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Constructing a Quadrilateral. 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. - PowerPoint PPT Presentation
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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
4 cm6 cm
5.5 cm 5 cm
S
R
Q
P
4 cm6 cm
RP
Step 1 :-Construct a triangle PQR using
SSS criterion.
7 cm
Q
STEP 2 :-WITH P AS CENTRE DRAW AN ARC OF RADIUS 5.5 CM .
4 cm6 cm
RP7 cm
Q
STEP 3 :-NOW, WITH R AS CENTRE DRAW AN ARC OF RADIUS 5 CM INTERSECTING ANOTHER ARC AT POINT S
4 cm6 cm
RP7 cm
Q
S
STEP 4 :-NOW JOIN PS AND RS.
PQRS is the required quadrilateral.
4 cm6 cm
S
P7 cm
Q
R
CONSTRUCTING A QUADRILATERAL WHEN TWO DIAGONALS AND THREE SIDES ARE GIVEN.
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
D
A
B7 cm5 cm
5.5 cm
5.5c
m
4.5 cm
STEP 1 :-DRAW TRIANGLE ACD USING SSS CRITERION
C
D
A5.5 cm
5 cm5.5 cm
STEP 2 :-WITH D AS CENTRE DRAW AN ARC OF RADIUS 7 CM.
C
D
A5.5 cm
5 cm5.5 cm
STEP 3 :-NOW, WITH C AS CENTRE DRAW AN ARC OF RADIUS 4.5 CM INTERSECTING ANOTHER ARC AT POINT B.
C
D
A5.5 cm
5 cm5.5 cm
B
STEP 4 :-JOIN AB, DB AND CB
C
D
A5.5 cm
5 cm5.5 cm
ABCD is required triangleB
4 cm7 cm
CONSTRUCTING A QUADRILATERAL WHEN TWO ADJACENT SIDES AND THREE ANGLES ARE KNOWN
120
120 S and 105 I ,75 M cm, 6.5 IS cm, 3.5 MI whereMIST ralquadrilate
aConstruct : Example M
T
S
I105
75
6.5 cm
3.5
cm
.105 MIXan make andcm 3.5 MI line a Draw
-: 1 Step
105
3.5 cmM I
X
.120 ISYmake Now S.point that name
and 5.6 IX Measure-: 2 Step
3.5 cm
105
M I
X120
Y
S
6.5
cm
75 IMZ make Now-: 3 Step
3.5 cm
105
M I
X
120
Y
75
Z
S
STEP 4 :-MARK THAT POINT T WHERE SY AND MZ MEET.
MIST is the required Quadrilateral.
T
3.5 cm
105
M I
X
120
Y
75
Z
S
CONSTRUCTING A QUADRILATERAL WHEN THREE SIDES AND TWO INCLUDED DIAGONALS ARE GIVEN.
.80 C and 105 B cm, 6.5 CD
cm, 5 Bc cm, 4 AB whereABCD, ralQuadrilate
aConstruct -:
Example
A B
CD
4 cm
5 cm
6.5 cm
BX. along105 of an Draw andcm 5 BC line a Draw
-: 1 Step
5 cmB C
105
X
A.point that name and cm 4 BX Measure
-: 2 Step
5 cmB C
105
X
A
4 cm
80 BCY make Now
-: 3 Step
5 cmB C
105
XY
4 cm
80
D.point at CY cutsthat cm 6.5length of arcan Draw
centre, as C with Now,-: 4 Step
5 cmB C
105
X
4 cm
80
YD
6.5 cm
ADJoin -:Step5
ABCDis the required
Quadrilateral.
5 cmB C
105
X
4 cm
80
Y
D
6.5 cm
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 SIDE 5 CM. Initially it appears
that only one measurements 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.
90
9090
4.5 cm
4.5 cm
4.5
cm
4.5 cm
90
A B
CD
EXAMPLE 2 :-CONSTRUCT A RHOMBUS ABCD WHERE AC = 6 CM, AND BD = 7 CM. As we know the diagonals of
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.
COA
B
D
7 cm
6 cm