Examples: Line and Rotational symmetry Video Lecture | Mathematics (Maths) Class 7 (Old NCERT)

hello friends this video on symmetry
part 15 is brought to you by example
comm no more fear from exam symmetry if
a figure has two or more lines of
symmetry should it have rotational
symmetry of order more than one well
this is a must that if a figure has
multiple lines of symmetry then it
should be of rotational symmetry of
order more than one so let us take a few
examples let us consider the alphabet o
so this was an example where we saw that
it had multiple lines of symmetry you
remember it had a horizontal line of
symmetry as well as a vertical line of
symmetry basically this is the
horizontal is the vertical so it has two
lines of symmetry and what is its
rotational symmetry if you calculate its
rotational symmetry you see that it has
a rotational the order of its rotational
symmetry is 2 and how many lines of
symmetry had it has two lines of
symmetry it is steep the example of the
letter M so here you see that how many
lines of symmetry it has it has one line
of symmetry and in this case what is its
rotational order so the order of its
rotational symmetry is also one so that
that's how it is proving that if you
have one line of symmetry you have
rotational order also one but the moment
you have more than one line of symmetry
the rotational order of symmetry is also
more than one let's take another example
of an equilateral triangle so in an
equilateral triangle we have learned
that they have three lines of symmetry
in equilateral triangle is a regular
polygon with three sides and number of
sides is equal to the number of lines of
symmetry so it has three lines of
symmetry what about its rotational order
of symmetry if you calculate its
rotational order that is also three so
this proves that whenever you have
multiple lines of symmetry then their
rotational order of symmetry is also
more than one now here I have not
calculated the rotational order of each
if you want you can draw the diagrams by
showing how it
dates and you'll be able to find out
their rotational order question number
four name the quadrilaterals which have
both line and rotational symmetry of
order more than one so let us first find
out the quadrilaterals with line
symmetry multiple lines of symmetry so
one such example would be a square
because Square has all sides equals it
is a regular polygon therefore it has
multiple lines of symmetry so how many
lines of symmetry does a square have
lines of symmetry is four and what is
the order of rotational symmetry the
order of rotational symmetry is on so
forth so if you want you to do it and
see it for yourself the other
quadrilateral would be a rectangle so in
rectangle the lines of symmetry is two
and the order of symmetry is also two so
let me quickly tell you how it the order
of symmetry in case of a square is four
so this is the square right so when you
rotate it by 90 degree you again get the
same thing you further rotate it 90
degree you again get the same thing if
any further rotate by 90 degree the same
thing so in this way how many times you
get identical identical squares you get
four times therefore the order is four
whereas in case of rectangle this is the
original man when rotated by 90 degree
you get this when further rotated by 90
degree you get this when further rotated
by 90 degree you get this so how many
identical images you get two identical
images therefore the order of symmetry
for a rectangle is to question number
five after rotating by sixty degree
about the center a figure looks exactly
the same as its original position at
what are the angles will this happen
quarter figure
so let us take an example of a figure
which when rotated by sixty degree it
reaches a point where it is identical to
its original position so I have taken
example of one of the images that we
have discussed in the last few slides so
for this image when we rotate it by 60
degree what happens we see that we
reject a image which is exactly
identical to the original image so when
we further rotate it by another 60
degree so this another 60 degree is
basically 60 plus 60 that is 120 degree
so after 120 degree again you will see
the same image again if you rotate it
for another 60 degree which is 120 plus
60 that is 180 degrees so after 180
degree or so you will get the same image
again if you rotate by another 60 degree
which is 180 plus 660 which is 240
degree so you get the same thing in a
similar way
240 plus 60 that would be 300 so
actually hundred also you will get the
same image and finally after 360 degree
you get back to the original image so
basically at what all angles this
reputation will happen so this
repetition will happen first at 60
degree then at 120 degree then at 180
degree and then at 240 degree then at
300 degrees and finally at 360 degrees
so it will happen at multiples of
sixties so this is one example of such a
figure if you want more examples you can
consider the example of a regular
hexagon so I am getting someone is
somewhat like this which has six equal
sides so just try out to try to find out
the rotational symmetry for a regular
hexagon so there also you will observe a
similar pattern so with this we have
reached towards the end of this lesson
on symmetry and I hope that the concept
of symmetry is clear please focus more
on the rotational symmetry part because
a lot of students have confusion about
that
so all more and more problems and gain
confidence I hope this lesson would have
helped you see you all in the next
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