Introduction to Practical Geometry Video Lecture | Mathematics Olympiad Class 7

hello friends this video on practical
geometry part 1 is brought to you by
exam for calm no more fear from exam
topics to be covered in this lesson our
introduction construct parallel lines
construct triangles wherein we look at
all the criteria that is sss criteria as
a is criteria a is a criteria and RHS
criteria practical geometry so here we
will look at the practical part of
geometry so in geometry we learn about
different shapes so we learn about
circles triangles rectangles lines line
segments so that's all those are the
things that come under geometry so here
we will get the practical aspect of
geometry that is will be learned how to
draw these different shapes now if I ask
let me give you a very simple task now
you all know what are lines you all know
what are parallel lines so two lines
which never meet each other they are
parallel lines now let's say that I
asked you to draw two lines which are
parallel to each other look so you need
to draw two lines which are exactly
parallel to each other that means they
should the distance between the two
lines should remain the same throughout
let's say you draw one line like this
and now you have to draw another line
which is parallel to this line now you
draw another line as well but what
happens is once you have drawn this line
how will you be sure whether the line is
exactly parallel to the given line or
not because you see you tend to make
slight modifications know sometimes
tilting it down sometime tilting it up
just to ensure when it is it exactly
parallel so the main question here is
how can I be sure that the line is
parallel so I can definitely draw two
lines but sometimes the difference
between the two lines
such that they look like parallel but
they are not actually parallel so what
can be done so for that we will learn
how systematically we can draw two
parallel lines or how we can draw a line
parallel to a given line so now we will
follow a certain process a certain
system and we will make sure that the
line that we draw is exactly parallel to
a given line so what are we waiting for
let us quickly get started so you would
need a couple of things to do
constructions so the first thing is a
ruler a pencil a compass so these are
the three things which are like
mandatory to do these constructions
without these you can order them so once
you have all of these let's get started
so how do we draw parallel lines let's
see what do you see on the screen right
now you see a line now we have to draw a
line parallel to this line so how are we
going to proceed about it so we will
look at it step by step so this is your
given line so the first thing that you
need to do is you mark
any point a on the given line so let us
see that let's name this given line let
us say that this line is n this is the
name of this line now we have marked any
point a on this line and we have also
identified a point B outside the line so
this B can here it could have been here
it could have been it anywhere basically
so you just mark a point B outside the
line so why are we marking this point B
because we will draw a line here which
would be parallel to L so we are
basically going to draw a line such that
B is a point on that line now the way a
is a point on the line L similarly B
would be a point on that line which
would be parallel to n so that is the
only purpose of considering this point B
so you have considered these two points
a on the line at
outside the line the next step you join
these two points that is you join a and
B perfect now what do we do in the next
step so here we are going to measure the
angles now is anything coming to your
mind is is there any concept that is
coming to your mind related to parallel
lines how do we know that two lines are
parallel what are the properties of two
parallel lines now we know that for two
parallel lines they're alternate angles
are equal their corresponding angles are
equal right so these are the properties
of parallel lines so we will make use of
those properties to draw a parallel line
so what are we trying to do here is so
what we have basically done here is we
have considered a as the center taking a
as center we have drawn an arc like this
similarly taking B as Center we have
drawn an arc like this now we have made
sure that we have kept the same radius
like you have kept the needle of the
compass here and you have drawn this arc
now keep this compass in the same
position take it here keep the needle
here and then draw this art so that's
how you draw the spine then what do you
do next now you take the compass and
measure this angle so how will you
measure this angle you keep one end of
the compass River and the other end of
the pencil here so that's how you
measure this angle now once you have
measure this angle what are you going to
do now you need to make sure that the or
interior alternate angles are equal so
if we want to draw a line somewhere here
then this angle and this angle they
would be inter interior alternate angles
so what do I do the same measurement we
do not alter the position of the compass
we keep it in the same position place it
here so one point is here and wherever
the other point is we mark that point so
we have marked this point as H hey now
what we do all we need to do is we just
join point B
and eight and we draw a straight line so
this line M is now parallel to L y is M
parallel to L that's because let's let
us call this as angle one and this as
angle - that's because angle one is
equal to angle 2 which is nothing but
alternate interior angles so how did we
construct two parallel lines we
basically made sure that the alternate
angles are equal
now you can do the same thing to make
corresponding angles equal maybe you
could have measured this angle like the
same way we did now and then you could
have ensured that this angle is equal
like let's say if you would have drawn
this line like this then you could have
also done something like this that this
angle and this angle they are equal so
that that's also another possibility so
basically this is the process that we
follow to ensure that the line we draw
that is the line M is exactly parallel
to line L so I hope the concept is clear
that how do we draw parallel lines by
ensuring that the alternate angles are
equal or the corresponding angles are
equal so we chose the alternate angles
to be equal thank you please visit exam
fee or comm for free quality education
you can learn with a simple four-step
learning process wherein you can watch
video lessons you can ask your questions
you can refer notes and you can take a
free online test we have content for
class 6 to 12 on physics chemistry
mathematics and biology along with
practical videos so please subscribe to
our channel for daily updates thank you