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)
△DCF
(ii)
△FDA
(iii)
△FEH
(iv)
△DAE
(v)
△ABH
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.
∠HFE =
(i)
∠HAB
(ii)
∠FDA
(iii)
∠AFD
(iv)
∠FEH
(v)
∠FAC
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.
∠ABH =
(i)
∠FDA
(ii)
∠EHF
(iii)
∠FEH
(iv)
∠ACF
(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.
∠DAF =
(i)
∠BHA
(ii)
∠AFD
(iii)
∠HFE
(iv)
∠EHF
(v)
∠CFA
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)
3
4
of area of △KLM
(ii)
1
3
of area of △KLM
(iii)
1
2
of area of △KLM
(iv)
1
4
of area of △KLM
(v)
2
3
of area of △KLM
Question
6
6.
In the given figure, points H , I and J are the mid-points of sides FG, GE and EF of △EFG. Which of the following are true?
a)
All four small triangles have equal areas
b)
Area of △EFG = 4 times area of △HIJ
c)
Area of
△EFG
=
1
3
area of
△HIJ
d)
Area of trapezium FGIJ is thrice the area of △EJI
e)
Area of trapezium
FGIJ
is
1
4
the area of
△EFG
(i)
{c,e,d}
(ii)
{a,b,d}
(iii)
{e,b}
(iv)
{c,a,b}
(v)
{c,a}
Question
7
7.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 21 cm. Find AP
(i)
6.40 cm
(ii)
10.40 cm
(iii)
8.40 cm
(iv)
7.40 cm
(v)
9.40 cm
Question
8
8.
From the given figure and values, find x
(i)
(
27
,
-6
)
(ii)
(
28
,
-7
)
(iii)
(
26
,
-7
)
(iv)
(
26
,
-8
)
(v)
(
-5
,
28
)
Question
9
9.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DH
=
(i)
DE
2
(ii)
EF
2
(iii)
DG
(iv)
EF
(v)
FD
2
Question
10
10.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DG
=
(i)
EF
(ii)
DE
2
(iii)
FD
2
(iv)
EF
2
(v)
DH
Question
11
11.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
EH
=
(i)
EI
(ii)
HF
(iii)
EF
(iv)
IG
(v)
GE
Question
12
12.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
JH
=
(i)
IG
(ii)
GH
(iii)
KI
(iv)
GK
(v)
GJ
Question
13
13.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BF
=
(i)
FD
(ii)
BE
(iii)
DB
(iv)
EC
(v)
BC
Question
14
14.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
MK
=
(i)
IM
(ii)
IL
(iii)
LJ
(iv)
IJ
(v)
KI
Question
15
15.
In the given figure, GHIJ is a parallelogram
such that
K
and
L
are mid-points of sides
GH
&
IJ
.
GL
meets
HJ
at
T
and
IK
meets
HJ
at
U
. Given
HJ
=
19 cm
, find
TJ
(i)
8.33 cm
(ii)
5.33 cm
(iii)
6.33 cm
(iv)
4.33 cm
(v)
7.33 cm
Question
16
16.
In the given figure, ABCD is a parallelogram such that P is the mid-point of AB and AB = 2DA. Find ∠DPC
(i)
91°
(ii)
88°
(iii)
92°
(iv)
90°
(v)
89°
Question
17
17.
In the given figure, MNOP is a trapezium. Q and R are mid-points of MP and NO.Given OP = 9 cm and QR = 14.5 cm, find MN
(i)
22.0 cm
(ii)
21.0 cm
(iii)
20.0 cm
(iv)
18.0 cm
(v)
19.0 cm
Question
18
18.
In the given figure, △CDE is a triangle.
F
,
G
&
H
are mid-points of
DE
,
EC
&
CD
respectively.
Given
FG = 10 cm
,
GH = 9 cm
&
HF = 9 cm
,
find the sides of the triangle.
(i)
21 cm
,
18 cm
&
18 cm
(ii)
20 cm
,
18 cm
&
18 cm
(iii)
17 cm
,
18 cm
&
18 cm
(iv)
20 cm
,
18 cm
&
21 cm
(v)
20 cm
,
17 cm
&
18 cm
Question
19
19.
CDEF is a quadrilateral. S, T, U and V are mid-points of CD, DE, EF and FC respectively.If CE = 31 cm and DF = 19 cm, find the measure of the sides of STUV.
(i)
16 cm
,
9.5 cm
,
16 cm
,
9.5 cm
(ii)
15.5 cm
,
9.5 cm
,
15.5 cm
,
9.5 cm
(iii)
17 cm
,
9.5 cm
,
17 cm
,
9.5 cm
(iv)
15.5 cm
,
7 cm
,
15.5 cm
,
7 cm
(v)
15.5 cm
,
8 cm
,
15.5 cm
,
8 cm
Assignment Key
1) (v)
2) (iii)
3) (iv)
4) (iv)
5) (iv)
6) (ii)
7) (iii)
8) (iii)
9) (v)
10) (ii)
11) (ii)
12) (v)
13) (i)
14) (i)
15) (iii)
16) (iv)
17) (iii)
18) (ii)
19) (ii)
