EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadrilaterals
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Name all quadrilaterals whose diagonals are perpendicular and bisect each other
(i)
rectangle,rhombus
(ii)
square,parallelogram
(iii)
square,rhombus
(iv)
square,kite
(v)
parallelogram,square,rhombus,rectangle
Question
2
2.
Which of the following statements are true?
a)
Every rhombus is a parallelogram
b)
Every rectangle is a parallelogram
c)
Every rectangle is a rhombus
d)
Every square is a rectangle
e)
Every square is a rhombus
f)
Every parallelogram is a trapezium
g)
Every parallelogram is a rectangle
(i)
{c,e,f}
(ii)
{g,b}
(iii)
{c,g,d}
(iv)
{c,a}
(v)
{a,b,d,e,f}
Question
3
3.
In the given figure, ABCD is a parallelogram such that R is the mid-point of AB and AB = 2DA. Find ∠DRC
(i)
92°
(ii)
91°
(iii)
89°
(iv)
90°
(v)
88°
Question
4
4.
Name all quadrilaterals whose all sides are equal
(i)
parallelogram,square,rhombus,rectangle
(ii)
square,rhombus
(iii)
rectangle,rhombus
(iv)
square,rectangle
(v)
square,kite
Question
5
5.
In the adjoining figure, equilateral △NMO surmounts square KLMN. If MOL = x°, find the value of x.
(i)
14°
(ii)
13°
(iii)
16°
(iv)
17°
(v)
15°
Question
6
6.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 36.68°
,
∠OMN = 23.79°
,
∠PQO = 113.69°
. Calculate
∠NOM
(i)
35.68°
(ii)
38.68°
(iii)
34.68°
(iv)
37.68°
(v)
36.68°
Question
7
7.
In the given figure,
OPQR
is a rectangle whose diagonals intersect at
S
.
Diagonal
OQ
is produced to
T
and
∠POT =
130.24°
. Find the angles of
△SQR
.
(i)
S
=
80.48°
,
Q
=
49.76°
,
R
=
49.76°
(ii)
S
=
78.48°
,
Q
=
49.76°
,
R
=
51.76°
(iii)
S
=
80.48°
,
Q
=
47.76°
,
R
=
51.76°
(iv)
S
=
82.48°
,
Q
=
49.76°
,
R
=
47.76°
(v)
S
=
78.48°
,
Q
=
51.76°
,
R
=
49.76°
Question
8
8.
In kite
FGHI
,
FH
and
GI
are diagonals. Then
∠IFJ
=
(i)
∠JHI
(ii)
∠JHG
(iii)
∠FJI
(iv)
∠IJH
(v)
∠GFJ
Question
9
9.
Which of the following properties apply for a kite ?
(i)
All Adjacent sides are equal
(ii)
Adjacent angles are equal
(iii)
Diagonals are perpendicular
(iv)
Opposite sides are equal
(v)
Opposite angles are parallel
Question
10
10.
The angles of the quadrilateral are
(i)
∠H , ∠I , ∠J , ∠M
(ii)
∠H , ∠I , ∠J , ∠K
(iii)
∠H , ∠I , ∠J , ∠L
(iv)
∠H , ∠I , ∠K , ∠L
(v)
∠H , ∠I , ∠K , ∠M
Question
11
11.
If one of the angles of a rhombus is a right angle, it is a
(i)
None of these
(ii)
parallelogram
(iii)
rectangle
(iv)
trapezium
(v)
square
Question
12
12.
In parallelogram
PQRS
,
diagonals
QS
and
PR
intersect at
T
. Then
PQ
∥
(i)
SP
(ii)
QS
(iii)
PR
(iv)
RS
(v)
QR
Question
13
13.
In the adjoining figure, side EF of parallelogram CDEF has been produced to G. If ∠DEG = 131.27° , find the measure of each angle of the parallelogram.
(i)
C
=
47.73°
,
D
=
129.27°
,
E
=
49.73°
,
F
=
133.27°
(ii)
C
=
50.73°
,
D
=
130.27°
,
E
=
46.73°
,
F
=
132.27°
(iii)
C
=
46.73°
,
D
=
133.27°
,
E
=
47.73°
,
F
=
132.27°
(iv)
C
=
49.73°
,
D
=
130.27°
,
E
=
50.73°
,
F
=
129.27°
(v)
C
=
48.73°
,
D
=
131.27°
,
E
=
48.73°
,
F
=
131.27°
Question
14
14.
In rhombus
BCDE
, diagonals
BD
and
CE
intersect at
F
. Then
△BCD
≅
(i)
△DEB
(ii)
△CDE
(iii)
△FBC
(iv)
△EBC
Question
15
15.
In rhombus
ABCD
, diagonals
AC
and
BD
intersect at
E
. Then
∠EDA
≠
(i)
∠ABE
(ii)
∠DEC
(iii)
∠EBC
(iv)
∠CDE
Question
16
16.
In rhombus
JKLM
, diagonals
JL
and
KM
intersect at
N
. Then
∠JKL
=
(i)
∠LMJ
(ii)
∠MJK
(iii)
∠JKN
(iv)
∠KLM
Question
17
17.
Two adjacent angles of a parallelogram PQRS are in the ratio 3 : 7. Find the measure of each of its angles.
(i)
P
=
52°
,
Q
=
128°
,
R
=
53°
,
S
=
127°
(ii)
P
=
54°
,
Q
=
126°
,
R
=
54°
,
S
=
126°
(iii)
P
=
55°
,
Q
=
125°
,
R
=
56°
,
S
=
124°
(iv)
P
=
53°
,
Q
=
124°
,
R
=
55°
,
S
=
128°
(v)
P
=
56°
,
Q
=
125°
,
R
=
52°
,
S
=
127°
Question
18
18.
In rhombus
NOPQ
, diagonals
NP
and
OQ
intersect at
R
. Then
∠ROP
≠
(i)
∠NOR
(ii)
∠PQR
(iii)
∠RQN
(iv)
∠QRP
Question
19
19.
A quadrilateral has three acute angles, each measuring 79°. What is the measure of its fourth angle?
(i)
122.00°
(ii)
125.00°
(iii)
121.00°
(iv)
123.00°
(v)
124.00°
Question
20
20.
In rhombus
BCDE
, diagonals
BD
and
CE
intersect at
F
. Then
△FBC
≇
(i)
△FDC
(ii)
△FDE
(iii)
△FBE
(iv)
△EBC
Question
21
21.
Which of the following properties apply for a rhombus ?
a)
Diagonals bisect each other
b)
Diagonals are equal
c)
Adjacent angles are equal
d)
Adjacent sides are equal
e)
Opposite angles are equal
f)
Opposite sides are parallel
g)
Opposite sides are equal
(i)
{b,f,g}
(ii)
{b,c,e}
(iii)
{b,a}
(iv)
{c,d}
(v)
{a,d,e,f,g}
Question
22
22.
Two adjacent angles of a parallelogram are in the ratio
12 : 18
.
Find the measure of each of its angles.
(i)
A
=
74°
,
B
=
107°
,
C
=
70°
,
D
=
109°
(ii)
A
=
70°
,
B
=
110°
,
C
=
71°
,
D
=
109°
(iii)
A
=
72°
,
B
=
108°
,
C
=
72°
,
D
=
108°
(iv)
A
=
71°
,
B
=
106°
,
C
=
73°
,
D
=
110°
(v)
A
=
73°
,
B
=
107°
,
C
=
74°
,
D
=
106°
Question
23
23.
The angles of a quadrilateral EFGH are in the ratio 5 : 4 : 11 : 20. Find the measure of each angle of the quadrilateral.
(i)
E
=
43°
,
F
=
38°
,
G
=
98°
,
H
=
181°
(ii)
E
=
46°
,
F
=
35°
,
G
=
101°
,
H
=
178°
(iii)
E
=
44°
,
F
=
34°
,
G
=
100°
,
H
=
182°
(iv)
E
=
45°
,
F
=
36°
,
G
=
99°
,
H
=
180°
(v)
E
=
47°
,
F
=
35°
,
G
=
97°
,
H
=
181°
Question
24
24.
In rhombus
CDEF
, diagonals
CE
and
DF
intersect at
G
. Then
∠FCG
≠
(i)
∠GCD
(ii)
∠DEG
(iii)
∠GEF
(iv)
∠CGF
Question
25
25.
In rhombus
OPQR
, diagonals
OQ
and
PR
intersect at
S
. Then
△SQP
≇
(i)
△SOP
(ii)
△SQR
(iii)
△SOR
(iv)
△ROP
Assignment Key
1) (iii)
2) (v)
3) (iv)
4) (ii)
5) (v)
6) (v)
7) (i)
8) (v)
9) (iii)
10) (ii)
11) (v)
12) (iv)
13) (v)
14) (i)
15) (ii)
16) (i)
17) (ii)
18) (iv)
19) (iv)
20) (iv)
21) (v)
22) (iii)
23) (iv)
24) (iv)
25) (iv)
