hello class welcome to geometry lesson 1 one of measuring segments and angles by the end of this lesson you should be able to use properties of segments and angles to find their measures we're going to start with some vocab for you so undefined terms are terms whose meanings are accepted without a formal definition so an example of that would be a point so a description for a point is you know you we typically draw it as a dot and then we give it a letter name so that would be a point a that is a point so you guys have been working with them for a long time the diagram and notation columns I really want you to pay attention to those because that is what you're going to be using throughout the whole year okay so a point you draw a dot you label it with the letter notation you do whatever letter was named they are always capital letters okay I don't want to see you naming points with lowercase letters always has to be capital a line is a line has arrows on both ends that keeps going in both directions forever and ever but we can't draw forever ever which is why we do that two arrows and a line needs at least two points in order to be a line so in this case we have point A and point B so we can title this line we can name it line a B and you can either write out the word line and put a B or you can do the symbol of the line above it another way to name a line is you take a lowercase letter it's usually written in cursive but if you do a lowercase letter you can name not erased you can name the line by the lowercase letter so in this case line L and then a plane is going to be it's gonna look like a 2d figure for you guys okay but it goes on forever and ever just like a line it goes on forever and ever in all directions so some ways that you can start to think about what a plane is you can think about like if you think about the floor in the classroom imagine that the floor keeps going on and on forever and ever at the same height and everything that's kind of a plane so with the ceiling or a wall and the way you can name a plane is there will either be a letter in the corner of the plane so in this case that's M so that's it can be called plane m or you need three points on the plane but they can't all be on the same line so see how if I were to try to draw I couldn't draw a straight line through all of them see it would curved or bent so you need at least three points that are not on the same line and that term is actually called nine go in here see what so then another good word to know is collinear I'm the same way so the second name for the plane would be plane X Y Z now some defined terms so some point things that you're used to a line segment has two end points and the notation it looks really similar to a line but you don't have the arrows on the ends okay so it's missing those arrows and that's because a line segment ends it doesn't keep going and yes I'm going to be picky about that okay so this is a segment not aligned the second one we have a Ray that's where you have an endpoint and one arrow it can be facing whatever direction you want but the way that you named it is you start with whatever point doesn't have the arrow the point with the endpoint and you can write the point near the arrow so and opposite rays are when you have to raise that point in the opposite directions so in this case it ends up looking like a line but another name for it is an opposite race so we could have raid TS and rain tu and then then angle we've worked with angles before quick review on naming ælis you can name them by the number inside of the angle you can name it by the vertex or using the three letters so in this case angle PQR another way that you could write it is angle R QP so you could go this way you know start up the R and go or you can start at the P and go through the angles okay all four of those are acceptable ways to name the angle now let's jump into you finding segment lengths how can you find the length of segment CD the way that you can find the length of segment CD you have a couple options you can either count and say oh it's three units away we're gonna label our answers in geometry okay so three units not just three three units or if they were super far apart and you didn't want to count each one what you can do is you can either say 4-1 and that's three units or you can do one minus four well that's negative three units but since we can't have negative distance we make it okay and the way that we would write that is using absolute value if you remember that okay so no matter what distance has to be positive go ahead and solve this one on your own hopefully you ended up with seven units if not please be sure to reach out for some help let's look at example 2 using the segment addition postulate so segment addition postulate is when you take multiple smaller segments and combine them to make the larger segments so in this case I could say C D plus D e equals C e the whole thing right if I add the bluish and purple segments together I would get the whole segment so if I want to solve and figure out what this question mark is what de is well I know the whole thing equals 30 so I have to find out 14 plus what number gives me 30 that would be 16 so I would say actually not going to box that I am going to say de equals 16 units all right the second one same idea just slightly different so AC whole thing equals 3x plus 3 a B equals negative 1 plus 2x and BC equals 11 so again are you going to add the two smaller segments together negative 1 plus 2x plus 11 I'm going to set it equal to the whole segment 3x plus 3 and I'll solve from there so I have 2x Plus 10 if I can find terms on the left hand side equals 3x plus 3 I want to get my X's on the same side of the equal sign so I'm going to move the 2x so I have tiny equals x plus 3 then I move the three next so x equals 7 and I was looking for X so I can say x equals 7 why don't you go ahead and try this first one on your own good luck hopefully you read the directions and ended up at H J equals 17 units if not please be sure to reach out for some help hopefully for the second one you ended up with x equals 13 if not please be sure to ask a friend or myself for help all right example 3 using the angle addition postulate so we want to find the measure of angle KLM if the measure of angle KL B equals 26 and the measure of angle B L M equals 60 so KL b is 26 and BLM is 60 this is the same ideas the cygwin addition postulate but this time we're using angles so if I add those together to make it the large-- angle then 94 KLM so I'm gonna add those two smaller ones together I get 86 degrees okay and I'm gonna be a little more specific I'm gonna say measure of angle K equals 86 or I could say okay this is a little different I'm gonna get nitpicky I'm not gonna be super harsh on just at the beginning but I do want you to learn the difference if there's an M here there is no degree symbol with the 86 if there's no M in front of the angle symbol there's no M here you have to use the degree symbol okay that is just some specific notation okay the second one here is the same idea but with variables this time so gfn this is 4x plus 10 NF e is 14 X plus 3 and the whole thing is 157 so I'm going to say 14x plus 3 plus 4 equals 57 if I add those together I get 18x plus 13 157 18 x equals 144 second subtract 13 from both sides divide by 18 and I get x equals 8 and I'm trying to find the measure of angle and Fe so nfe was the 14 X so instead of X I'm going to plug in an 8 plus 3 so that's 112 plus 3 or 115 degrees I could say angle and e equals 115 or to the measure of angle and go ahead and try this first one on your own good luck hopefully for this first one you ended up at 84 degrees for the angle of W DC if not please be sure to reach out for some help and go ahead and try this second one on your own good luck hopefully for the second one you ended up at x equals 0 if you have any questions please be sure to reach out for some help and our last section so we have already talked about congruent symbols and understanding that in class so I'm just gonna do a quick review if a line segment has the same number of dashes on it that means that they are congruent okay so anything with two lines it looks like is 11 so I'm gonna label this 11 centimeters anything with one line is 8 centimeters that's what my picture tells me and I don't know what the three lines what that measure is yet okay so I'm just gonna leave that if I want to figure out what each F is okay HF is this right here so I'm going to add 11 to 8 in order to get 19 centimeters you do that the same idea over here but with angles remember anything with the same number of Arc's in it mean that those angles are congruent they are the same so if that first one 232 that second one is also 32 and I know that this whole angle is 127 so what I can say is I have 32 plus I don't know what this Center angle is so I'm going to say X plus 32 equals 127 V it 2 and that is 64 plus x equals 127 or x equals that would be 63 ok so that Center angle is 63 degrees so this is the measure of angle ywb equals 63 or angle y WB equals 63 remember you don't have to write both of these ways you can write it one way or the other I'm just doing it to help you get used to both ways later on I'll start just doing one way or the other go ahead and try this problem on your own good luck hopefully through the first one here you ended up with 41 point five degrees if not please be sure to ask for some help go ahead and try this next one on your own and remember perimeter means that it's the distance around the outside okay so perimeters the distance around the outside good luck hopefully for the second one you added up all the distances around the outside set it equal to the perimeter and when you did that you should have ended up with a be equally 11 and AV is congruent to GE so we can assume that ge is also 11 units if you have any questions at all about that problem or anything from this video please be sure to reach out for some help and I'd be more than happy to help have a great day