EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Mid-Point and Intercept Theorems
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In the given figure, HIJK is a parallelogram
such that
L
and
M
are mid-points of sides
HI
&
JK
.
HM
meets
IK
at
T
and
JL
meets
IK
at
U
. Given
IK
=
16 cm
, find
TU
(i)
7.33 cm
(ii)
3.33 cm
(iii)
6.33 cm
(iv)
4.33 cm
(v)
5.33 cm
Question
2
2.
In the given figure, ABCD is a trapezium. E and F are mid-points of AD and BC.Given CD = 8 cm and AB = 18 cm, find EF
(i)
15.0 cm
(ii)
11.0 cm
(iii)
12.0 cm
(iv)
14.0 cm
(v)
13.0 cm
Question
3
3.
In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
∠HAB =
(i)
∠FDA
(ii)
∠FEH
(iii)
∠AFD
(iv)
∠HFE
(v)
∠FAC
Question
4
4.
In the given figure, points F , G and H are the mid-points of sides DE, EC and CD of △CDE. Which of the following are true?
a)
Area of
△CDE
=
1
3
area of
△FGH
b)
Area of trapezium DEGH is thrice the area of △CHG
c)
All four small triangles have equal areas
d)
Area of trapezium
DEGH
is
1
4
the area of
△CDE
e)
Area of △CDE = 4 times area of △FGH
(i)
{a,b}
(ii)
{a,d,e}
(iii)
{d,c}
(iv)
{b,c,e}
(v)
{a,b,c}
Question
5
5.
In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
∠FDA =
(i)
∠EHF
(ii)
∠DAF
(iii)
∠ABH
(iv)
∠FEH
(v)
∠ACF
Question
6
6.
In the given figure, the area of the △KLM is x sq.cm. N,O,P are the mid-points of the sides LM , MK and KL respectively. The area of the △NOP is
(i)
1
2
of area of △KLM
(ii)
3
4
of area of △KLM
(iii)
2
3
of area of △KLM
(iv)
1
3
of area of △KLM
(v)
1
4
of area of △KLM
Question
7
7.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
LJ
=
(i)
KI
(ii)
IM
(iii)
IJ
(iv)
MK
(v)
IL
Question
8
8.
In the given figure, DEFG is a parallelogram such that S is the mid-point of DE and DE = 2GD. Find ∠GSF
(i)
92°
(ii)
91°
(iii)
88°
(iv)
89°
(v)
90°
Question
9
9.
In the given figure, △CDE is a triangle.
F
,
G
&
H
are mid-points of
DE
,
EC
&
CD
respectively.
Given
FG = 10 cm
,
GH = 9 cm
&
HF = 10 cm
,
find the sides of the triangle.
(i)
21 cm
,
18 cm
&
20 cm
(ii)
20 cm
,
18 cm
&
20 cm
(iii)
17 cm
,
18 cm
&
20 cm
(iv)
20 cm
,
17 cm
&
20 cm
(v)
20 cm
,
18 cm
&
23 cm
Question
10
10.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
KO
=
(i)
KN
(ii)
OM
(iii)
KL
(iv)
NL
(v)
MK
Question
11
11.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FJ
=
(i)
FG
(ii)
HF
(iii)
JH
(iv)
IG
(v)
FI
Question
12
12.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
HF
=
(i)
DH
(ii)
FD
(iii)
DE
(iv)
GE
(v)
DG
Question
13
13.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 23 cm and AP = 9 cm. Find PB
(i)
14.00 cm
(ii)
12.00 cm
(iii)
15.00 cm
(iv)
13.00 cm
(v)
16.00 cm
Question
14
14.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FI
=
(i)
HF
(ii)
FJ
(iii)
FG
(iv)
JH
(v)
IG
Question
15
15.
In the given figure, HIJK is a parallelogram
such that
L
and
M
are mid-points of sides
HI
&
JK
.
HM
meets
IK
at
S
and
JL
meets
IK
at
T
. Given
IK
=
19 cm
, find
ST
(i)
7.33 cm
(ii)
5.33 cm
(iii)
8.33 cm
(iv)
4.33 cm
(v)
6.33 cm
Question
16
16.
In the given figure, the area of the △GHI is x sq.cm. J,K,L are the mid-points of the sides HI , IG and GH respectively. The area of the △JKL is
(i)
1
3
of area of △GHI
(ii)
1
2
of area of △GHI
(iii)
3
4
of area of △GHI
(iv)
1
4
of area of △GHI
(v)
2
3
of area of △GHI
Question
17
17.
EFGH is a quadrilateral. Q, R, S and T are mid-points of EF, FG, GH and HE respectively.If EG = 30 cm and FH = 17 cm, find the measure of the sides of QRST.
(i)
15 cm
,
7 cm
,
15 cm
,
7 cm
(ii)
15 cm
,
6 cm
,
15 cm
,
6 cm
(iii)
15 cm
,
8.5 cm
,
15 cm
,
8.5 cm
(iv)
16 cm
,
8.5 cm
,
16 cm
,
8.5 cm
(v)
18 cm
,
8.5 cm
,
18 cm
,
8.5 cm
Question
18
18.
In the given figure, △HIJ is a triangle.
K
,
L
&
M
are mid-points of
IJ
,
JH
&
HI
respectively.
Given
KL = 9 cm
,
LM = 8 cm
&
MK = 8 cm
,
find the sides of the triangle.
(i)
16 cm
,
16 cm
&
16 cm
(ii)
18 cm
,
16 cm
&
16 cm
(iii)
18 cm
,
15 cm
&
16 cm
(iv)
18 cm
,
16 cm
&
19 cm
(v)
19 cm
,
16 cm
&
16 cm
Question
19
19.
In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
∠DAF =
(i)
∠CFA
(ii)
∠HFE
(iii)
∠BHA
(iv)
∠AFD
(v)
∠EHF
Question
20
20.
In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
△FEH ∼
(i)
△DCF
(ii)
△FDA
(iii)
△DAE
(iv)
△ACF
(v)
△ABH
Question
21
21.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
GE
=
(i)
CD
(ii)
CF
(iii)
FD
(iv)
EC
(v)
CG
Question
22
22.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DG
=
(i)
DE
(ii)
DH
(iii)
HF
(iv)
FD
(v)
GE
Question
23
23.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DG
=
(i)
EF
2
(ii)
DH
(iii)
FD
2
(iv)
EF
(v)
DE
2
Question
24
24.
From the given figure and values, find x
(i)
(
31
,
1
)
(ii)
(
-1
,
29
)
(iii)
(
-1
,
28
)
(iv)
(
1
,
29
)
(v)
(
0
,
30
)
Question
25
25.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
KO
=
(i)
KL
2
(ii)
KN
(iii)
LM
(iv)
MK
2
(v)
LM
2
Assignment Key
1) (v)
2) (v)
3) (v)
4) (iv)
5) (iv)
6) (v)
7) (v)
8) (v)
9) (ii)
10) (ii)
11) (iii)
12) (i)
13) (i)
14) (v)
15) (v)
16) (iv)
17) (iii)
18) (ii)
19) (v)
20) (ii)
21) (v)
22) (v)
23) (v)
24) (ii)
25) (iv)
