What is Reflection Symmetry? Video Lecture | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET

hello friends this video on symmetry
path 11 is brought to you by exam for
calm no more fear from exam now there is
a very close relationship between
symmetry and reflection so what comes to
your mind when you think of reflection
we stand in front of a mirror so I'm
sure all of you stand in front before
main eventing get ready and what do you
see you could see yourself other better
so how are you able to see yourself on
the better this is possible because of
the reflection of light you would have
observed that you can see yourself in
the mirror
only in presence of light so if you
switch off the light in the room even if
you stand in front of the mirror you'll
not be able to see yourself so this
happens due to reflection okay the
Deuter reflection of light what happens
you can see yourself in the mirror and
you see yourself exactly the same as you
actually are for example when you stand
in front of the plane mirror which you
call your dressing mirror your size or
your shape doesn't change you are highly
torn everything here your appearance
remains the same but have you noticed
any difference between you and your
image which you see on the mirror so
have you ever observed any difference if
you have observed that that's perfectly
fine if you haven't observed try this
out next time when you stand in front
the familiar just raise your left hand I
am going to you see on the middle on the
middle it appears as if you have reached
your right hand even though you have
used your left hand for example on this
on the screen in the image you see that
this girl she has raised her left hand
from our perspective if we consider that
this girl is me so then the girl has
raised
but when you look at the middle it seems
as if she has reached her right hand
so what happens is when you would stand
in front of a middle right becomes left
and left becomes right everything else
remains identical but it ensures that
everything get Latin and this is what we
call this lateral inversion that is
right becomes left left it becomes like
even though nothing changes everything
remains as it is it ensures that the
image is laterally inverted when
compared to the object so that is one
speciality of your million image now how
the symmetry and reflection related so
they are related because of this concept
so let's see now when we talk about line
symmetry we basically say that line
symmetry mean there will exist a line
which would divide that object into two
equal halves such that the two halves
will overlap each other so there is
another way of telling the same thing so
we can also say that a shape has line
symmetry if one half of it is the middle
image of the other half that's
interesting right let's take this
example so these are some examples from
nature so they naturally exist like if
you look at the trees if you if you
visit a river or a lake or a pond and
you look at the trees you see that how
much is the actually so these are the
actual trees right but what does this
this is nothing but the mirror image of
the trees so this is the real tree and
this is the real image right but when
you look at when you when you look at
the overall picture you see that the all
that which was part of the bottom of the
tree is on the top in the image so you
look at the image the image in the image
this portion is on the top and this
portion is at the bottom but in reality
this portion is on the top and this
portion is at the bottom and that is
what we call as lateral inversion
similarly in case of this duck you see
the faces on the top and in the image
the faces of the bottom so that is the
inversion which we are
talking about so many images are all
being slide please so even though the
mirror images are exactly identical but
what happens is if you now imagine that
let's say that this duct is a painting
on a sheet of paper so if you imagine
this line and if you think that way let
me fold the paper along this line so
what would happen these two halves would
exactly overlap each other and that
that's how we can say that this line is
a line of symmetry okay so if we
consider this overall thing as one
object then we can say that this line
acts as a line of symmetry so this
basically tells us that tell now we have
been telling that there exists a line
which divides the image into two equal
halves so those two equal halves are
just like the middle images which are
exactly identical but they are laterally
important that is why when you fold them
they exactly over that each other so
let's take the example of the butterfly
so I have already told you before that a
butterfly has a symmetry so it is like
this lets you take a picture of a
butterfly on a sheet of paper
you draw the line of symmetry fold it
you see that the two halves exactly
overlap each other which proves then
that that vertical line is the length of
symmetry now you do this thing you keep
that sheet of paper with the picture of
butterfly on the table please
a mirror like this exactly along the
line of symmetry so this is your line of
symmetry so exactly along this line you
place the mirror observe the mirror
image that you see so you would see that
the middle image will will actually be
the other half of the butterfly so you
are just looking at one half of the
butterfly and the mirror image of that
one half of the butterfly is nothing but
exactly identical to the other half of
the butterfly so this shows that the
lines of symmetry actually divides the
entire object into two equal halves such
that the two halves are mirror images of
each other so this is the best way to
understand this now I would urge you to
do this on your own so that you know you
can
for yourself that okay this happens all
you need to do is take a picture of a
butterfly on a sheet of paper take a
mirror place the mirror along the line
of symmetry and you would be able to see
the mirror image of one half of the
butterfly is nothing but the other half
of the butterfly which shows that the
two halves of the butterfly and mirror
images of each other so this type of
symmetry is nothing but reflection
symmetry because it is a symmetry where
we see that one half is mirror image of
the other half so whenever we talk about
mirror image Villard images happen due
to reflection so this type of symmetry
is also referred to as a reflection
symmetry and that is why we see that
line symmetry and reflection symmetry
have a very close relation thank you
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