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Lines Cut by a Transversal Zoom Lesson

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okay so sorry about forgetting to record this so I'm kind of apologizing to people who are going to watch it online I don't record every meeting I only record the ones where we have lessons for those are the ones I post online and thank you for to my attention cuz I totally forgot so yeah I guess we got the first page done it's not that big deal so let's talk about words to know okay so first word is analyzed and that is see to examine study their carefully and in detail hopefully you're actually had a clue what that one was right okay justify is a she'd Defender show to show to be correct transformation is D an operation on a figure that may change his orientation shape or location in a plane and of course the last one is the transversal which is a line intersecting two or more coplanar lines at different points so like we showed on the map you have streets that are cross find another street so the two streets there across the street that crosses the other two streets that straight to be a transversal not words just came out of my mouth are we doing I will post this on my teacher page along with the video sorry I do not will these no Google classroom in a class work yeah that's why I fell I don't like to eat yes oh and remember if your if your behind of you go to Links Master copies of notebooks at. best rappers of my notebooks and the videos video lessons Okay so I'm moving on So Long by a transverse so lime zest and Q are cut by transversals are so this is all right here this line see how it how it goes through the other two lines that's the transversals someone needs to be muted to the hair lot of background marijuana yoga music yeah I think I got it okay all right so interior angles are the ones that are in between so in this case there are three four five and six one thing that I frequently will do when we do these on paper I will note to let me do that LOL what I like to do is I like to these are the interior look interior k345 and 6 the exterior angles are the ones side babe so 1 2 7 and 8 totally not trying to confuse you guys the ones that are in between the two lines of the Interior the ones that are outside the two lines are the exterior okay and vertical angles are opposite angles so like angle 2 and angle 3 you see other directly across from each other they shared vertex is 2 + 3 1 + 4 + 7 + 5 + 8 + notice we use the congruence symbol they are congruent to each other correspondence angles have the same relative position so we're talkin like angles 6 and 2 of 2 and 6 cc equal 6 is sitting on top of the blind que if you're looking at it like reading it from top to bottom and angle 2 is sitting on top of mine s so and they're both on the right side of the transversal so they're in the same position on the different lines that's what we mean by corresponding responding as well as ones that sometimes takes a while to understand birds that make some kind of sense we made some kind of sense all right we got more angles so we have alternate interior angles do you know what the word alternate means yes it was it mean the song what do you mean I don't want to hang up first alright to alternate means to go back and forth right back and forth back and forth like when you're marching we're running use you filled in left right left right left right alternate interior angles are on opposite sides of the transversal 3 + 6 + 4 + 5 inside a they are not side by side. linear pair alternate exterior angles yes sir you'll probably class working Edgenuity or any of your other question okay I know nothing of ingenuity where is wind direction today yes horse horse all right so are alternate exterior angles are angles on the exterior angle so we're talkin 1 + 8 + 2 + 7 do you find interior you also heard someone needs me again please it's not me I'm not like that's not me all right the same side interior angles are interior angles on the same side of the transversal and 6 yeah yeah there's always going to be extra noise whether it's in class or if it's on Zoom there's always extra noise okay alright the relationship between angle pairs now when parallel lines now Tremors I said only if they are parallel when parallel lines are cut by a transversal angle pairs have special relationships on the last slide these rules that were coming up with right now would not hold true because those not parallel line these are parallel lines you can see from the little check marks your little chevron's if you will so it's a parallel lines in the corresponding angles are congruent so are a example angle 2 and angle 6 they're in the same position relative to the transversal so those two are congruent the alternate exterior angles so Princeton's angles 3 and 6 these are examples about the only ones angles 3 and 6 are congruent have the exact same measure the exterior angles alternate exterior angles are also congruent congruent and the same size interior angles are supplementary supplementary angles 3 and 5 you add those together they will equal 180 for the most part everything to come up with has some sort of congruence thing except for the same side interior angles there is also a rule for same-side exterior angles and it's the same thing they would add up to 180 but they chose not to put that means no anthem all right so the corresponding angles theorem is always at their if a transversal intersects two parallel lines results in corresponding angles are congruent a spell that right hey I thought I had I didn't Porche I guess I apologize usually usually what I do when you have to have a congruence symbol is out have a bunch of who's on the side here to be some mistake in my slides doesn't there so this is supposed to be congruent what I will do for you guys if you can't figure out how to put a congruence symbol in there cuz I'm familiar with my keyboard yours how do I get to congruence symbol as I pull up these Emoji things on but I've got a Windows laptop where is congruent I saw it earlier my my not seeing it no no no no no but yeah and I said I'm sorry I forgot these so if you can't figure out how to do it yourself I will add the I totally missed it where is it that's a little different where is the right one then what time is I had lost my charger but I found it I'm glad you found it I can't seem to find the right symbol right now so that once. going to have to have you put symbols in I'll put the symbols on the side and it's drag-and-drop I just obviously forgot it so what I did is I got a Windows laptop Surface the Windows button and but I don't remember how you get to emojis in that kind of things on operation when I check your notes that said this is totally my bad in fact I mean I'm looking for the right some of that one's actually wrong it's slightly off the correct one little bit later and I'll and said sorry I'll do better next time all right so I don't think the corresponding angles so angle 1 and angle 5 will be congruent to in 60 other in the same positions sitting on top of the line right there on the right side 150 on the left side same thing goes for like angle 3 and angle 7 are both on the bottom of the wine and on the left side the transversal and foreign ain't so your support here's 8 they're both on the bottom of their parallel lines and they're both on the right side of the transversal and honestly the whole thing with the weed of a translation is it was just move it up or down they will fit exactly in those spaces so that's why there that's how we know different congruent are we good Elsa guess I'll fix that one for you I'm sorry I usually will do that hopefully there's no more of that all right so prudent corresponding angles are congruent so I already mentioned this a little bit we can use transformations prove that the corresponding angles the corresponding angles of parallel lines cut by a transversal are congruent the remember translation we did this mine at your duty - 3, one that kind of thing the translation preserves size and shape and orientation of figure so if take line q and we move it down of M freight line S of because of translate preserves the size and shape angle measures we just we just made a copy of Q and then split it down two BS so all the angles are still going to be the same as the ones below so angles located in the same place but a different intersections have the same measure so that is why angle 1 is congruent to angle 5 to make sense Maybe you know I'm going to help you guys with your working all that and most days okay sorry didn't ask if everybody got this down yet I lost my train of thought Avant okay so the alternate exterior angles theorem so now we're talking about the ones that are on opposite sides of a transversal two parallel lines then the resulting alternate exterior angles are congruent so one is on Nissan exterior and write 8 is an exterior and to the left those two are going to be congruent and angle to hear on the exterior on the right is congruent to angle 7 which is on exterior and the left so far so good okay the next one we are going to prove it we are going to prove it we're doing the butt line age is parallel to line B and then C is a transversal okay the last line again yep yeah okay so so we put those two things and given remember when I'm when I usually write these I would just put both the Givens in the same line but sometimes it's helpful if you haven't broken up easier to understand alright so say that angle 1 is congruent to angle 3 and that is with the steering we just talked about earlier that is the corresponding angles theorem you see how one in three years same places but they're on the different parallel lines so next Mornin talk about are some vertical angles ran talk about 3 + 8 3 + 8 equal angles and this will all make sense right now he's sleepy wanted to mess with either 1 or 3 so we chose 323 and 8 are vertical angles that is the definition of vertical angles they are directly across from each other share one vertex we can also say that 3 is congruent it is also well that is also because they're vertical angles vertical angles and so by the transitive property we can say that angle is congruent to angle 8 so we just proved the exterior angles theorem alternate exterior angles theorem sorry so this making any kind of sense we are going to use properties of parallel lines a lot for the rest of the year so even if you don't a hundred percent get it right now if you will pick it up you will pick it up and I'd only when you pick it up I'm going to really help you trying to pick it up yes so the alternate interior angles theorem the alternate interior angles theorem says if a transversal intersects two parallel lines then the resulting alternate interior angles are congruent so what is angle for going to be Droid 2 based off of this theorem what do you say what is 4 going to be congruent you based off of this theorem SB on the inside what is 4 look like it'll be equal to is 4 acute or obtuse is it a big angle Smalling does it look like it's more than 90 degrees castle looking at the other pair on interior which one of these looks like it's an obtuse angle 6 or 5 5 yeah exactly the look with pear you can usually trust your eyes as long as you know there parallel you can usually trust your eyes so then obviously angle 3 and angle 6 months okay all right the same side interior angles theorem okay this is also called course not corresponding consecutive consecutive interior angles are the only reason I bring that up is that is how I was taught of this particular through that they were called consecutive interior angles so sometimes we come across different resource things like that people say the other instead of same side so I always want to tell you both is same side interior the same as consecutive interior all right so it says 26 two parallel lines then the resulting same same side interior angles are supplementary so on the same side so look here again tangle-free and on the same side on the interior is angle 5 they have to add up to 180 degrees same thing with four and six they have to add up to 180 degrees goodish oh yeah I remember this one we're going to prove it now I think this one took me a couple of slides to do it so I mean on my paper it's the whole length of the paper so we going to prove the same side interior angles theorem so we're told that Sandy are parallel you can see the little check marks here and days the transversal of BC so we wrote that down that's begin you can tell I was actually change this from what they had because I wanted to save some space all right so angle 1 and angle 3 form a linear pair now the reason I know it's a linear pairs because their side by side they make a line they share and angle 2 and 4 are linear pair so one free are supplementary angles and 2 and 4 are supplementary angles and that is the linear pair postulate Cape so anytime we got a linear pair their supplementary so the measure of angle 1 plus the measure of angle 3 equals 180 and the measure of angle 2 and measure angle 4 equal 180 yeah we're really spelling this out we're breaking it down piece by piece that's really what proofs are about and we know that because that's the definition of supplementary angles so far so good they were about halfway there all right so we know angle 1 and angle side or congruent angles 2 and angle 6 or because their corresponding angles here's one your spot their corresponding and here's to and here 6 so that means that measures are equal and that's definition of congruent angles so if I were to add angle 5 + angle 3 an angle 6 Plus angle 4 I get 180 what I did there is I substituted hey it's spelled it right all I did was I took that I took one or place with five I took 2 and replace it with 6 so far so good okay so that means at 4 and 6 or so Mary and and 6 are supplementary and 5 and 3 are supplementary and that is the definition of supplementary angles which I would have written down same side interior angles are supplementary definition of September angles but they chose not to I don't do proofs the way I was taught to do proof so it's a little Annoying only slightly different but still I find it online do we have any questions on the proof are you are you just like oh my gosh I'm glad I didn't have to do that on my own probably the oh my gosh I'm glad I didn't have to do that on my own not for me we are going to apply the angle pair relationships here okay so Lyme disease is a transversal of these parallel lines you're finding your some parallel lines 100 degree angle and angle 15 are alternate exterior angles New York SPX ber little too small means that the measured in can you call the 100 15 + 6 kahoot why can't I see it vertical angles so so far we have we know for teens 115-100 11 yeah let it burn bright yeah it was 11:00 has to be somebody linear pair with one of the 100 angles if we get AIDS so all those other things are 80 so with knowing only one angle we got all the rest on that on that transversal all right now all right and we are going to justify the answer okay so line message lines are marked as parallel we see this angle here is marked as x + 10 + this one over here is 2x - 30 they are alternate exterior angles they're both on the outside and they are on opposite sides of the transversal that's on alternate exterior based on the alternate exterior angles theorem I keep hoping I spell that right so in other words I can take those two angle measures whats 10 + 7 equal 2x - 30 and then we just do Algebra will subtract the extra plus size ladder you both sides and we get is 30 + 1040 what's up what's up do I lose anybody so far so good and get back to you in person I will definitely I've got a couple of days built-in I was going to do one the place I wanted to say it is definitely not the place that we're going to have all right I should have continued slide we are going to substitute 44 ex-soviet 40 + 10 + 2 * 40 - 30 is 80 - 30 is 50 so this just spies that our work was correct correct until each angle measures 50 which was the point so angle 3 and the marked Ingles free and okay yeah you don't know the way we could post it and its corresponding angle 3 another way we could approach it as We Know. 50 and angle 3 is vertical to it so when will 350 the same information all right so are summation thing corresponding angles are congruent last and last fight the scores by the angles are congruent alternate exterior the only one that's different Augustine same side interior angles those are supplementary no I did not give myself enough space to that way I usually double check that I don't know what I was thinking that day shame on me or answer same side interior angles are supplementary so basically what it boils down to and I know this is like making it way up simplified they are either congruent or they add to 180 really when it comes to parallel lines cut by transversal those angle pairs are either congruent or add to 180 and more often than not their congruent so things I want to show you what are those things doing over there I did not clean this up very well alright so these are the word wall words this is this is stuff that we just talked about this just in a different format what is a meme this one here is actually very useful this shows you what all the it doesn't have on here is a linear pair but I like this cuz it's colorful and I have one that you guys can tell her and I usually having the color in in class but I'm not touching paper this year okay and do you summon quiz on Edgenuity do I have any questions on the lesson before going to something else can you go back to White I got kicked out Bank of America

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Lines Cut by a Transversal Zoom Lesson

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