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
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
FD
=
(i)
CD
(ii)
CG
(iii)
EC
(iv)
CF
(v)
GE
Question
2
2.
BCDE is a quadrilateral. Q, R, S and T are mid-points of BC, CD, DE and EB respectively.If BD = 29 cm and CE = 19 cm, find the measure of the sides of QRST.
(i)
14.5 cm
,
8 cm
,
14.5 cm
,
8 cm
(ii)
15 cm
,
9.5 cm
,
15 cm
,
9.5 cm
(iii)
14.5 cm
,
9.5 cm
,
14.5 cm
,
9.5 cm
(iv)
14.5 cm
,
7 cm
,
14.5 cm
,
7 cm
(v)
16 cm
,
9.5 cm
,
16 cm
,
9.5 cm
Question
3
3.
In the given figure, the area of the △HIJ is x sq.cm. K,L,M are the mid-points of the sides IJ , JH and HI respectively. The area of the △KLM is
(i)
1
4
of area of △HIJ
(ii)
2
3
of area of △HIJ
(iii)
3
4
of area of △HIJ
(iv)
1
3
of area of △HIJ
(v)
1
2
of area of △HIJ
Question
4
4.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 22 cm and AP = 9 cm. Find PB
(i)
13.00 cm
(ii)
14.00 cm
(iii)
11.00 cm
(iv)
12.00 cm
(v)
15.00 cm
Question
5
5.
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 △CDE = 4 times area of △FGH
e)
Area of trapezium
DEGH
is
1
4
the area of
△CDE
(i)
{e,c}
(ii)
{b,c,d}
(iii)
{a,b}
(iv)
{a,b,c}
(v)
{a,e,d}
Question
6
6.
In the given figure, IJKL is a parallelogram such that T is the mid-point of IJ and IJ = 2LI. Find ∠LTK
(i)
89°
(ii)
90°
(iii)
88°
(iv)
91°
(v)
92°
Question
7
7.
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)
∠ACF
(ii)
∠ABH
(iii)
∠EHF
(iv)
∠DAF
(v)
∠FEH
Question
8
8.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GJ
=
(i)
KI
(ii)
IG
(iii)
JH
(iv)
GK
(v)
GH
Question
9
9.
In the given figure, △LMN is a triangle.
O
,
P
&
Q
are mid-points of
MN
,
NL
&
LM
respectively.
Given
OP = 10 cm
,
PQ = 9 cm
&
QO = 10 cm
,
find the sides of the triangle.
(i)
20 cm
,
18 cm
&
23 cm
(ii)
20 cm
,
18 cm
&
20 cm
(iii)
18 cm
,
18 cm
&
20 cm
(iv)
20 cm
,
17 cm
&
20 cm
(v)
21 cm
,
18 cm
&
20 cm
Question
10
10.
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.
∠FAC =
(i)
∠FDA
(ii)
∠FEH
(iii)
∠HAB
(iv)
∠HFE
(v)
∠AFD
Question
11
11.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JM
=
(i)
JK
(ii)
JN
(iii)
NL
(iv)
MK
(v)
LJ
Question
12
12.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
KN
=
(i)
LM
(ii)
MK
2
(iii)
KO
(iv)
LM
2
(v)
KL
2
Question
13
13.
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)
∠AFD
(ii)
∠CFA
(iii)
∠EHF
(iv)
∠BHA
(v)
∠HFE
Question
14
14.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FJ
=
(i)
GH
(ii)
HF
2
(iii)
FI
(iv)
GH
2
(v)
FG
2
Question
15
15.
In the given figure, CDEF is a trapezium. G and H are mid-points of CF and DE.Given GH = 15.5 cm and EF = 11 cm, find CD
(i)
21.0 cm
(ii)
20.0 cm
(iii)
19.0 cm
(iv)
18.0 cm
(v)
22.0 cm
Question
16
16.
In the given figure, the area of the △HIJ is x sq.cm. K,L,M are the mid-points of the sides IJ , JH and HI respectively. The area of the △KLM is
(i)
1
3
of area of △HIJ
(ii)
1
2
of area of △HIJ
(iii)
3
4
of area of △HIJ
(iv)
1
4
of area of △HIJ
(v)
2
3
of area of △HIJ
Question
17
17.
From the given figure and values, find x
(i)
(
16
,
8
3
)
(ii)
(
(
-1
3
)
,
13
)
(iii)
(
1
3
,
14
)
(iv)
(
(
-1
3
)
,
14
)
(v)
(
(
-1
5
)
,
15
)
Question
18
18.
In the given figure, FGHI is a parallelogram
such that
J
and
K
are mid-points of sides
FG
&
HI
.
FK
meets
GI
at
S
and
HJ
meets
GI
at
T
. Given
GI
=
16 cm
, find
SI
(i)
5.33 cm
(ii)
7.33 cm
(iii)
6.33 cm
(iv)
3.33 cm
(v)
4.33 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.
△FDA ∼
(i)
△FEH
(ii)
△DAE
(iii)
△ACF
(iv)
△ABH
(v)
△DCF
Question
20
20.
From the given figure and values, find x
(i)
(
22
,
(
-1
2
)
)
(ii)
(
23
,
(
-1
4
)
)
(iii)
(
25
,
(
-1
2
)
)
(iv)
(
3
2
,
24
)
(v)
(
22
,
-1
)
Question
21
21.
In the given figure, △EFG is a triangle.
H
,
I
&
J
are mid-points of
FG
,
GE
&
EF
respectively.
Given
HI = 9 cm
,
IJ = 8 cm
&
JH = 7 cm
,
find the sides of the triangle.
(i)
18 cm
,
16 cm
&
17 cm
(ii)
18 cm
,
16 cm
&
14 cm
(iii)
15 cm
,
16 cm
&
14 cm
(iv)
18 cm
,
15 cm
&
14 cm
(v)
19 cm
,
16 cm
&
14 cm
Question
22
22.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
LJ
=
(i)
KI
(ii)
JH
(iii)
HI
(iv)
HK
(v)
HL
Question
23
23.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JN
=
(i)
JM
(ii)
KL
2
(iii)
LJ
2
(iv)
KL
(v)
JK
2
Question
24
24.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DH
=
(i)
GE
(ii)
HF
(iii)
DG
(iv)
FD
(v)
DE
Question
25
25.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 27 cm. Find AP
(i)
12.80 cm
(ii)
11.80 cm
(iii)
10.80 cm
(iv)
8.80 cm
(v)
9.80 cm
Assignment Key
1) (iv)
2) (iii)
3) (i)
4) (i)
5) (ii)
6) (ii)
7) (v)
8) (iii)
9) (ii)
10) (iii)
11) (iv)
12) (v)
13) (iii)
14) (ii)
15) (ii)
16) (iv)
17) (iv)
18) (i)
19) (i)
20) (i)
21) (ii)
22) (v)
23) (iii)
24) (ii)
25) (iii)
