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.
△FDA ∼
(i)
△ABH
(ii)
△ACF
(iii)
△DCF
(iv)
△DAE
(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)
∠HFE
(ii)
∠HAB
(iii)
∠FDA
(iv)
∠FEH
(v)
∠AFD
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.
∠FDA =
(i)
∠ACF
(ii)
∠ABH
(iii)
∠EHF
(iv)
∠FEH
(v)
∠DAF
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.
∠BHA =
(i)
∠AFD
(ii)
∠DAF
(iii)
∠EHF
(iv)
∠CFA
(v)
∠HFE
Question
5
5.
In the given figure, the area of the △CDE is x sq.cm. F,G,H are the mid-points of the sides DE , EC and CD respectively. The area of the △FGH is
(i)
1
3
of area of △CDE
(ii)
1
2
of area of △CDE
(iii)
1
4
of area of △CDE
(iv)
3
4
of area of △CDE
(v)
2
3
of area of △CDE
Question
6
6.
In the given figure, points M , N and O are the mid-points of sides KL, LJ and JK of △JKL. Which of the following are true?
a)
Area of trapezium
KLNO
is
1
4
the area of
△JKL
b)
All four small triangles have equal areas
c)
Area of △JKL = 4 times area of △MNO
d)
Area of trapezium KLNO is thrice the area of △JON
e)
Area of
△JKL
=
1
3
area of
△MNO
(i)
{b,c,d}
(ii)
{e,c}
(iii)
{a,e,d}
(iv)
{a,b,c}
(v)
{a,b}
Question
7
7.
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)
16.00 cm
(ii)
17.00 cm
(iii)
18.00 cm
(iv)
15.00 cm
(v)
14.00 cm
Question
8
8.
From the given figure and values, find x
(i)
(
-6
,
34
)
(ii)
(
-9
,
33
)
(iii)
(
-9
,
34
)
(iv)
(
-8
,
35
)
(v)
(
36
,
-7
)
Question
9
9.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
AB
2
(ii)
BC
2
(iii)
AD
(iv)
CA
2
(v)
BC
Question
10
10.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HK
=
(i)
IJ
(ii)
JH
2
(iii)
IJ
2
(iv)
HI
2
(v)
HL
Question
11
11.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FI
=
(i)
IG
(ii)
FJ
(iii)
FG
(iv)
HF
(v)
JH
Question
12
12.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
NL
=
(i)
MK
(ii)
KN
(iii)
OM
(iv)
KO
(v)
KL
Question
13
13.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
CA
(ii)
EC
(iii)
AB
(iv)
DB
(v)
AD
Question
14
14.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
HF
=
(i)
DG
(ii)
DH
(iii)
DE
(iv)
GE
(v)
FD
Question
15
15.
In the given figure, FGHI is a parallelogram
such that
J
and
K
are mid-points of sides
FG
&
HI
.
FK
meets
GI
at
U
and
HJ
meets
GI
at
V
. Given
GI
=
19 cm
, find
UI
(i)
8.33 cm
(ii)
6.33 cm
(iii)
4.33 cm
(iv)
5.33 cm
(v)
7.33 cm
Question
16
16.
In the given figure, HIJK is a parallelogram such that P is the mid-point of HI and HI = 2KH. Find ∠KPJ
(i)
92°
(ii)
88°
(iii)
89°
(iv)
90°
(v)
91°
Question
17
17.
In the given figure, LMNO is a trapezium. P and Q are mid-points of LO and MN.Given NO = 7 cm and LM = 20 cm, find PQ
(i)
11.5 cm
(ii)
15.5 cm
(iii)
14.5 cm
(iv)
13.5 cm
(v)
12.5 cm
Question
18
18.
In the given figure, △EFG is a triangle.
H
,
I
&
J
are mid-points of
FG
,
GE
&
EF
respectively.
Given
HI = 9 cm
,
IJ = 9 cm
&
JH = 8 cm
,
find the sides of the triangle.
(i)
18 cm
,
18 cm
&
16 cm
(ii)
18 cm
,
17 cm
&
16 cm
(iii)
19 cm
,
18 cm
&
16 cm
(iv)
18 cm
,
18 cm
&
19 cm
(v)
15 cm
,
18 cm
&
16 cm
Question
19
19.
CDEF is a quadrilateral. P, Q, R and S are mid-points of CD, DE, EF and FC respectively.If CE = 31 cm and DF = 18 cm, find the measure of the sides of PQRS.
(i)
15.5 cm
,
6 cm
,
15.5 cm
,
6 cm
(ii)
16 cm
,
9 cm
,
16 cm
,
9 cm
(iii)
15.5 cm
,
8 cm
,
15.5 cm
,
8 cm
(iv)
15.5 cm
,
9 cm
,
15.5 cm
,
9 cm
(v)
18 cm
,
9 cm
,
18 cm
,
9 cm
Assignment Key
1) (v)
2) (ii)
3) (iv)
4) (iv)
5) (iii)
6) (i)
7) (i)
8) (iii)
9) (iv)
10) (iv)
11) (i)
12) (ii)
13) (ii)
14) (ii)
15) (ii)
16) (iv)
17) (iv)
18) (i)
19) (iv)
