L13 : Example of Rotational Symmetry - Symmetry, Mathematics, CBSE Class 7 Video Lecture

hello friends this video on symmetry
part 13 is brought to you by exam for
calm no more fear from exam now let us
find orders of rotational symmetry for a
few examples so we first take the
example of B so we saw that in case of B
as we rotated it clockwise by 90 degree
it came to this position
when we further rotated it clockwise 90
degrees it came to this position on
further rotation of 90 degrees in
clockwise direction it came to this
position and again on further rotation
it came back to the original position so
that means between zero degree and 360
degree how many identical position it
came across this is the only identical
position so that means the order of
symmetry in this case is 1
let's take the example of this cross
this example also we had taken before so
this is the original position
let us rotate it by 90 degree in the
clockwise direction so we come to this
position it is again rotated in the
clockwise direction by 90 degree and we
arrive at this position when you further
rotate it by 90 degrees you arrive at
this position and on further rotation of
90 degree you come back to the same
position so basically you see now you
have completed 360 degree so in one
complete cycle
how many identical positions you have to
this is 1 and this is 2 so you have a
total of two identical positions so the
order of symmetry would be 2 so now that
we have learnt about both lines symmetry
and rotational symmetry let us speak of
certain shapes and analyze if that shape
pizzelles line symmetry or rotational
symmetry or can we even come across a
situation where the shape has both lines
rotational symmetry so let us pick up a
few alphabets so let's pick up the
alphabet T so what do you think let's
first talk about line symmetry what kind
of line symmetry T has T has a vertical
line of symmetry something like this if
you draw a line here so this acts as a
line of symmetry right so T has vertical
line of symmetry do you think it has
horizontal line of symmetry not really
because horizontally no matter from
wherever you try to divide it into two
equal halves you will not get that so T
only has vertical line of symmetry now
let us talk about the rotation what
happens when you rotate T so this is the
original position now let us rotate it
by 90 degrees in the clockwise direction
so it would be somewhat like this if we
further rotate it by 90 degrees in the
clockwise direction it would be somewhat
like this further rotation by 90 degree
it would be like this and on further
rotation by 90 degree it would reach
back to the original position so what do
we see that in one complete rotation
between zero degree and 360 degree how
many identical positions exist only one
identical position so there is no other
position which is exactly identical to
the original position so if you talk
about its degree of rotational symmetry
so the degree is one perfect ok now let
us look at another alphabet M so in case
of M also if you talk about line
symmetry this also has a vertical line
of symmetry so M also has vertical line
of symmetry let us talk about rotation
so this is M when you rotate it by 90
degrees it becomes like this if you
further rotate it by 90 degree it
becomes like a W when you further rotate
by 90 degree it becomes like
this on further rotation by 90 degree it
comes back to the original position so
in this case also there is just one
position that is the original position
which is identical to itself there is no
other position which is identical so in
this case also the degree of rotational
symmetry is one let us look at the
alphabet s so if you talk about the line
of symmetry you see that there exists no
line of symmetry so line symmetry
doesn't exist in s you try drawing the
line here or here or anywhere you will
never see getting divided into two equal
halves but when you talk about rotation
this is s when you rotate it by 90
degree it becomes like this when you
further rotate it by 90 degree it
becomes like this on further rotation by
90 degree it becomes like this and on
further rotation by 90 degree it comes
back to the original so between zero
degree and 360 degree we come across two
identical positions this and this
so therefore the order of rotational
symmetry for s is two so s possess
rotational symmetry but no lines
symmetry but if you talk about P or em
they possess line symmetry but no
rotational symmetry because all objects
possess rotational symmetry of degree
one that basically means that they do
not have any identical positions between
0 and 360 degree let us look at the
letter O
how about o if you talk about its line
symmetry you see that there exists a
vertical line of symmetry there also
exists of horizontal line of symmetry so
it has both horizontal and vertical line
of symmetry
now what about rotation so this is o so
if you rotate it by 90 degree it becomes
like this if you further rotate by 90
degree it becomes like this further
rotate by 90
comes this and it comes back to this so
if you look at identical position there
are two identical position therefore the
order of rotational symmetry is two
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