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, 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)
∠AFD
(ii)
∠HFE
(iii)
∠FEH
(iv)
∠HAB
(v)
∠FDA
Question
2
2.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
CA
2
(ii)
BC
2
(iii)
AB
2
(iv)
AD
(v)
BC
Question
3
3.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
NL
=
(i)
JN
(ii)
JM
(iii)
LJ
(iv)
JK
(v)
MK
Question
4
4.
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.
∠CFA =
(i)
∠EHF
(ii)
∠AFD
(iii)
∠DAF
(iv)
∠HFE
(v)
∠BHA
Question
5
5.
In the given figure, DEFG is a parallelogram such that P is the mid-point of DE and DE = 2GD. Find ∠GPF
(i)
89°
(ii)
92°
(iii)
91°
(iv)
88°
(v)
90°
Question
6
6.
From the given figure and values, find x
(i)
(
17
,
(
-1
2
)
)
(ii)
(
5
2
,
19
)
(iii)
(
20
,
(
-1
2
)
)
(iv)
(
18
,
(
-1
4
)
)
(v)
(
17
,
-1
)
Question
7
7.
BCDE is a quadrilateral. R, S, T and U are mid-points of BC, CD, DE and EB respectively.If BD = 26 cm and CE = 18 cm, find the measure of the sides of RSTU.
(i)
13 cm
,
8 cm
,
13 cm
,
8 cm
(ii)
14 cm
,
9 cm
,
14 cm
,
9 cm
(iii)
16 cm
,
9 cm
,
16 cm
,
9 cm
(iv)
13 cm
,
9 cm
,
13 cm
,
9 cm
(v)
13 cm
,
7 cm
,
13 cm
,
7 cm
Question
8
8.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JM
=
(i)
NL
(ii)
JN
(iii)
LJ
(iv)
JK
(v)
MK
Question
9
9.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
HF
=
(i)
IG
(ii)
EF
(iii)
EH
(iv)
GE
(v)
EI
Question
10
10.
In the given figure, GHIJ is a parallelogram
such that
K
and
L
are mid-points of sides
GH
&
IJ
.
GL
meets
HJ
at
Q
and
IK
meets
HJ
at
R
. Given
HJ
=
15 cm
, find
QR
(i)
4.00 cm
(ii)
6.00 cm
(iii)
5.00 cm
(iv)
7.00 cm
(v)
3.00 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.
△FEH ∼
(i)
△DCF
(ii)
△ACF
(iii)
△ABH
(iv)
△DAE
(v)
△FDA
Question
12
12.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 26 cm and AP = 10 cm. Find PB
(i)
17.00 cm
(ii)
16.00 cm
(iii)
15.00 cm
(iv)
14.00 cm
(v)
18.00 cm
Question
13
13.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GJ
=
(i)
IG
(ii)
GK
(iii)
JH
(iv)
GH
(v)
KI
Question
14
14.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
IM
=
(i)
IL
(ii)
LJ
(iii)
MK
(iv)
IJ
(v)
KI
Question
15
15.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
LJ
=
(i)
JH
(ii)
HI
(iii)
KI
(iv)
HL
(v)
HK
Question
16
16.
In the given figure, the area of the △MNO is x sq.cm. P,Q,R are the mid-points of the sides NO , OM and MN respectively. The area of the △PQR is
(i)
3
4
of area of △MNO
(ii)
1
2
of area of △MNO
(iii)
1
3
of area of △MNO
(iv)
2
3
of area of △MNO
(v)
1
4
of area of △MNO
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.
∠FDA =
(i)
∠ABH
(ii)
∠DAF
(iii)
∠ACF
(iv)
∠EHF
(v)
∠FEH
Question
18
18.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CF
=
(i)
DE
(ii)
CD
2
(iii)
CG
(iv)
EC
2
(v)
DE
2
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.
∠CFA =
(i)
∠HFE
(ii)
∠EHF
(iii)
∠BHA
(iv)
∠AFD
(v)
∠DAF
Question
20
20.
In the given figure, GHIJ is a parallelogram such that Q is the mid-point of GH and GH = 2JG. Find ∠JQI
(i)
91°
(ii)
92°
(iii)
90°
(iv)
88°
(v)
89°
Question
21
21.
In the given figure, points D , E and F are the mid-points of sides BC, CA and AB of △ABC. Which of the following are true?
a)
Area of △ABC = 4 times area of △DEF
b)
Area of trapezium
BCEF
is
1
4
the area of
△ABC
c)
Area of
△ABC
=
1
3
area of
△DEF
d)
All four small triangles have equal areas
e)
Area of trapezium BCEF is thrice the area of △AFE
(i)
{c,d}
(ii)
{b,a,d}
(iii)
{b,c,e}
(iv)
{a,d,e}
(v)
{b,a}
Question
22
22.
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)
∠DAF
(ii)
∠ACF
(iii)
∠EHF
(iv)
∠FDA
(v)
∠FEH
Question
23
23.
In the given figure, CDEF is a parallelogram
such that
G
and
H
are mid-points of sides
CD
&
EF
.
CH
meets
DF
at
R
and
EG
meets
DF
at
S
. Given
DF
=
16 cm
, find
DS
(i)
6.33 cm
(ii)
4.33 cm
(iii)
7.33 cm
(iv)
5.33 cm
(v)
3.33 cm
Question
24
24.
In the given figure, BCDE is a trapezium. F and G are mid-points of BE and CD.Given BC = 20 cm and FG = 15 cm, find DE
(i)
8.0 cm
(ii)
9.0 cm
(iii)
10.0 cm
(iv)
11.0 cm
(v)
12.0 cm
Question
25
25.
In the given figure, △CDE is a triangle.
F
,
G
&
H
are mid-points of
DE
,
EC
&
CD
respectively.
Given
FG = 7 cm
,
GH = 8 cm
&
HF = 10 cm
,
find the sides of the triangle.
(i)
14 cm
,
16 cm
&
22 cm
(ii)
15 cm
,
16 cm
&
20 cm
(iii)
14 cm
,
16 cm
&
20 cm
(iv)
12 cm
,
16 cm
&
20 cm
(v)
14 cm
,
15 cm
&
20 cm
Assignment Key
1) (iv)
2) (i)
3) (i)
4) (v)
5) (v)
6) (i)
7) (iv)
8) (v)
9) (iii)
10) (iii)
11) (v)
12) (ii)
13) (iii)
14) (iii)
15) (iv)
16) (v)
17) (v)
18) (ii)
19) (iii)
20) (iii)
21) (iv)
22) (ii)
23) (iv)
24) (iii)
25) (iii)
