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)
△FEH
(ii)
△ABH
(iii)
△DAE
(iv)
△FDA
(v)
△DCF
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)
∠FDA
(ii)
∠FAC
(iii)
∠HFE
(iv)
∠HAB
(v)
∠FEH
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)
∠EHF
(iii)
∠DAF
(iv)
∠ABH
(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.
∠BHA =
(i)
∠CFA
(ii)
∠DAF
(iii)
∠HFE
(iv)
∠AFD
(v)
∠EHF
Question
5
5.
In the given figure, the area of the △IJK is x sq.cm. L,M,N are the mid-points of the sides JK , KI and IJ respectively. The area of the △LMN is
(i)
1
2
of area of △IJK
(ii)
3
4
of area of △IJK
(iii)
2
3
of area of △IJK
(iv)
1
4
of area of △IJK
(v)
1
3
of area of △IJK
Question
6
6.
In the given figure, points L , M and N are the mid-points of sides JK, KI and IJ of △IJK. Which of the following are true?
a)
Area of trapezium JKMN is thrice the area of △INM
b)
Area of trapezium
JKMN
is
1
4
the area of
△IJK
c)
Area of
△IJK
=
1
3
area of
△LMN
d)
Area of △IJK = 4 times area of △LMN
e)
All four small triangles have equal areas
(i)
{b,c,e}
(ii)
{a,d,e}
(iii)
{c,d}
(iv)
{b,a,d}
(v)
{b,a}
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)
15.00 cm
(ii)
18.00 cm
(iii)
16.00 cm
(iv)
14.00 cm
(v)
17.00 cm
Question
8
8.
From the given figure and values, find x
(i)
(
20
,
20
)
(ii)
(
22
,
22
)
(iii)
(
20
,
19
)
(iv)
(
23
,
20
)
(v)
(
21
,
21
)
Question
9
9.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
EI
=
(i)
EH
(ii)
FG
2
(iii)
EF
2
(iv)
GE
2
(v)
FG
Question
10
10.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GJ
=
(i)
GH
2
(ii)
HI
2
(iii)
IG
2
(iv)
GK
(v)
HI
Question
11
11.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CF
=
(i)
CD
(ii)
GE
(iii)
EC
(iv)
CG
(v)
FD
Question
12
12.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
DB
=
(i)
AE
(ii)
AB
(iii)
AD
(iv)
EC
(v)
CA
Question
13
13.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CG
=
(i)
CD
(ii)
GE
(iii)
FD
(iv)
EC
(v)
CF
Question
14
14.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
KI
=
(i)
JH
(ii)
GK
(iii)
GJ
(iv)
IG
(v)
GH
Question
15
15.
In the given figure, BCDE is a parallelogram
such that
F
and
G
are mid-points of sides
BC
&
DE
.
BG
meets
CE
at
P
and
DF
meets
CE
at
Q
. Given
CE
=
20 cm
, find
PQ
(i)
6.67 cm
(ii)
8.67 cm
(iii)
5.67 cm
(iv)
7.67 cm
(v)
4.67 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)
88°
(ii)
90°
(iii)
89°
(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 = 14.5 cm, find FG
(i)
9.0 cm
(ii)
10.0 cm
(iii)
8.0 cm
(iv)
11.0 cm
(v)
7.0 cm
Question
18
18.
In the given figure, △MNO is a triangle.
P
,
Q
&
R
are mid-points of
NO
,
OM
&
MN
respectively.
Given
PQ = 9 cm
,
QR = 10 cm
&
RP = 9 cm
,
find the sides of the triangle.
(i)
18 cm
,
20 cm
&
18 cm
(ii)
18 cm
,
20 cm
&
20 cm
(iii)
18 cm
,
19 cm
&
18 cm
(iv)
16 cm
,
20 cm
&
18 cm
(v)
19 cm
,
20 cm
&
18 cm
Question
19
19.
BCDE is a quadrilateral. Q, R, S and T are mid-points of BC, CD, DE and EB respectively.If BD = 30 cm and CE = 19 cm, find the measure of the sides of QRST.
(i)
16 cm
,
9.5 cm
,
16 cm
,
9.5 cm
(ii)
15 cm
,
7 cm
,
15 cm
,
7 cm
(iii)
15 cm
,
8 cm
,
15 cm
,
8 cm
(iv)
17 cm
,
9.5 cm
,
17 cm
,
9.5 cm
(v)
15 cm
,
9.5 cm
,
15 cm
,
9.5 cm
Assignment Key
1) (ii)
2) (iii)
3) (v)
4) (i)
5) (iv)
6) (ii)
7) (iii)
8) (i)
9) (iv)
10) (i)
11) (v)
12) (iii)
13) (ii)
14) (ii)
15) (i)
16) (ii)
17) (i)
18) (i)
19) (v)
