Examples: Order of Rotational Symmetry Video Lecture - Class 7

hello friends this video on symmetry
part 14 is brought to you by exam fear
calm no more fear from exam so based on
whatever we have learnt about rotational
symmetry let us try to attempt a few
questions question number one which of
the following figures have rotational
symmetry of order more than one why am I
asking about order more than one because
all objects have rotational symmetry of
order one so the uniqueness is when an
object has rotational symmetry of order
more than one so let us look at this
triangle so in this case by what angle
should we rotate this strangle just to
see if rotational symmetry exists or not
so you can apply the same logic you have
three sides right so if we want one side
to move to the position of the next
slide
next side so by what and then should I
rotate it so calculate the angle which
each side subtends at the center now we
assume that all the three angles are
equal now there are three angles which
are formed and total is 360 so 360 by
three that is 120 degree so let us
rotate it by 120 degree in the clockwise
direction so when you rotate it by 120
degree you come to this position
yeah now let us try to rotate it further
by 120 degrees so then you take it
further by 120 degree it comes to this
position and my name further rotate it
by 120 degree it comes back to the
original position so basically in one
complete rotation how many identical
triangles do you get so you actually get
three identical triangles 1 2 3 because
all the time
therefore the order of symmetry for this
is three let us look at the next object
so what happens spend me by what angle
are we going to rotate this object we
will rotate it by 90 degree so the
moment we rotate it in the clockwise
direction by 90 degree it gives the
shape now on further rotating it by 90
degree in the clockwise direction it
comes back to this shape now we further
rotate it by 90 degrees and we get the
shape when you further rotate it by 90
degrees so where are you going
this is 90 180 270 and 360 so you have
completed 360 degrees and now it has
come back to its original position so in
one complete rotation
how many identical positions do you have
this is one identical I mean identical
to the original position so this is the
original position and this is the next
identical position so you have two
identical position therefore the order
of rotational symmetry is to question
number two give the order of rotational
symmetry for each figure so we will
follow the same process for each of
these figures now it doesn't matter what
figure do you have oh the all only thing
that you need to decide is by what angle
should you rotate it so for the first
figure can you tell me by what angle
should you rotate it if you wearing
clothes they observe this figure this is
your center of rotation so the angle
that they subscript at the center is 90
degrees so let us rotate it by 90 degree
so the moment you rotate it by 90 degree
in the clockwise direction this is what
you get again rotate it by 90 degree so
what do you get on further rotation by
80 degree you get this let us rotate it
further by another 90 degree and
get this one further rotation by 90
degree you come back to the original
position so basically in one complete
rotation
how many identical position do you find
one two three and four because all the
four positions are identical so that
shows that the order of rotational
symmetry in this case is four let us
look at the next one so in this image
you have to first decide that by what
angle you are supposed to rotate it for
that you need to find out the angle that
is subtended at the centre of rotation
this is your center of rotation now here
you see there are six different segments
this is one segment 2 3 4 5 and 6 so
there are 6 parts basically so we want
that after one rotation this part should
get moved should take the position of
the next part so part by part it should
get displaced so basically we have to
see what is the angle that is subtended
by each part at the center that means
you have to get an idea about this angle
that they are subtending at the center
so how many angles are there 1 2 3 4 5 6
and what is the total angle it is 360 so
360 divided by 6 that is equal to 60
billion so let us rotate it by 60
degrees so when you rotate it by 60
degree in the clockwise direction you
get this let us further rotate it by 60
degrees in the clockwise direction we
get this on further rotation of 60
degree in the clockwise direction we can
this we still rotate further in the
clockwise direction like 60 degree and
thereafter also we will rotate it by 60
degree to get this and finally we rotate
it by another 60 degree and we come back
to the original position so how do we
know that after this we are coming back
to the original position that's because
this is 60 this is 60 plus 60 which is
120 this is 60 plus 60 plus
60 does 180 this is 180 plus 16 just 240
this is to particular 60 that is 300
this is 300 plus 60 that is 360 and
after 360 degree that is after one
complete rotation you come back to the
original position you must come back to
the original position so we know that
this is one complete cycle so how many
identical positions did you come across
so they are actually one two three four
five and six identical positions you see
all of them are identical therefore the
order of symmetry for this would be six
let us look at the third image this is
how it looks like so here the center of
rotation would be this point so here you
see there are three parts this is 1 part
2 part and three part
so what is the angle that this obtained
here that would be given by 360 divided
by 3 that is equal to 120 degree so let
us rotate it in the clockwise direction
by 120 degree so what do we get we get
this position if we further rotated by
120 degree in the clockwise direction we
get this and for the rotation of 120
degrees in the clockwise direction we
get this so basically in one complete
rotation we get three identical images
therefore the order of symmetry would be
three so I hope that you are getting the
concept of finding out the order of
rotational symmetry this is a very
important concept and a lot of students
get confused with rotational symmetry so
please pay attention and try to solve
more and more questions thank you please
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