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Symmetry Lesson Video

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Zoom lesson video on symmetry of geometric figures.

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okay so I just said the big ferris wheel because it has both rotational or Point symmetry as you can see those around a particular Point that's the one right smack in the middle or line surgery if we sold it over it would be the same on both sides they be like a reflection interesting day okay question is how can you identify how can you identify symmetry in the figure listen to realize is this is not Transformations which is what we've been doing up to this point it's related to its related to transformation transformation what I mean by is related to is we'll talk about rotations and Reflections but they're about a particular figure not of not copying a figure okay so we're going to Analyze This geometric figures and identify the lines of reflectional symmetry also called line symmetry and will identify the angles of rotational which is also called Point symmetry okay so our vocabulary words so symmetry are we still going to have to do the The Notebook even though you're doing it right now we have to do it on our own to yes okay yeah and I I am grading them I'm getting them in the gradebook property of having an object flip rotated or moved to exactly match itself so is a SED folding a half or rotating it ends up in the same the same on both sides or should you rotate it it looks exactly like it did before the rotation so a line of symmetry is a line and a plane ticket can be reflected reduce image that Maps perfectly onto itself so as I said that would be the line where you put the mirror and you'd have the same image and rotation really going to be like rotational symmetry an image that maps onto the original return it and it looks the same return it and it looks the same art similar words reflectional symmetry the next vocab I figure the state of being able to be reflected across the line and thereby produce an image that Maps precisely on the original also known as line symmetry so the same thing order of rotational symmetry is the number of rotations of figure greater than 0 but no greater than less than 360 Degrees that recent image identical to the original so how many ways that it can be turned and still look the same simplification all right in Geometry a lot a lot a lot so regular polygon is a polygon These Boots equiangular and equilateral that means they have the same angle measures and they have the same side measures all right so symmetry is the property of having an object flipped rotated exactly map to self so these letters all have some kind of symmetry so we take one of these are limes like with the letter M here is it right now how old is a Tim and 1/2 he be the same on both sides however if I took c14 similar line when he gets like this ended like this it definitely there's no place where we end up looking the same so we just put that side so with the letter A with the same things but down the middle it looks the same on both sides but if I try to fold it down there's no place where it would look the same same thing with the letter t where to buy folded across the Slime it's going to look the same on both sides but yet again if I throw this one right here it doesn't do anything it's theirs it would look different set the letter H I do like I've done before if it straight down the middle if I fold it in half maybe the same on both sides play my cheapest this one that's operate so difficult pretend like it's in the right spot downward and it would still be the same on both sides soap for making sense all right so restrictions okay so reflectional symmetry of a geometric figure is the characteristic of a figure onto itself across the line of symmetry reflectional the tree we think of the number of lines reflection for lines of symmetry can be drawn on a figure that would produce a mirror image itself on either side now we will actually do this on another slide but I wanted to show you where the line of symmetry is on this triangle so if I stay vertex here draw line out the longest side of the hypotenuse you can see these two we don't to be congruent so fast forward 1/2 like that that would be the line of symmetry that's actually the only line of symmetry for the triangle but we're going to talk about it a little bit more for instance these lines are no laundry reflections of this triangle noticed when I drew it I drew it from point C in the vertex to eat opposite side if I tried folding it at point he's going to the opposite side doesn't quite match up same thing with Point D it doesn't match up when you fold it the number of lines of reflectional symmetry will vary for each geometric speaker said to have N Fold rotational symmetry where n is the number symmetry of course I started this okay so criteria for lines of symmetry when Crossing from an angle 2 and angle so I threw in some examples here so going from vertex to vertex angle bisector Bojangles UCF with the little tick marks here it definitely cut those angles in half when Crossing from the vertex to the side so we're starting at Birth I'm going to the side it is an angle bisector of the vertex what is a perpendicular bisector of the side of the finger sign don't know what I'm reading anymore but yeah yes sir in class Play Store posted on my Links Page however right now I'm I'm messing with it so right now is not done this is my master copy alright so when Crossing from a side to another side it is a perpendicular perpendicular bisector of both sides so on this trapezoid here and go back and look at I'm sorry be aware that this is being recorded So if you don't want to be seen bye everybody I teach geometry to you might want to Hydra Hydra picture what can I do in bed without a shirt on yellow really a mutagen don't worry about it onefold reflectional symmetry so I know we already did this on the previous one but let's go ahead and dry again so I'm going to draw a line here give me up whatever anyway so as you can see here we cut the figure in half and each half would look exactly the same so far so good questions you can unmute yourself or can a mute yourself let me know okay trouble earlier with people not being able to unmute themselves you going to save this is can go back and look at it right okay are y'all trying to mute myself but I can so I can copy I can't do it like now it won't let me completely understand I'm glad you're here to ask questions during the lesson though so yeah it's already on My Links Page if it's already there it'll be there for you when you keep me up time Google Classroom are we going to do it exactly the way we did when we were in class you'll do this good morning why do this myself but yes so like so like tomorrow I will also be having meetings at 10 and 2 and I will teaching a lesson so if you're having trouble with an assignment or quiz that's when you're going to ask me questions just like you wouldn't class today I'm just doing I'm doing today so let's talk about the reflectional symmetry of trapezoid isosceles trapezoid has one fold reflectional symmetry right so if I sold it straight down it would be the same on both sides at this right trapezoid with all right trapezoid because of the two right angles there there's no place where I could put a line where it would reply so this figure has none there is no there's no reflection symmetry for the speaker all right so reflectional tree of regular polygons that interested in other words will have installed reflectional symmetry does a regular polygon that has in other words however many sides it has that's how many lines of reflectional symmetry we can make so friends with this equal a equilateral triangle that has three but it will be a reflectional symmetry and lunch over here and you can see right here straight down the middle it would fold in half and they be the same again will spend all the Angles and all the sides of the same I could do the same with the other side yeah this is my Church of God be right as I kind of put it on the spot I want and then it just a little bit CNC same thing as from the from the first one and then with this one it'll be exactly the same cuz it is an equilateral triangle all the side lengths are the same all the angles have the same a regular hexagon will have six lines symmetry six different lines of symmetry because there are six sides means this one should be pretty obvious straight down the middle Tremec down low so going from side to side look I'm going to do all the sides first going side to side Ellen side to side so you can see all the ones connecting the midpoints of the sides those are all Symmetry and just just to make it nice and easy to see him to go ahead and change the color of these arrows changing a red you do not have to do this if you don't want to and now I'm going to go angle to angle vertex to vertex let's see if I split it right down the middle hexagon actually breaks into two congruent have symmetry from another angle opposite angle that definitely looks like it was folded in half the same cuz it would only got one more I'm just glad it wasn't like gum something with 10 sides madeca Jones so we can see we have six lines of symmetry there six lines of symmetry so if you don't get perfect that's okay obviously if you were doing it on paper it be a lot easier to do but there you go all right so leave it on the next page so a rotational symmetry additional symmetry of a geometric figure is a carrot a characteristic of a sticker to map onto itself through the center of rotation the rotations that map the figure onto itself is called the order of rotational symmetry so a lot of these words that were using sound a lot like what we used in transformation because they are we're talkin about Reflections and rotations Uber to the Transformations we talked about and Transformations but remember this is not a transformation this is about a particular figure okay so the rotational occur for an a between 0 and 360 including 360 every figure has an order of at least one because then always rotate 360 to map the figure onto itself basically like you turn completely around and you're facing the same direction so even if the thing has no kind of symmetry at all it's still an order of one because we can turn it completely around and still so looking at this rectangle this is the center of rotation now we're about to discuss this on the next fly but I really want you to think about it if I turn this rectangle to think of it like this book here if I turn this rectangle 90 degrees does it look the same everybody needs himself now but if I did a 180 it looks the same right so I can do a 180 in a 360 suit that has a rotation at order rotational to so now what's going on with the actually looking at our rectangle here the 45 degree rotation does not does not match the original rectangle back onto itself but a 180 rotation a rotation of 360 Degrees would bring the rectangle back to the original position so this isn't a rotational symmetry order of because I can twist it twice 180 and it looks the same and I can treat Twisted 360 and it would look the same so far so good facial symmetry of trapezoid a symmetry would be a fool would you mind yes ma'am I know what happens in the background all right so the order rotation would just be one because we can for it before 3 sixty and it would look exactly the same but there's no other way of rotating it where it would look exact look like it's in the same position and the right trapezoid only map into itself after a 360 rotation so it also only has an order of one things I miss sleeping I'm drinking my throat gets dry all right so rotational symmetry of regular polygons we're going to look at this equilateral triangle so a regular polygon with n equal sides will have in order rotational symmetry and other words how many sides it has tells you how many rotation you can do so does find the smallest angle of rotation where can I take the 360 and divide it by the number of sides so 360 / 3 sides is 120 so every 120 degrees it looks exactly the same as it did before so we've got three and also we got the 122nd unit 120 so like not sitting on BC if I turned it 120 counterclockwise it would be on segments Davie if I turned it to 40 is 120 + 120 240 easy on segment AC and then if I turned it another 120 suit 360 if you back to BC next one so for a regular hexagon hexagon geometry really do we use them a lot so order rotational symmetry equals the number of equal sides so the smallest angle of the Symmetry 360 Body by the numbers so far hexagon it has to be in order six Define what that angle is will divide 360 by 6 so we end up with 60 and that one meet you ukj did you ever question rotational symmetry and then 60 + 60 so 120 and then 120 + 60 that's 180 and then 180 + 6240 to 40 + 6300 300 + 6300 six different rotations and look the same each time we got it we good all right so identifying symmetry so we're determined the reflection and rotational symmetry for this regular pentagon rotational symmetry the order of rotational symmetry will be the number of sides in Pentagon has five sides the smallest angle of rotational symmetry will be the 360 / 5 which I totally can't do in my head but I have it written down so it says 72 degrees I do have a very basic calculator at home that I use for this kind of stuff it does we're not doing complicated math here so every angle measure that is a multiple of 72 the regular pentagon onto itself what they mean by maps onto itself is when you turn it it looks the same that's all they're saying it just is a very well Massey way of saying and I was talking about the reflectional Symmetry reflectional symmetry how many folds is how many size so you capitalize do you wanted but it's actually going to be fine. All right last live the key concept a figure maps onto itself across a line of symmetry regular polygons have in fold symmetry wherein is the number of rotational symmetry as figure maps onto itself about a center of rotation by a certain angle angle measure a certain angle measure do polygons have an order in of rotational symmetry so in other words reflectional symmetry of a line of symmetry and however many sides a regular polygon has how many times you can fold it that's what they need my info with rotational symmetry everything has at least an order of one but for regular polygons in Tower Minnesota you can turn it I want to add on slide 20 here we have some beautiful examples of line symmetry line symmetry is also called reflectional symmetry I'm just going to go ahead and add those words cuz they're not here so it's also reflection and point symmetry which was not actually used in the lesson but Point symmetry is the same as rotational symmetry the reason being me can you see the words because rotation rotational symmetry is symmetry about a point so Point symmetry would be symmetry so it's all good and that is obsolescence so let me go ahead and stop the recording

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