How to 𝙁𝙄𝙉𝘿 axis of symmetry order of rotational symmetry in shapes Examples

when we talk about line symmetry in shape line symmetry in shape is line which divides the shape into two identical halves but in particular two halves where one half is perfect reflection of the other half so should be able to take the two halves basically and and fold one over the other and it should line up okay now so line of symmetry is also called an axis of symmetry and so shapes can have more than one axis of symmetry like square for example it's got four axis of symmetry the plural of axis is the word axis okay so instead of the instead of an will replace the within the shade can also have rotational symmetry so if you take shape and basically turn apart way around and the shape looks identical to what it was before you turned up part way around that's called rotational symmetry okay the number of times basically that shape could be turned or in terms of and how many part turns okay so how many part turns shape has where it fits on itself is called its order of symmetry okay and in particular at the number of times it fits in on itself in one revolution okay that's very important then okay so in 360 degrees if shape basically you stopped at multiple sort of times along the way and in the full 360 that's called it to order let's have look at some examples okay so let's start off with the equilateral triangle okay might just put that there in the middle there how many lines of symmetry would an equilateral triangle have okay let's count them so we've got one two three so three lines of symmetry what about rotational symmetry so if turn this part way around would it look the same or would it look identical okay look where the red side is at the moment okay one two three okay so could could stop it basically three times or in 360 degrees there's three positions where the shape looks the same okay where the vertices are all lined up where they were before so an equilateral triangle has rotational symmetry of order three okay so again one two three let's have look at sort of similar shape in terms of the fact that it's regular regular polygon which is square okay so another regular polygon here we have one two three four okay the square has four lines of symmetry in fact I'm not just I'm cool to me can say that little bit clearer okay so you know one to say it can be folded this this shape or this squeak can be folded across the line of symmetry there or could cross the axis of symmetry and one half will fit perfectly over the other and you've also got these ones here okay not through the diagonals but just through the the middle of the shape through that'll through the length of the shack or cancer sites so there's in fact four lines of symmetry there so what about rotational symmetry okay so might just rotate the entire board so just watch the blue side there okay reflected ninety degrees so there's one still looks like it still looks like square oriented in exactly the same way as it was originally that's how it was originally okay so one so starting off here one part two two part turns three part turns four part turns so back to where we started that's full 360 degrees so there's four lines of symmetry and it has rotational symmetry of order four okay let's have look at rectangle okay so rectangle how many lines of symmetry would rectangle have okay it certainly has these okay so through the two lengths and the two widths of the rectangle so there's two lines of symmetry that rectangle could we fold it fold it over that way it can also be folded this way as well could it be fold along the diagonal in fact yeah well just get piece of paper think I've seen this happen few times where people say yeah use this okay so he said he's rectangle okay now imagine folded it across the diagonal wouldn't fall perfectly across the diagonal let's see okay well just do it as best as can all right well you can see there that the diagonal in fact does not work so the diagonals of rectangle they're not excessive symmetry at all even though the two halves look like they're identical it needs to be reflection perfect reflection so one half is not reflection of the other okay the two corners have to line up as well so it works in square but not in rectangle okay what about rotational symmetry okay so two lines of symmetry what about rotational okay so if rotate at 90 degrees the rectangle is originally that way rise originally like landscape just sort of long ways across not up down where the length is okay so but if turn another 90 degrees so that's hundred eighty degrees okay so basically 1/2 - it looks the same as it was half turn you go back to where it was the red at the bottom alright rotated half turn Reds now at the top but the rectangle the orientation of the rectangle is as it was before another half turn later okay to make full turn there's in fact rotational symmetry of order 2 might just look at one more shape now and shape that's in fact similar to rectangle look of sorts the only thing is it them have 90-degree angles of course in the its vertices and that's parallelogram okay sorry parallelograms so you're probably thinking the the number of lines of symmetry is equal to the order of rotational symmetry of that shape and it's not always the case how many lines of symmetry as parallelogram have and you can investigate this for yourself if you like but can tell you from now none there are no lines of symmetry on in parallelogram but what about rotational symmetry okay so this one here has and might just write this down there are no axis of symmetry no what about rotational symmetry half-turn still looks it looks like the original parallelogram doesn't in terms of the way it was situated all the way it was oriented okay another half turn later okay back to where we started but it looks identical to where it was half turn ago so parallelogram has no axis of symmetry but it has rotational symmetry order to okay so it's not always the case where the axis of symmetry is equal to the order of rotational symmetry here's one example where it's clearly not the case okay think about some other shapes like hexagon Pentagon for example kite okay does it quite have rotational symmetry does it have axis of symmetry kite has one axis of symmetry Marcus might just draw this in fact so draw kite because think this is good one to see as well no quite the another example okay where you have an axis of symmetry down the middle there so you can fold the card over that's fine so it does have one line of symmetry there or one axis of symmetry but what about rotational symmetry okay in fact kite is one of those in an example of shape where you'd have to turn it 360 degrees around for it to look exactly the same as it was before so it's not like square for example where you can turn it partway and it looks it looks identical with kite there is no part turns that you could make with it so that it looks identical in terms of how its where it's pointing or the shape of it there's there's no part turns you can do so this one has one axis of symmetry right that's one axis of symmetry the spelling of axis is and it has rotational symmetry of order one in other words anything any shape that has rotational symmetry of order one you could say that it has no rotational symmetry in other words every shape when you turn it 360 degrees it's granted it's going to look the same as it was 360 degrees ago okay so but this is an example of shape where the rotational symmetry you can turn it part way around doesn't matter which way how many degrees it's not gonna look the same okay it's gonna look like it's pointing in different direction clearly and it doesn't look like quite that's oriented this way okay think of some other shape some weather maybe in fact the case and look forward to the next video that we're going to make where we talk about classifying triangles