hello everyone we now need to talk about parallel lines parallel lines are like railway lines they don't have to have the same length but they are always the same distance apart okay so they can look like this see they don't have to have the same length they can have the same length but they must be parallel always the same distance apart how would you know if lines are parallel they will show you by using those arrows so there's some really interesting stuff that happens when you have parallel lines for example if we do these parallel lines like this if i then draw a line going through then would you agree with me that this angle here can you see how open it is will be the same as that one over there it's also open by the same amount now i want to see what shape that is so if i do this there we go we can see almost a f see if i do this that's an upside down f this one here will be the same as this one over here now what shape is that well that's going to form a z okay so let's keep that in mind the z now if this one's 70 and we said that this one over here is the same because of the f then if we look at this point over here that is a straight line so that means that this angle these two angles must be 180 which means that this one is 110. so then something interesting that happens is that this angle plus this angle will always add up to 180. now what shape are those ones forming well they forming a u so we've got something like that so these are the types of shapes you need to look for you need to look for a shape with an f a shape with a u and a shape with a z or an n and so always remember when you're dealing with parallel lines they are fun okay so if you can remember these three things you are good so those lines over there would be parallel those lines must be parallel and those lines must be parallel so then these angles are always equal these two over here always add up to 180 they are not equal but then these ones are always going to be equal to each other the f is called corresponding in a test you can't say because of the f you say corresponding the u is called co in terrier and then the n or the z is called alternating all right so if i look at this diagram over here i've got two parallel lines how do i know that because of these arrows i want to know what x is and i want to know whether it's the u the f or the z or the n the z and the n can be the z can look like that or it can be an n so what we do is if we do this ah we can see that it's a z so we know that angles and a z are the same so x would equal 45. if i look at this one now this angle is 120 so what will this one be well the shape that these two are forming is the u and remember o and these two should be parallel if you have a u then they're not the same but they do add up to 180 so x would equal to 180 minus 120 and so x will be 60 degrees all right now if this is 30 degrees i want to know how much is or how much this one is so we need to look at the shape that they are forming so if we do this there we've got our f and so this angle for the f's they're the same so this will also be 30 degrees and that's because of the f all right so here's we're going to look for x and for y oh i must say that these lines are parallel okay so if we look at the x and the 60 well that shape is an f so x would be 60. i'm not worrying about the reasons just yet i'm just getting you guys into the hang of this onto the swing of things if i look at the 70 and the y and i form the shape that's a z so y would be 70. okay so here we need to find x y and z so for the x one we can see that this shape here is af so x would be 60. if we look at the next one the y and the hundred well that shape there is a u so remember with a u they don't add up i mean they don't equal each other but they rather add up to 180 so this one would have to be 80 degrees and then if we look at the last one we've got a z and so the z's are equal so this is 120. okay so here's another one so with the 70 and the x if we form the shape that's a z it's a bit of a backwards z but it is a z shape as long as it does something like this or like this like that like that it doesn't matter so that means the x will be 70 degrees if i look at the shape that is being formed over here that is an f and so y will be 30 degrees and here's the last one so if we look at the 30 and the x that is a z and so x is 30. if i look at the y and the 100 ah that's also a z and so y is 100 and so there we have it guys a small little introduction to parallel lines if you have parallel lines please remember the f's the u's and the ends