EduSahara™ Assignment
Name : Mid-Point and Intercept Theorems
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.
△ACF ∼
(i)
△ABH
(ii)
△DAE
(iii)
△DCF
(iv)
△FDA
(v)
△FEH
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)
∠HAB
(iii)
∠FEH
(iv)
∠AFD
(v)
∠HFE
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.
∠ACF =
(i)
∠ABH
(ii)
∠DAF
(iii)
∠EHF
(iv)
∠FDA
(v)
∠FEH
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)
∠BHA
(ii)
∠HFE
(iii)
∠AFD
(iv)
∠DAF
(v)
∠EHF
Question
5
5.
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)
1
4
of area of △KLM
(iii)
3
4
of area of △KLM
(iv)
1
3
of area of △KLM
(v)
2
3
of area of △KLM
Question
6
6.
In the given figure, points P , Q and R are the mid-points of sides NO, OM and MN of △MNO. Which of the following are true?
a)
All four small triangles have equal areas
b)
Area of trapezium
NOQR
is
1
4
the area of
△MNO
c)
Area of
△MNO
=
1
3
area of
△PQR
d)
Area of trapezium NOQR is thrice the area of △MRQ
e)
Area of △MNO = 4 times area of △PQR
(i)
{b,c,e}
(ii)
{b,a}
(iii)
{b,a,d}
(iv)
{a,d,e}
(v)
{c,d}
Question
7
7.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 24 cm. Find AP
(i)
10.60 cm
(ii)
7.60 cm
(iii)
11.60 cm
(iv)
9.60 cm
(v)
8.60 cm
Question
8
8.
From the given figure and values, find x
(i)
(
-11
,
45
)
(ii)
(
-10
,
47
)
(iii)
(
-11
,
46
)
(iv)
(
-8
,
46
)
(v)
(
48
,
-9
)
Question
9
9.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BF
=
(i)
CD
(ii)
BC
2
(iii)
BE
(iv)
CD
2
(v)
DB
2
Question
10
10.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JM
=
(i)
KL
2
(ii)
KL
(iii)
JN
(iv)
JK
2
(v)
LJ
2
Question
11
11.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FI
=
(i)
FG
(ii)
IG
(iii)
JH
(iv)
HF
(v)
FJ
Question
12
12.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
HF
=
(i)
IG
(ii)
EF
(iii)
EI
(iv)
GE
(v)
EH
Question
13
13.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JN
=
(i)
MK
(ii)
NL
(iii)
LJ
(iv)
JK
(v)
JM
Question
14
14.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
IG
=
(i)
GE
(ii)
EF
(iii)
EH
(iv)
EI
(v)
HF
Question
15
15.
In the given figure, IJKL is a parallelogram
such that
M
and
N
are mid-points of sides
IJ
&
KL
.
IN
meets
JL
at
R
and
KM
meets
JL
at
S
. Given
JL
=
18 cm
, find
JS
(i)
7.00 cm
(ii)
6.00 cm
(iii)
8.00 cm
(iv)
5.00 cm
(v)
4.00 cm
Question
16
16.
In the given figure, IJKL is a parallelogram such that S is the mid-point of IJ and IJ = 2LI. Find ∠LSK
(i)
89°
(ii)
90°
(iii)
88°
(iv)
92°
(v)
91°
Question
17
17.
In the given figure, DEFG is a trapezium. H and I are mid-points of DG and EF.Given DE = 20 cm and HI = 14 cm, find FG
(i)
6.0 cm
(ii)
7.0 cm
(iii)
10.0 cm
(iv)
9.0 cm
(v)
8.0 cm
Question
18
18.
In the given figure, △BCD is a triangle.
E
,
F
&
G
are mid-points of
CD
,
DB
&
BC
respectively.
Given
EF = 8 cm
,
FG = 8 cm
&
GE = 10 cm
,
find the sides of the triangle.
(i)
16 cm
,
16 cm
&
20 cm
(ii)
14 cm
,
16 cm
&
20 cm
(iii)
17 cm
,
16 cm
&
20 cm
(iv)
16 cm
,
16 cm
&
23 cm
(v)
16 cm
,
15 cm
&
20 cm
Question
19
19.
DEFG is a quadrilateral. Q, R, S and T are mid-points of DE, EF, FG and GD respectively.If DF = 34 cm and EG = 18 cm, find the measure of the sides of QRST.
(i)
17 cm
,
6 cm
,
17 cm
,
6 cm
(ii)
18 cm
,
9 cm
,
18 cm
,
9 cm
(iii)
20 cm
,
9 cm
,
20 cm
,
9 cm
(iv)
17 cm
,
8 cm
,
17 cm
,
8 cm
(v)
17 cm
,
9 cm
,
17 cm
,
9 cm
Assignment Key
1) (i)
2) (ii)
3) (i)
4) (i)
5) (ii)
6) (iv)
7) (iv)
8) (iii)
9) (v)
10) (iv)
11) (ii)
12) (v)
13) (ii)
14) (iv)
15) (ii)
16) (ii)
17) (v)
18) (i)
19) (v)
