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Parallel and Perpendicular Lines Lesson

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Video of a lesson on parallel and perpendicular lines based off the guided notes from Edgenuity.

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record this next unit and take this off for a little bit so if you look at the parking lot we have lots of parallel and perpendicular lines everywhere lines cross because you don't want cars running into each other those are perpendicular lines and I'll be we can see how the set of lines just will never touch those are parallel all right so lesson question is what special ocean ships exists between two lines not tow lines to or a line segment in a line Cygnet have a long question this time alright so we are going to solve problems include involved try this again we're going to solve problems involving the relationships relationships between lines we're going to fly train I thought you had something transformations to construct parallel lines we're going to solve problems involving distance for point on a perpendicular bisector bisector and we will identify their little perpendicular and skew skew lines if they're not it is not a three-dimensional figure what do the fire thing here I like emojis let's do some vocabulary they move my face out of the way here okay so words to no lines that lie in the same plane and do not intersect that is would be parallel line parallel lines never meet I have so much in common lines that are non coplanar and do not intersect are skew lines so just like parallel lines they never intersect but they are not going the same way so but I like this all right lines that intersect to form right when I degree angles are perpendicular lines and a line ray or line segment that intersects a segment is it is and is perpendicular to the segment at its midpoint is a perpendicular bisector we've actually talked a lot about perpendicular bisectors already please are words that are alright let's talk about parallel and perpendicular lines so here are the lines are there coplanar and do not intersect not intersect not intersect and if you see here's your example right here and they use these little orange check marks here to show parallel you also see like triangles but they have appointments and there must be the exact same number of those check marks are triangles to show that there parallel cuz you can have milk multiple sets of parallel lines in a figure but they do not necessarily all parallel to each other so we need to make it to stay MN perpendicular lines are coplanar lines that intersect to form right or 90° angle and so yes we we can mark that by putting the little right angle in the corner so square box you said click it look at it dude write the word coplanar means lines in the same plane I like to think about it just like think of a lines in a book so if they're on if we are on the same page they're on the same plane if they're on a date is brown a different page that's a different plane I feel like I've just been talking for hours okay and a plane and euclidean geometry is a two dimensional object that extends indefinitely in infinitely not indefinitely goodness in so it extends indefinitely in both of its dimensions and has no height so it will spread out it'll go likes when you still glass of water on the floor it just spreads right that's a plane but you can't measure how tall it is it has no depth okay oh wait oh yes we are alright so we got some serums going on here geometry the shortest distance from a given line I'm a given line through a point not on the line is the length of the segment perpendicular to the line through the point so in other words if I take align and I couldn't see and I go straight down that looks short if I did like this that lines obviously longer right that is the shortest distance Clovis point be a line going straight down perpendicular to the line will be the shortest distance to I think I said that right I was just checking my emails while I was waiting all right so where should I brew it now I know I said that we always given statement they didn't do it that way so I don't really consider this a proper proof but take whatever that's what they put in there I personally am not this is not a good proof to me because I didn't start with the given all right what they said is to draw a perpendicular segment from C down to the nurse Xavier. r6tab at Point d i remember they must be capitalized or it's wrong we're talking points we're proving the shortest distance are on right now so unique line postulate through any two points is a unique line that's what that is so then they draw they drew a segment c o okay I did I not catch that earlier I think they actually said to see a spyware John online to see between seeing seems to be so it doesn't he just needs to be on the line actually name that Cee and I wish I caught that I would have stopped because it's obviously they put hey there whatever there's a red line segment CD all right also unique line postulate so triangle ecd is a right triangle triangle ecd is a right triangle and how do we know that that's the definition of a right triangle has exactly one right angle you can see it right there okay segment C is the hypotenuse of that triangle and that is the definition of hypotenuse your prayers aren't supposed to be hard it's supposed to be logical like so we know it's a right triangle because it meets the definition of right triangles we know that's a hypotenuse because the hypotenuse is always directly so definition of hypotonic so good my internet connection is unstable alright see you the longest side of ECB so CD is less than obviously see that because that's again the definition of hypotenuse is the longest side therefore the shortest distance from C to a b to line a b is segment CD SS completion from set 5 cuz I said this is when I write a proof we start with the given and the last statement is the proof statement this is what they had on Edgenuity so this is what we did I am so confused don't worry too much about the proof important thing it to realize is that the shortest distance from a point not on the find to the line is a perpendicular CD is definitely the shortest this segment here is definitely shorter than these other two right yeah that's the whole point Raymond Vaughn yes so the parallel postulate it says given the line and a point not on the line there exists exactly one one line in the same plane that passes through the given point and is parallel any given line sneaky one just do that yeah I put an arrow on top of the arrow that they gave they can see those two lines are parallel actually really easy to understand that because I mean I pulled it right off the line I made a carbon copy of that line and I didn't I didn't I just I just lit it up so it's like I translated it up so many spaces so that's how we get parallel lines like that I think again yes yes all right you are okay skew lines are lines that are noncoplanar and do not intersect Bronco player and they do not intersect so we got this diagram here planes R and W are parallel not only can lines be parallel like the floors of buildings all right so you can see on this plane here d e and f g on the other plane they are skew lines and we know their skew lines because they're not on the same plane and they're definitely not point in the same direction mean what kind of like perpendicular lines are not skew lines because they in the same plane enter a little lines are not skew lines because they're in the same plane now reason I can say they're in the same plane even if I were to draw another line on either one of the planes if I made it parallel to a point in the same direction those planes are parallel so all the lines on that plane that are pointing that direction are also go can you parallel they can make new planes going through those two lines hopefully that helped him yeah I don't know it's all good all right so we're going to identify any parallel perpendicular or skew lines from the diagram okay so looking at the diagram here we got a lot of crazy stuff going on right now we have lying to here and on the same line are in the same plane going a different direction is line M look how clever I was already italicize the letters for you I'm so good sorry all right now the perpendicular lines I can see who's this 90 right here and so I C line L and line In-N-Out just now looks like I put one or whatever can a skew lines skew lines are going to be well I can say P & L did you see they're not touching so they're definitely not perpendicular and or they don't even intersect but they're actually physically on different planes even though L goes through the those two planes of the planes intersect with those lines you nuts that's what are you same thing over here line L & M M is parallel to pee so it's a also going to be skewed to l are we good yes okay the perpendicular Factor theorem so the perpendicular bisector theorem states that the points on the perpendicular by sector which is a line ray or line segment that intersects a segment is perpendicular segment equidistant it looks wrong but it's alright from the endpoints all right so what this means this line SE at a 90 degree and it goes right through the midpoint so this would be the midpoint right here that breaks QR into two congruent two congruent segments so we can say that another thing that we can say another line here us yzma lunch with us and then draw a line from r2s now the reason why we did that is we going to say que es is equal Sr shame on me and guess maybe she Justin Moore it would be nice to Lyon r e s o r e is congruent to or equal to no those four segments are not can be to each other but this is congruent to this one and this is congruent to this one that's a perpendicular bisector theorem I don't listen in this. okay okay so we know the standard distance from QR right it's whatever Q2 the midpoint is Jimmy s to the midpoint so if you look at this this is definitely congruent to itself right and then this piece will this Beast is congruent to this piece yeah we got two congruent right triangles so they're hypotenuse has her iPod and I am not sure what the plural of moose is Katniss's are going to have the same measure okay that makes sense yes two pairs of congruent triangles Easter triangles are congruent so their pieces are congruent these two triangles are congruent severe pieces are congruent yes all right so far I'm really liking this this is probably the one I'm alright so okay so we are given that p is a point on perpendicular bisector of line L of segment MN that just rolls off the tongue doesn't prove that the measure of GM is equal to the measure of segment Keegan actually going to prove what we just we just just discussed so by the by the unique line postulate you can draw only one segment p.m. that's it we can't make you unique line through any two points is one unique line so using the definition of reflection all that stuff we just did on Transformations write a reflective over l by the definition of reflection he is the image of itself and in and it is the image of M in other words when we supposed it M&M touch right if we fold in half they're going to be lying on top of each other so since Reserve length GM is equal to p.m. remember will be reflected across that line it ends up being the exact same thing on the other side of line so there you go what is the proof help you understand that little better love it I like hearing that there's a reason we do proofs so we are going to apply the perpendicular bisector theorem so what is the length of segment AC William on the wrong page right there register all right what is the length of segment AC a case of line L is a perpendicular bisector line segment a b k I think I forgot to actually type in the question was the length of segment AC that would be a mistake and always points equidistant from the endpoints of line segment a b so a C equals e c driving a net over it again so lynel so here's line L is the perpendicular bisector of segment a b Tweetsie is the safe cooking this here is congruent to this year I think it's the same distance so another words for x minus 5 equals 3x so now we can actually solve for x so we combined ask him if we move the 3x over we're going to get x - 5 and that equals 2 and then if we move the five over will add 522 will get 7 so replacing there in AC is 4 * 7 - 5:00 so that be 23 and so BC also has to be equal 23 wait can you go over that again the math over there of course all right so you have we know these two pieces have to be congruent so we set them equal to each other so first thing I did is I subtracted 3x from Forex oh, no problem I mean that's that's one of the reasons why I like how I don't want to record these because you guys are going to catch stuff and go get that explain it to me again yeah that's what I want to do is I mean I think I'm clear but then again sometimes I'm not moving home so the converse of the perpendicular bisectors theorem equidistant distance from the endpoints of a segment then it is on the perpendicular bisector perpendicular bisector so it says if Point p is equidistant from m&n then the line that lies on the perpendicular bisector of MN so this is the perpendicular bisector of Congress just means we're taking it's just like we did in Logic the converse the converse took the hypothesis and the conclusion and switch them so that's what we're doing with this particular theorem we switch the hypothesis and conclusion and it's still true we must be done soon right volume the same plane and they intersect at right angles parallel lines are in the same play and never intersect wait another that never intersect and this is the summer cementation I can almost say the word summation right skew lines are on different planes Emma never intersect but now we will discuss all the theorems we just talked about real quick like so we have the first one was the shortest distance formula formula that said if you have a line and a point that's not on the line the shortest distance between that point in the line if the length of the segment which connects the two points that is perpendicular should have given line Edwards if you go straight straight up or straight anyway you can make to the other two that line Ellie 90° not give you the shortest distance it just a couple more so the parallel postulate if you have a line and a point that's not on the line there this is exactly one line that goes through a point and is parallel to the given line my percent means if I have a line and I have a point right here only one line will go through it that'll be the also parallel let me have the perpendicular bisector theorem every point along the perpendicular bisector of a lot line segment is equidistant from the line segments and points in other words we make little right triangles and those high cotton cotton cotton I may have to be the same totally not right but at least I know it's not right all right and then the converse of the perpendicular bisector theorem is a point is equidistant Army in Winter line segment then the point must be on the segment perpendicular bisector so if we know that they're the same distance then we know that line is going to perpendicular bisector the only other things I have left on the slides are worthwhile stuff so I'll go ahead and show you those aren't they pretty we're going to go much further stuff to do perpendicular lines and perpendicular line bisector obviously you can see there's a lot more stuff as you can actually see these on a few more notebooks because we will be discussing midpoint formula distance formula that kind of thing that all comes in with this one so that's it I'm going to have another one. do we have to do and it's due Monday right oh yeah and I'll do that lesson with us on Friday what time is it in time on the same time recess my plan

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Parallel and Perpendicular Lines Lesson

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