When 2 Diagonals and 3 Sides are Given Video Lecture - Class 8

hello friends this video on practical
geometry part 3 is brought to you by
exam viacom no more fear from exam so
let us now look at time 2 that is
another type where we would construct a
quadrilateral but this time not all the
sides would be given something else will
be given
so here the quadrilateral with three
sides and two diagonals so instead of
one diagonal now we will know both the
diagonals but this time we will not know
all the four sides we will just know
three sides so let's see in this case
how do we go about it so let's say that
you have to construct the quadrilateral
g o LD such that Oh L is equal to 7
point 5 centimeters GL is equal to 6
centimeters G D is equal to 6
centimeters LD is equal to 5 centimeters
and OD is equal to 10 centimeters so
these are the lengths that are given so
for that let us first try to do a rough
sketch so this is how the rough sketch
could be so let us say this is G o L D
so here Oh L is given so this oh L is
given a 7.5 G n G L is nothing but the
diagonal so G L is given as 6 g D that
is this length is given as 6 again LD LD
is this length which is given as 5 and
OD which is again the diagonal is given
as 10 so both the diagonals are given
and three sides are given so a G is the
site which is not mentioned so in this
case how do we go about it so here also
we will draw one of the diagonals first
so which diagonal will be drawn so we
can draw as such any diagonal so here we
have drawn the diagonal OD first so
first we draw a line segment of length
OD which is equal to 10 cent
so once we have drawn OD let us try to
find out this point in because this is
the triangle so if you look at it in
triangle ODL we know the values of all
the three sides so one we have already
drawn that is OD so we know olv also
know BN so let us first try to draw this
triangle so at from point O we draw an
arc at a distance of seven point five
centimeters similarly from point D we
draw an arc at a distance of five
centimeters and then we see that these
two arcs they meet at a point so we
joined this point from O as well as D so
that's how we are able to construct one
part one half of the quadrilateral is
almost done so now let's try to do it
for the other side so now we do not know
the length of this side but we know this
length which is 6 and we also know this
length which is 6 so what we would do is
we would keep our centre at point L and
then we will draw an arc using and come
using a compass at a distance of 6
centimeters at a distance of 6
centimeters from L we draw an arc
similarly at a distance of 6 centimeters
from D we draw another arc and we would
see that this are two arcs they need at
a point at this point from this point
you join these two lines so basically
what is this point look at the rough
sketch and try to find out what is this
point this point is nothing but Point G
so now you have found out G you already
knew oh so what you need to do is just
join G and O so what do you get this is
nothing but the quadrilateral gol D so
you see whenever you are given both the
diagonals and three sides there also
your first approach would be to draw one
diagonal and then draw one triangle or
which you know all the three sides so
once you have drawn one triangle then
your task becomes comparatively easier
so then in that case you can take the
help
the second diagonal and the third side
to draw the fourth side so let us have a
quick recap
so in these kind of problems we first
draw one of the diagonals then we draw
one of the triangles using the SSS
construction condition now in order to
draw a triangle by SSS construction
condition it is important that the
measurement of all the sides of the
triangle are given draw an arc from
point L to locate the point G because
now we know the measurement of this
diagonal draw another arc from point B
to locate the point G so this is how we
will locate point G and finally we
joined oh gee which was the fourth side
of the quadrilateral so the result was
that we obtained gol D gold of
quadrilateral thank you please visit
exam fee or come 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