12 7 Parallel Lines and Transversals Part 1

hello everyone this is simple math for you our lesson today is parallel lines and transverses math for you and this is part one first part will include parallel lines and transverses we will learn what is the meaning of parallel lines and what is the difference between parallel lines and skew lens if two lines do not intersect then they are either parallel or skew what is the difference parallel lines are Coplay in our lines Coplay in our lines means same plane and they do not intersect they don't meet leather pattern and for example this this line line and line are parallel lines and usually to indicate that the lines are parallel we put same arrows if you want also two arrows here two arrows here they indicate indicates that the lines are parallelism so we can say here that is parallel to the double slash skew lines are lines that do not intersect and not complaining for example here line is lying on plane line is lying on plane and if you extend the lines they will never meet and that means they are called skew lines now what are parallel planes parallel planes are planes that do not intersect just reminder how can we name the plane we can name the plane with capital letter at the corner as they had have done here or we can name the plane using three non-collinear points and for example here if you have here points so we can say also that this plane can be named as plane instead in addition to naming it as plane so let's take an exercise about that here identify each of the following using the cube show me the assume lines are planes that appear to be parallel or perpendicular or parallel or perpendicular for example here this surface This Plane looks parallel to that one so we will assume that they are parallel as they have asked us so let's see the first question all lines to BC this is line BC what are the lines skewed to BC now if you look at ad here for example line line do not intersect with BC but they are both in the same plane which is this surface so we cannot say that these lines are skew they are parallel but he is asking you to find skew lines to BC so let's check for example AF if you extend AF forever it will not intersect with BC if you extend forever also it will not intersect with BC if you extend GH here no GH is the same plane from the back side plane so we cannot say GH is parallel to BC okay we can have here FG yes FG FG is also skewed with BC look at here it's skew with so easily we can't identify the skew lines now easier than the skew lines are parallel lines what are lines parallel to where's this is so you have to find out as I'm in Delaware I'll align not intersecting Phoenix is parallel to CD it is also parallel to Phillips and it is also parallel to now let's discuss the because this is little bit confusing and are not directly parallel but we can say that is parallel to CD is and so would write it here is parallel to CD also we have is parallel to B8 so they are the same plane by transitive property since this line is parallel to this this same line is parallel to third line so kid these lines are parallel remember what is the transitive property for example equals to and at the same time equals to for kid is equal to that that will be this is the transitive property so this is little bit confusing for many students and hope this is clear now we also need now all planes that are parallel to plane let's clean that one what are the planes parallel to plane DCH where is DCH is the plane that includes these points we are talking about the surface so what is the plane parallel data it is very clear that the only parallel plane is this one you can name it this one you can name it you can name it you can name it and you can also switch the orders okay hope now the skew lines are clicked also here we have something called transversal what is that transversal line that intersects two or more lines in plane at different points is called transverse line yet lines and are two different points so we call it transversal blood is transversal of lines and notice that line forms total of eight angles with line square if you have any two lines cut by transversal then you will have eight angles we will study also relations between these angles let's take an exercise here identify each of the following using the figure shown assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular respectively three segments parallel to AE what are the segments parallel to AE what are they let's first identify AE where is is this one okay what are the segments parallel to AE Let's see we have here kid parallel to that one also CG because is parallel to is parallel to CG by transitive property is parallel to CG also there is anything else we can say also the BF by the way BF also is we can say that so we can say here that the lines parallel are let's take examples here it's all only three so and you know segments to let's Erase here the highlighted there's here segments to this is we are looking for lines that not intersect with and at the same time on different thing is if you extend it forever so DH is an option what else let's check what else is this one it will not intersect with we have many here Matalan GF also can be skew lines with language so here let's arrange here our writing question three pair of parallel planes parallel planes now the only parallel planes that we have here is what do we have only one parallel planes we have two parallel planes actually we have this this is parallel to that one to basis that are parallel to each other so we can say that plane is parallel to plane we can also say plane we can say that this plane the the front one this one front one is parallel to the back one you can say that plane is parallel to pin have taken only three letters to name the plane sometimes you will see that they are naming it as rectangle and rectangle is parallel to rectangle it's also correct now segment parallel to where is this is parallel to it is this one so first one is very clear is parallel to we have any other one so far cannot see any other one segment for three segments parallel to is this one the first one can see directly is this one at EF not here what else up or we can say DC is easier DC and since DC is parallel to so we will consider as well now five segments to is this one what is skew two we have many here we can say that AE foreign let's change the color is skew with BC what else the edge is okay as well what else go ahead now HG is okay so we have many many we have we can't name many five segments that are skew two so we can name we can name we can name HG we can name we can name is not intersecting is not intersecting is this one yes we have many segments how could characterize the relation between faces and let's check these faces we can call them plain as well as well and other one uh-huh is this one they are intersecting as you see they are meeting at this Edge and if you imagine this prism right prism as we can see here as we expect we will say that these planes are perpendicular so foreign okay let's see here this part transversal angle per relationship this is very important part actually that will help us to understand how can we find the missing angles if you have two lines and transversal in special condition first of all we have here as you see two lines and they are cut by transversal and as we have mentioned we have eight angles formed from one to eight it's very clear here now we have four interior angles this is interior angle this is interior and between the transversal and one of the lines this is interior this is interior we have also exterior angles outside one two eight seven are exterior angles that not between lines and here so determine the relation between these angles as you see here for the interior angles four and five they are coming after each other and on the same transversal the same side and to the left of the transversal both are interior and same size and both are left so we can call them consecutive interior angles another way of naming it we can say that they are called same side interior angles so we can name these consecutive interior angles or same side interior angles same applied to angles 3 and 6 so 3 and 6 as well both are interior both on the same side of the transversal and we call them same side interior or consecutive animal consecutive interior angles that now this is the relationship between angles four and five three six now let's check here and gill4 and angle six what's the relation between them both are interior but each one of them on difference and one to the left of the transversal one to the right of the transversal so they are alternating so that's why we call them alternate interior angles so they are called alternate interior angles and there are non-adjacent interior angles so they are none adjacent and they are an opposite side of that transversal so it applies also for angles three and five so three and five four and six are called alternate interior angles we have two pairs of alternate interior angles same Applause for alternate exterior angles we have here angle two angle eight both are exterior everyone each one of them is an opposite side of the transversal one to the right word to drift or you can say one up one down so they are called alternate exterior angles clear also we have one and seven are alternative serial angles last there that we need to emphasize on is corresponding angles they are lying on the same side of the transversal so here this is the transversal and on the same side of lines QR as you see here one interior one exterior so four and eight are corresponding three and seven are corresponding also five and one are corresponding usually teach this to my students can actually make this similar to letter in English so letter the one in all directions can be also upside down one in but not one in and out these are called corresponding angles but for alternate interior angles they look like letter it can be also upside down or reversed or whatever these are called alternate interior angles however for consecutive interior angles it is like letter both are inside or it can be as also in all Direction this and that also they are called consecutive interior angles so this is the summary of the relation between angles let's take and exercise here identify the transversal connecting each pair of angles then classify the relationship between each pair of angles as alternating key interior alternate exterior corresponding or consecutive interior angles let's see angle 4 and angle 5. let's highlight four and five four and five together are lying on transversal so the transversal is what's the relation between them both are interior on the same side so we can call them constitutive interior angles next we have angle 5 and angle 15. 5 and 15. so this is angle five and this is angle 15 where is the transverse that both lie at least duh and as you see these are exterior angles so we can call them alternate exterior angles and the transversal in our case is this line which is so the transversal is the and they are alternate exterior angles okay let's see here angle 4 and angle five this is angle 4 and this is angle five angle four and five we have repeated that again four and five same same we can say the transversal we are repeating the questions it seems so we will cancel this then we have we have mentioned that before by mistake it seems so angle 12 and angle 14 now angle 12 and angle 14 alternate interior angles because both are lying on the same transversal one to the right one to the left are both are interior so the transversal in our case is line next angle 7 and angle 15. let's highlighted seven and fifteen they are both lying on this line as you see this lion cuts this line and the other line so let's see what's the relation between this and that angle as you see they are forming like letter one interior one exterior both on the same side of the transversal so we call them corresponding angles and the transversal is angle 2 and angle 12 let's change the color angle 2 and angle 12 they are lying on transversal and this transversal cutting these lines both are interior and they are in opposite sides so they are called alternate interior angles in this case our transversal is that's it is everything now and restart another you have angle three and six three and six they are lying on this transversal and this transverse cell is cutting these lines so both are inferior on the same side so it is called same side interior angles or we can call it consecutive interior angles angle one and angle nine one and nine let's check one and nine this is one this is nine both are on transversal as you see they are corresponding like letter and the transversal is as well yes it is angles three and nine now that's true let's check three and nine this is angle three and this is angle nine this is the transverse and this transmission is cutting these lines as you see one up one down different sides both interior and different sides of the transversal so so we call them alternate interior angles and the transversal in our case is this is okay no actually it's nothing okay now angle 10 and 16 shift 10 and 16 10 and 16 maybe little bit annoying this is 10 and 16 10 and 16 both lying on this transversal and this transversal cutting this and that line that means we have two angles are exterior angles and each of them is lying in opposite direction of the other so angle 10 and 16 are exterior angles both lying on transversal so call transversal and we have this alternate exterior angles finally angles 5 and 13 that's C5 and 13 where are they this is five and as you see it's better to highlight the angles that you are talking about this is 5 and 13. they are both lying on this transversal which is and it this transversal cutting these lines so they are posing like the letter as have mentioned so we call them corresponding angles and the transversal is so transversal is and there are corresponding and yes very good now finally before we move to part two what type of angles 3 and 10 here in the sketch C3 and 10. what is the relation between 3 and 10 in the sketch is there any relation between them three and ten both are dying on the transversal so there is common transversal which is as you see here this transversal is cutting this line and that line and this line these angles are lying exterior in exterior way but different ways the opposite sides of this transversal both of them are exterior so until 10 and angle tree are alternate exterior angles angle line State the transversal that connects angle 11 and angle 13. let's change the color to check 11 and 13. this is 11 and this is 13. both are lying on this transversal which is and this is cutting this line and both angles are lying inside interior in the interior way and on the same side so we call them same side interior or consecutive interior angles or another way same side interior angles so inshallah next part we will discuss four elections related to these pairs and hope everyone understands how we can classify the angles as corresponding like it's the summary we have corresponding angles they are looking like letter we have alternate interior angles they are looking like zetamine in all rotation we have consecutive interior angles like letter this is we are talking about these angles actually and these angles and this is angles the last one exterior angles we cannot find letter relating them and next time shall next part we will continue discussing the relation between and thank you