means next to so basically any two angles that are next to each other two is next to angle four two is also next to angle one we could have highlighted two and one they're adjacent angles two and four are adjacent angles here's another example five and six those are adjacent angles one and three are adjacent angles there's lots of sets of adjacent angles and adjacent angles if you look at this example is seven and eight here you'll notice something that angle seven plus angle eight give you straight line so that means that adjacent angles and you saw that with every case angle one plus angle two gives you straight line angle 2 plus angle four gives you straight line these angles are supplementary angles in other words they add up to be 180 degrees all right and that is the key for finding like said if you're given one angle measurement you can find all other eight because you know that the adjacent angles equal 180° and they added them up all right the final type of angle that we're going to talk about are vertical angles vertical angles are another way of saying angles that are exactly opposite each other all right like angles five and eight are set of vertical angles you pick out another set of vertical angles perhaps you said angles six and seven those ones are vertical angles all right also angle two and three are vertical angle one and four are also vertical angles and vertical angles are congruent so that is our lesson on parallel lines and transversals and some of the properties made by or some of the properties of the angles that are created when you have transversal cut across two parallel lines if you enjoyed this lesson or found it helpful you can go ahead and share it with your friends share it with your math teacher share it to anyone you'd like