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.
△ABH ∼
(i)
△ACF
(ii)
△FEH
(iii)
△DCF
(iv)
△DAE
(v)
△FDA
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.
∠AFD =
(i)
∠FAC
(ii)
∠HFE
(iii)
∠HAB
(iv)
∠FEH
(v)
∠FDA
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.
∠FEH =
(i)
∠ACF
(ii)
∠EHF
(iii)
∠DAF
(iv)
∠FDA
(v)
∠ABH
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)
∠DAF
(ii)
∠EHF
(iii)
∠HFE
(iv)
∠BHA
(v)
∠AFD
Question
5
5.
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
2
of area of △HIJ
(ii)
1
4
of area of △HIJ
(iii)
3
4
of area of △HIJ
(iv)
1
3
of area of △HIJ
(v)
2
3
of area of △HIJ
Question
6
6.
In the given figure, points E , F and G are the mid-points of sides CD, DB and BC of △BCD. Which of the following are true?
a)
Area of
△BCD
=
1
3
area of
△EFG
b)
Area of trapezium CDFG is thrice the area of △BGF
c)
Area of trapezium
CDFG
is
1
4
the area of
△BCD
d)
Area of △BCD = 4 times area of △EFG
e)
All four small triangles have equal areas
(i)
{b,d,e}
(ii)
{a,b,d}
(iii)
{c,d}
(iv)
{a,b}
(v)
{a,c,e}
Question
7
7.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 22 cm. Find AP
(i)
9.80 cm
(ii)
10.80 cm
(iii)
8.80 cm
(iv)
6.80 cm
(v)
7.80 cm
Question
8
8.
From the given figure and values, find x
(i)
(
71
,
-38
)
(ii)
(
72
,
-39
)
(iii)
(
70
,
-39
)
(iv)
(
70
,
-40
)
(v)
(
-37
,
72
)
Question
9
9.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
IM
=
(i)
IL
(ii)
JK
2
(iii)
KI
2
(iv)
IJ
2
(v)
JK
Question
10
10.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HK
=
(i)
IJ
2
(ii)
HL
(iii)
HI
2
(iv)
IJ
(v)
JH
2
Question
11
11.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
EH
=
(i)
HF
(ii)
EI
(iii)
EF
(iv)
GE
(v)
IG
Question
12
12.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
KI
=
(i)
JH
(ii)
HK
(iii)
HL
(iv)
LJ
(v)
HI
Question
13
13.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HL
=
(i)
JH
(ii)
HK
(iii)
LJ
(iv)
KI
(v)
HI
Question
14
14.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
HF
=
(i)
FD
(ii)
DH
(iii)
DG
(iv)
GE
(v)
DE
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
P
and
KM
meets
JL
at
Q
. Given
JL
=
16 cm
, find
PQ
(i)
6.33 cm
(ii)
7.33 cm
(iii)
3.33 cm
(iv)
5.33 cm
(v)
4.33 cm
Question
16
16.
In the given figure, DEFG is a parallelogram such that Q is the mid-point of DE and DE = 2GD. Find ∠GQF
(i)
91°
(ii)
88°
(iii)
90°
(iv)
89°
(v)
92°
Question
17
17.
In the given figure, DEFG is a trapezium. H and I are mid-points of DG and EF.Given HI = 13.5 cm and DE = 19 cm, find FG
(i)
7.0 cm
(ii)
9.0 cm
(iii)
10.0 cm
(iv)
6.0 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 = 8 cm
,
find the sides of the triangle.
(i)
17 cm
,
16 cm
&
16 cm
(ii)
16 cm
,
15 cm
&
16 cm
(iii)
16 cm
,
16 cm
&
19 cm
(iv)
14 cm
,
16 cm
&
16 cm
(v)
16 cm
,
16 cm
&
16 cm
Question
19
19.
EFGH is a quadrilateral. P, Q, R and S are mid-points of EF, FG, GH and HE respectively.If EG = 32 cm and FH = 17 cm, find the measure of the sides of PQRS.
(i)
16 cm
,
8.5 cm
,
16 cm
,
8.5 cm
(ii)
16 cm
,
7 cm
,
16 cm
,
7 cm
(iii)
19 cm
,
8.5 cm
,
19 cm
,
8.5 cm
(iv)
17 cm
,
8.5 cm
,
17 cm
,
8.5 cm
(v)
16 cm
,
5 cm
,
16 cm
,
5 cm
Assignment Key
1) (i)
2) (ii)
3) (iv)
4) (iv)
5) (ii)
6) (i)
7) (iii)
8) (iii)
9) (iii)
10) (iii)
11) (i)
12) (ii)
13) (iii)
14) (ii)
15) (iv)
16) (iii)
17) (v)
18) (v)
19) (i)
