Transcript Constructing a Quadrilateral

CONSTRUCTING
A
QUADRILATERAL
WE SHALL LEARN HOW TO
CONSTRUCT A UNIQUE
QUADRILATERAL BY FOLLOWING
METHODS :




When four sides and one diagonal are given.
When two diagonals and three sides are given.
When two adjacent sides and three angles are given.
When three sides and two included angles are given.
When other special properties are known.
CONSTRUCTING A QUADRILATERAL
WHEN FOUR SIDES AND ONE
DIAGONAL ARE GIVEN
Example : Construct a
quadrilateral PQRS
where PQ = 4cm, QR =
6cm, RS= 5cm, PS =
5.5cm and PR = 7cm
7 cm
Step 1 :Construct a triangle PQR using
SSS criterion.
7 cm
STEP 2 :WITH P AS CENTRE DRAW AN
ARC OF RADIUS 5.5 CM .
7 cm
STEP 3 :NOW, WITH R AS CENTRE DRAW AN
ARC OF RADIUS 5 CM INTERSECTING
ANOTHER ARC AT POINT S
7 cm
STEP 4 :NOW JOIN PS AND RS.
7 cm

PQRS is the required quadrilateral.
CONSTRUCTING A
QUADRILATERAL WHEN TWO
DIAGONALS AND THREE SIDES
ARE GIVEN.
D
7 cm
B
5.5cm
Example : Construct a
quadrilateral ABCD, given
that BC =4.5 cm, AD = 5.5
cm, CD = 5 cm, AC = 5.5
cm and diagonal BD = 7
cm.
C
A
STEP 1 :DRAW TRIANGLE ACD USING SSS
CRITERION
D
A
5.5 cm
C
STEP 2 :WITH D AS CENTRE DRAW AN
ARC OF RADIUS 7 CM.
D
A
5.5 cm
C
STEP 3 :NOW, WITH C AS CENTRE DRAW AN ARC
OF RADIUS 4.5 CM INTERSECTING
ANOTHER ARC AT POINT B.
D
A
5.5 cm
B
C
STEP 4 :JOIN AB, DB AND CB
D
7 cm
A
5.5 cm
B
C
ABCD is
required
triangle
CONSTRUCTING A
QUADRILATERAL WHEN TWO
ADJACENT SIDES AND THREE
ANGLES ARE KNOWN
M
Example : Construct a
quadrilate ral MIST where
MI  3.5 cm, IS  6.5 cm,
 M  75 ,  I  105  and
 S  120 
120 
T
I
105 
75 
S
Step 1 : Draw a line MI  3.5 cm
and make an  MIX  105  .
X
105 
M
3.5 cm
I
Step 2 : Measure
IX  6 . 5 and
name that point S. Now make
 ISY  120  .
Y
X
120 
105 
M
3.5 cm
I
S
Step 3 : Now make  IMZ  75 
Z
Y
X
120 
75 
M
3.5 cm
105 
I
S
STEP 4 :MARK THAT POINT T WHERE SY AND MZ
MEET.
Z
Y
T
X
120 
75 
M
3.5 cm
105 
I
S
MIST is the
required
Quadrilateral.
CONSTRUCTING A
QUADRILATERAL WHEN
THREE SIDES AND TWO
INCLUDED DIAGONALS ARE
GIVEN.
Example : - Construct a
D
Quadrilate
C
ral ABCD, where
AB  4 cm, Bc  5 cm,
CD  6.5 cm,  B  105 
and  C  80  .
A
4 cm
B
Step 1 : Draw a line BC  5 cm
and Draw an  of 105 
along BX.
X
105 
B
5 cm
C
Step 2 : Measure BX  4 cm and
name that point A.
X
A
105 
B
5 cm
C
Step 3 : Now make
 BCY  80 
Y
X
105 
B
5 cm
80 
C
Step 4 : Now, with C as centre,
Draw an arc of length 6.5 cm
that cuts CY at point D.
Y
D
X
105 
B
5 cm
80 
C
Step5 : Join AD
Y
X
D
105 
B
5 cm
ABCD
is the required
Quadrilateral.
80 
C
CONSTRUCTING A
QUADRILATERAL WHEN
OTHER SPECIAL PROPERTIES
ARE KNOWN.
Some examples are :1. Draw a square of side 5 cm.
2. Construct a rhombus ABCD where AC =
6 cm, and BD = 7 cm.
EXAMPLE 1 :DRAW AN SQUARE ABCD OF
Initially 5
it appears
that
4.5 cm
SIDE
CM.
D
only one measurements
90 
90 
4.5 cm
4.5 cm
has been given. Actually
we have many more
details with us, because
the figure is special
quadrilateral namely a
square. We know that
each of its angles is a
Right angle.
C
90 
A
90 
4.5 cm
B
Rhombus are Perpendicular
bisectors of one another.
So, first we draw AC = 7
cm and construct its perpendicular
bisector. Let them meet at O. cut off
3 cm lengths on either side of the
drawn bisector . You get now B and
D.
A
6 cm
XAMPLE 2 :CONSTRUCT A RHOMBUS ABCD
WHERE
AC = of6 CM, AND BD = 7D CM.
As we
know the diagonals
O
7 cm
B
C