Examples: Construction of Circle, Line Segment, Perpendicular Bisectors Video Lecture - Class 6

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let's try this one
draw a line segment of length twelve
point eight centimeters using compass
divided into four equal parts verify by
actual measurement okay so first let's
draw a line segment of length twelve
point eight centimeters using a ruler so
let's see this is the line segment of
the desired length okay now we have to
divide it into four equal parts so let's
say that this is a B now just a rough
sketch here so if this is a B and you
want to divide it into four equal parts
how will you do that so what we can do
is first let's draw a perpendicular
bisector so what being the perpendicular
bisector do it will be perpendicular to
a B and it will also divide a B into two
equal parts so let's say it properly
intersects a B at Point C such that AC
is equal to CD so you have divided a B
into two equal parts but how many parts
do you want to divide it four equal
parts so for that what you can do is
again draw a perpendicular bisector of
AC so you can draw a perpendicular
bisector of AC so this will divide AC
into two equal parts such that ad is
equal to BC similarly you draw a
perpendicular bisector of BC like this
such that C E is equal to EB so now if
you look at the line segment ad it is
divided into four equal parts that is ad
DC c e and E so we are going to do the
same thing here so even though it might
sound complex but it is very simple you
just need to remember the steps to draw
perpendicular bisector so let's start so
let's draw a perpendicular bisector of a
B so you consider a as the center and
radius slightly
then half a B so half the length of a B
is suppose this this so you slightly
take more radius and then draw a circle
like this similarly consider B has the
center slightly more radius than half
the length of a B draw us another circle
now these two circles they intersect at
these two points this point at this
point so join these two points and what
do you see you see that this point
passes through the center of the circle
so this point is C so C is the midpoint
of a therefore you can say a C is equal
to C me perfect now let's draw a
perpendicular bisector of easy so for
that again what we will do take compass
he has the centered radius slightly
greater than midpoint of AC that means
if this is the midpoint so slightly more
than that draw a circle
similarly considering C has the center
radio slightly greater than half the
length of easy draw down the circles and
these two circles again they intersect
at these two points so chopped join
these two points so you get
perpendicular bisector of AC so this is
our point D so from this we can say ad
is equal to BC in a similar fashion
let's draw a perpendicular bisector of
BC so it's C as the center radius
slightly greater than half BC draw a
circle again with B as Center radius
slightly greater than half BC draw
another circle these two circles they
intersect each other at these two points
join these two points so if this point
is e such that C E is equal to EB
therefore we can say that ad is equal to
BC is equal to C E is equal to B e so we
have successfully divided the line
segment a-b into four equal parts so if
you want
how will you verify this measurement by
using the rule and take a ruler measure
each part separately and you would see
that all of your measurements would be
equal let's look at this one
draw a B of length seven point three
centimeters and find its axis of
symmetry so what exactly is axis of
symmetry for a line segment
now axis of symmetry is that line along
which if you divide the entire line
segment into two halves the two halves
would be identical and they would be
mirror images of each other that is they
would cover each other complete even
overlap so that is the axis of symmetry
so this very clearly proves that an axis
of symmetry has to divide the line
segment into two equal halves let's say
that you have a line segment of length
seven point three centimeters so this is
a B of length seven point three
centimeters so what could be that line
which would divide a B into two equal
halves
such that the two equal halves would
exactly cover each other when folded so
what could be the client absolutely that
could be nothing but the perpendicular
bisector because perpendicular bisector
bisects the line that means it divides
the line into two equal halves so let's
draw the perpendicular bisectors same
process again ere Center radius slightly
greater than half a B draw a circle be a
center radius slightly greater than half
a B draw a circle point where the two
circles intersect join those two points
together so you get a line which is a
perpendicular bisector line this lines
also the axis of symmetry form the line
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