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
JH
=
(i)
GJ
(ii)
KI
(iii)
GH
(iv)
GK
(v)
IG
Question
2
2.
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
3
3.
From the given figure and values, find x
(i)
(
-13
,
38
)
(ii)
(
41
,
-11
)
(iii)
(
-11
,
39
)
(iv)
(
-12
,
40
)
(v)
(
-13
,
39
)
Question
4
4.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
AB
2
(ii)
CA
2
(iii)
AE
(iv)
BC
(v)
BC
2
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.
∠DAF =
(i)
∠AFD
(ii)
∠HFE
(iii)
∠CFA
(iv)
∠BHA
(v)
∠EHF
Question
6
6.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DH
=
(i)
DE
2
(ii)
EF
(iii)
EF
2
(iv)
FD
2
(v)
DG
Question
7
7.
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
=
18 cm
, find
GT
(i)
4.00 cm
(ii)
8.00 cm
(iii)
7.00 cm
(iv)
6.00 cm
(v)
5.00 cm
Question
8
8.
In the given figure, points N , O and P are the mid-points of sides LM, MK and KL of △KLM. Which of the following are true?
a)
Area of
△KLM
=
1
3
area of
△NOP
b)
Area of trapezium LMOP is thrice the area of △KPO
c)
All four small triangles have equal areas
d)
Area of trapezium
LMOP
is
1
4
the area of
△KLM
e)
Area of △KLM = 4 times area of △NOP
(i)
{b,c,e}
(ii)
{d,c}
(iii)
{a,d,e}
(iv)
{a,b,c}
(v)
{a,b}
Question
9
9.
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)
∠FEH
(ii)
∠HFE
(iii)
∠HAB
(iv)
∠FDA
(v)
∠FAC
Question
10
10.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 24 cm and AP = 10 cm. Find PB
(i)
15.00 cm
(ii)
13.00 cm
(iii)
12.00 cm
(iv)
14.00 cm
(v)
16.00 cm
Question
11
11.
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)
∠FDA
(ii)
∠EHF
(iii)
∠DAF
(iv)
∠ABH
(v)
∠FEH
Question
12
12.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
MK
=
(i)
JN
(ii)
JK
(iii)
JM
(iv)
NL
(v)
LJ
Question
13
13.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BF
=
(i)
BE
(ii)
BC
(iii)
DB
(iv)
FD
(v)
EC
Question
14
14.
In the given figure, △CDE is a triangle.
F
,
G
&
H
are mid-points of
DE
,
EC
&
CD
respectively.
Given
FG = 8 cm
,
GH = 9 cm
&
HF = 8 cm
,
find the sides of the triangle.
(i)
16 cm
,
18 cm
&
18 cm
(ii)
13 cm
,
18 cm
&
16 cm
(iii)
17 cm
,
18 cm
&
16 cm
(iv)
16 cm
,
18 cm
&
16 cm
(v)
16 cm
,
17 cm
&
16 cm
Question
15
15.
In the given figure, △BCD is a triangle.
E
,
F
&
G
are mid-points of
CD
,
DB
&
BC
respectively.
Given
EF = 10 cm
,
FG = 8 cm
&
GE = 8 cm
,
find the sides of the triangle.
(i)
20 cm
,
16 cm
&
18 cm
(ii)
17 cm
,
16 cm
&
16 cm
(iii)
20 cm
,
16 cm
&
16 cm
(iv)
21 cm
,
16 cm
&
16 cm
(v)
20 cm
,
15 cm
&
16 cm
Question
16
16.
CDEF is a quadrilateral. T, U, V and W are mid-points of CD, DE, EF and FC respectively.If CE = 28 cm and DF = 18 cm, find the measure of the sides of TUVW.
(i)
15 cm
,
9 cm
,
15 cm
,
9 cm
(ii)
14 cm
,
6 cm
,
14 cm
,
6 cm
(iii)
16 cm
,
9 cm
,
16 cm
,
9 cm
(iv)
14 cm
,
9 cm
,
14 cm
,
9 cm
(v)
14 cm
,
8 cm
,
14 cm
,
8 cm
Question
17
17.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
AE
(ii)
AB
2
(iii)
BC
2
(iv)
CA
2
(v)
BC
Question
18
18.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BE
=
(i)
FD
(ii)
DB
(iii)
EC
(iv)
BF
(v)
BC
Question
19
19.
In the given figure, FGHI is a parallelogram such that P is the mid-point of FG and FG = 2IF. Find ∠IPH
(i)
89°
(ii)
92°
(iii)
88°
(iv)
90°
(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)
∠DAF
(ii)
∠EHF
(iii)
∠HFE
(iv)
∠CFA
(v)
∠AFD
Question
21
21.
In the given figure, the area of the △BCD is x sq.cm. E,F,G are the mid-points of the sides CD , DB and BC respectively. The area of the △EFG is
(i)
1
2
of area of △BCD
(ii)
1
3
of area of △BCD
(iii)
1
4
of area of △BCD
(iv)
2
3
of area of △BCD
(v)
3
4
of area of △BCD
Question
22
22.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FJ
=
(i)
FG
(ii)
JH
(iii)
HF
(iv)
FI
(v)
IG
Question
23
23.
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)
△DCF
(ii)
△ABH
(iii)
△DAE
(iv)
△FEH
(v)
△FDA
Question
24
24.
In the given figure, CDEF is a trapezium. G and H are mid-points of CF and DE.Given CD = 18 cm and GH = 12.5 cm, find EF
(i)
8.0 cm
(ii)
6.0 cm
(iii)
7.0 cm
(iv)
5.0 cm
(v)
9.0 cm
Question
25
25.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
EC
=
(i)
CA
(ii)
AE
(iii)
AB
(iv)
AD
(v)
DB
Assignment Key
1) (i)
2) (iii)
3) (v)
4) (i)
5) (v)
6) (iv)
7) (iv)
8) (i)
9) (ii)
10) (iv)
11) (iv)
12) (iii)
13) (iv)
14) (iv)
15) (iii)
16) (iv)
17) (ii)
18) (iii)
19) (iv)
20) (iv)
21) (iii)
22) (ii)
23) (ii)
24) (iii)
25) (ii)
