Construction of Quadrilaterals(Full Chapter): All Cases Video Lecture - Class 8

construction of quadrilaterals
in this module you will learn about the
topic construction of a quadrilateral we
know that a triangle had three sides and
three angles and to construct a triangle
we require at least three measurement
including sides and angles of a triangle
now do you think four measurements would
be sufficient to draw unique four-sided
closed figure namely a quadrilateral no
as different quadrilaterals can be
identified on the basis of their
properties of sides diagonals and angles
quadrilaterals are made up of ten parts
however to construct them
we do not need to know the measurement
of all of them in case of special
quadrilaterals like the rectangle just
two measurements the lengths of its
adjacent sides are enough to construct
now let us learn how to construct a
unique order lateral when following
measurements are given one by one
let us first learn to construct a
quadrilateral when the length of its
four sides and one diagonal are given
construct a quadrilateral e f g h where
EF is equal to 4 centimeters FG is equal
to 7 centimeters g h five centimeters eh
five point five centimeters and EG is
equal to eight centimeters let us draw
the quadrilateral step-by-step step one
let us first draw a triangle efg using
sss construction condition draw a line
segment eg equal to 8 centimeter with e
as centre and radii 4 centimeters and
gia centre and radii as seven centimeter
draw arcs to cut each other at F now
join EF and GF step 2 now we have to
locate the fourth point edge this edge
would be on the side opposite to F with
reference to eg for that we have two
measurements H is five point five
centimeters away from E and five
centimeters from G so with E as Center
draw an arc of radius 5 point 5
centimeter and G has Center draw an arc
of radius 5 centimeter such that they
intersect at a point
step 3 we know that H would be the point
of intersection of the two arcs as H
should lie on both the arcs drawn so
mark it as H and join eh and gh to form
a quadrilateral ends EFG H is the
required quadrilateral
let us learn how to construct a unique
quadrilateral when it's three sides and
two daemul
are known construct a quadrilateral be q
r s such that sides QR is equal to three
point five centimeter
PS is equal to 4 point 5 centimeter RS
is equal to 4 centimeter and the
diagonals PR is equal to four point five
centimeter and Q s equal to six
centimeter we saw that when four sides
and a diagonal were given we first drew
a triangle with the available data and
then try to locate the fourth point the
same technique is used here also let us
now construct it step by step
step 1 draw a triangle P R s using SSS
construction now
to locate queue at a distance of three
point five centimeter from our and six
centimeter from s step to draw an arc of
radius 6 centimeter with s as Center we
would get Q somewhere on the drawn arc
step 3
now draw an arc of radius 3 point 5
centimeter with our a Center we would
get Q somewhere on this drawn arc also
step 4 now Q is the point of
intersection of two arcs since Q lies on
both the arcs so mark their intersection
as Q and join P Q and R Q to complete it
as p q r s hence PQRS is the required
quadrilateral let us now learn how to
construct a unique quadrilateral when
it's two adjacent sides and three angles
are known given to construct a
quadrilateral m n o P where sides MN is
equal to 6 centimeter MP is equal to 3
centimeter angle M is equal to 80 degree
angle n is equal to 65 degree and angle
P is equal to 120 degree step 1
draw a line segment m n is equal to 6
centimeter using a ruler step 2
now draw angle m is equal to 80 degree
with the help of the protractor step 3
cut an arc on this line with M as Center
and radius 3 centimeter and mark the
point as P as we know MP is equal to 3
centimeter step 4 at n draw an angle of
65 degree with the help of the
protractor
step 5 at P draw an angle of 120 degree
with the help of a protractor
step 6 now join the arms of these angles
to meet at O hens we get the required
quadrilateral m n o P let us now learn
how to construct a quadrilateral when
it's three sides and two included angles
are known to construct a quadrilateral e
f g h where sides EF is equal to 4
centimetre FG is equal to 5 centimeter G
H is equal to 6 point 5 centimeter an
angle F is equal to 105 degree and angle
G is equal to 80 degree step 1 draw a
line segment FG equal to 5 centimeter
using a ruler now draw angle f equal to
105 degree with the help of the
protractor step 2 cut an arc on this
line with F as Center and radius 4
centimeter mark the intersecting point
as e step 3 add G draw an angle of 80
degree with the help of the protractor
now cut an arc on this line with G as
Center and radius 6 point 5 centimeter
mark the intersecting point as H join eh
and complete the quadrilateral here of
GH ends EFG H is the required
quadrilateral till now we have seen
constructing a quadrilateral using five
measurements is there any quadrilateral
which can be drawn with less number of
available measurements the following
examples are such special cases draw a
square m n o P of side 3 point 5
centimeter R here we can see that only
one measurement has been given actually
we have many more details with us
because the figure is a special
quadrilateral namely a square
we know that each of its angles is a
right angle this enables us to draw
triangle M N or using SAS condition then
P can be easily located now let us try
to draw the square with the given
measurements
now construct a rhombus ABCD where
diagonals AC is equal to four centimeter
and BD equal to five centimeter your
measurements of only two diagonals of
the rhombus are given however since it
is a rhombus we can find more help from
its properties the diagonals of a
rhombus are perpendicular bisectors of
one another so first draw a C equal to 4
centimeter and then construct its
perpendicular bisector let them meet at
O cut off to point 5 centimeter lens on
either side of the drawn bisector you
now get B nd now we can draw the rhombus
based on the method described let us
revise all that we learned in this
module on construction of quadrilaterals
you