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
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GJ
=
(i)
IG
(ii)
KI
(iii)
GK
(iv)
JH
(v)
GH
Question
2
2.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
IG
=
(i)
EH
(ii)
EI
(iii)
HF
(iv)
EF
(v)
GE
Question
3
3.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 27 cm and AP = 11 cm. Find PB
(i)
17.00 cm
(ii)
16.00 cm
(iii)
18.00 cm
(iv)
14.00 cm
(v)
15.00 cm
Question
4
4.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
BC
(ii)
BC
2
(iii)
CA
2
(iv)
AB
2
(v)
AE
Question
5
5.
From the given figure and values, find x
(i)
(
21
,
(
-9
4
)
)
(ii)
(
(
-3
2
)
,
22
)
(iii)
(
20
,
-3
)
(iv)
(
23
,
(
-5
2
)
)
(v)
(
20
,
(
-5
2
)
)
Question
6
6.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DG
=
(i)
DE
(ii)
HF
(iii)
GE
(iv)
FD
(v)
DH
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.
△ABH ∼
(i)
△DCF
(ii)
△FEH
(iii)
△ACF
(iv)
△FDA
(v)
△DAE
Question
8
8.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
LJ
=
(i)
IM
(ii)
KI
(iii)
IL
(iv)
MK
(v)
IJ
Question
9
9.
In the given figure, CDEF is a parallelogram such that S is the mid-point of CD and CD = 2FC. Find ∠FSE
(i)
92°
(ii)
88°
(iii)
89°
(iv)
90°
(v)
91°
Question
10
10.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
KN
=
(i)
LM
(ii)
LM
2
(iii)
KL
2
(iv)
MK
2
(v)
KO
Question
11
11.
In the given figure, the area of the △FGH is x sq.cm. I,J,K are the mid-points of the sides GH , HF and FG respectively. The area of the △IJK is
(i)
3
4
of area of △FGH
(ii)
2
3
of area of △FGH
(iii)
1
3
of area of △FGH
(iv)
1
4
of area of △FGH
(v)
1
2
of area of △FGH
Question
12
12.
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.
∠ACF =
(i)
∠DAF
(ii)
∠ABH
(iii)
∠FDA
(iv)
∠EHF
(v)
∠FEH
Question
13
13.
In the given figure, points O , P and Q are the mid-points of sides MN, NL and LM of △LMN. Which of the following are true?
a)
Area of △LMN = 4 times area of △OPQ
b)
Area of trapezium MNPQ is thrice the area of △LQP
c)
Area of trapezium
MNPQ
is
1
4
the area of
△LMN
d)
All four small triangles have equal areas
e)
Area of
△LMN
=
1
3
area of
△OPQ
(i)
{a,b,d}
(ii)
{c,e,d}
(iii)
{c,a,b}
(iv)
{e,b}
(v)
{c,a}
Question
14
14.
CDEF is a quadrilateral. R, S, T and U are mid-points of CD, DE, EF and FC respectively.If CE = 31 cm and DF = 17 cm, find the measure of the sides of RSTU.
(i)
16 cm
,
8.5 cm
,
16 cm
,
8.5 cm
(ii)
15.5 cm
,
8.5 cm
,
15.5 cm
,
8.5 cm
(iii)
15.5 cm
,
6 cm
,
15.5 cm
,
6 cm
(iv)
15.5 cm
,
7 cm
,
15.5 cm
,
7 cm
(v)
17 cm
,
8.5 cm
,
17 cm
,
8.5 cm
Question
15
15.
In the given figure, △GHI is a triangle.
J
,
K
&
L
are mid-points of
HI
,
IG
&
GH
respectively.
Given
JK = 10 cm
,
KL = 8 cm
&
LJ = 10 cm
,
find the sides of the triangle.
(i)
18 cm
,
16 cm
&
20 cm
(ii)
20 cm
,
16 cm
&
22 cm
(iii)
20 cm
,
15 cm
&
20 cm
(iv)
21 cm
,
16 cm
&
20 cm
(v)
20 cm
,
16 cm
&
20 cm
Question
16
16.
In the given figure, BCDE is a parallelogram
such that
F
and
G
are mid-points of sides
BC
&
DE
.
BG
meets
CE
at
Q
and
DF
meets
CE
at
R
. Given
CE
=
16 cm
, find
QE
(i)
3.33 cm
(ii)
7.33 cm
(iii)
4.33 cm
(iv)
5.33 cm
(v)
6.33 cm
Question
17
17.
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.
∠EHF =
(i)
∠CFA
(ii)
∠AFD
(iii)
∠HFE
(iv)
∠DAF
(v)
∠BHA
Question
18
18.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 21 cm. Find AP
(i)
9.40 cm
(ii)
7.40 cm
(iii)
6.40 cm
(iv)
10.40 cm
(v)
8.40 cm
Question
19
19.
In the given figure, HIJK is a parallelogram such that T is the mid-point of HI and HI = 2KH. Find ∠KTJ
(i)
90°
(ii)
89°
(iii)
88°
(iv)
92°
(v)
91°
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.
∠BHA =
(i)
∠HFE
(ii)
∠DAF
(iii)
∠EHF
(iv)
∠AFD
(v)
∠CFA
Question
21
21.
In the given figure, points H , I and J are the mid-points of sides FG, GE and EF of △EFG. Which of the following are true?
a)
Area of
△EFG
=
1
3
area of
△HIJ
b)
Area of trapezium
FGIJ
is
1
4
the area of
△EFG
c)
All four small triangles have equal areas
d)
Area of △EFG = 4 times area of △HIJ
e)
Area of trapezium FGIJ is thrice the area of △EJI
(i)
{a,c}
(ii)
{c,d,e}
(iii)
{b,d}
(iv)
{a,b,e}
(v)
{a,c,d}
Question
22
22.
In the given figure, GHIJ is a trapezium. K and L are mid-points of GJ and HI.Given IJ = 7 cm and KL = 13.5 cm, find GH
(i)
20.0 cm
(ii)
22.0 cm
(iii)
21.0 cm
(iv)
18.0 cm
(v)
19.0 cm
Question
23
23.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HL
=
(i)
KI
(ii)
LJ
(iii)
HK
(iv)
HI
(v)
JH
Question
24
24.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
BC
(ii)
AB
2
(iii)
CA
2
(iv)
BC
2
(v)
AD
Question
25
25.
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.
∠AFD =
(i)
∠HFE
(ii)
∠HAB
(iii)
∠FEH
(iv)
∠FDA
(v)
∠FAC
Assignment Key
1) (iv)
2) (ii)
3) (ii)
4) (iv)
5) (v)
6) (iii)
7) (iii)
8) (iii)
9) (iv)
10) (iii)
11) (iv)
12) (ii)
13) (i)
14) (ii)
15) (v)
16) (iv)
17) (iv)
18) (v)
19) (i)
20) (v)
21) (ii)
22) (i)
23) (ii)
24) (iii)
25) (i)
