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)
△ACF
(ii)
△ABH
(iii)
△DCF
(iv)
△FEH
(v)
△DAE
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.
∠HAB =
(i)
∠FAC
(ii)
∠FEH
(iii)
∠AFD
(iv)
∠HFE
(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)
∠FDA
(ii)
∠ABH
(iii)
∠ACF
(iv)
∠DAF
(v)
∠EHF
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)
∠HFE
(ii)
∠BHA
(iii)
∠EHF
(iv)
∠CFA
(v)
∠AFD
Question
5
5.
In the given figure, the area of the △ABC is x sq.cm. D,E,F are the mid-points of the sides BC , CA and AB respectively. The area of the △DEF is
(i)
2
3
of area of △ABC
(ii)
3
4
of area of △ABC
(iii)
1
4
of area of △ABC
(iv)
1
3
of area of △ABC
(v)
1
2
of area of △ABC
Question
6
6.
In the given figure, points K , L and M are the mid-points of sides IJ, JH and HI of △HIJ. Which of the following are true?
a)
All four small triangles have equal areas
b)
Area of △HIJ = 4 times area of △KLM
c)
Area of trapezium IJLM is thrice the area of △HML
d)
Area of
△HIJ
=
1
3
area of
△KLM
e)
Area of trapezium
IJLM
is
1
4
the area of
△HIJ
(i)
{d,a}
(ii)
{e,b}
(iii)
{d,e,c}
(iv)
{d,a,b}
(v)
{a,b,c}
Question
7
7.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 21 cm and AP = 8 cm. Find PB
(i)
15.00 cm
(ii)
11.00 cm
(iii)
12.00 cm
(iv)
14.00 cm
(v)
13.00 cm
Question
8
8.
From the given figure and values, find x
(i)
(
23
,
-1
)
(ii)
(
22
,
-3
)
(iii)
(
0
,
24
)
(iv)
(
24
,
-2
)
(v)
(
22
,
-2
)
Question
9
9.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
IM
=
(i)
JK
2
(ii)
JK
(iii)
IJ
2
(iv)
IL
(v)
KI
2
Question
10
10.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
AE
(ii)
CA
2
(iii)
BC
2
(iv)
BC
(v)
AB
2
Question
11
11.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
EC
(ii)
AB
(iii)
CA
(iv)
DB
(v)
AE
Question
12
12.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
EC
=
(i)
BF
(ii)
DB
(iii)
BE
(iv)
BC
(v)
FD
Question
13
13.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BF
=
(i)
DB
(ii)
BC
(iii)
BE
(iv)
FD
(v)
EC
Question
14
14.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
KI
=
(i)
GH
(ii)
GK
(iii)
JH
(iv)
GJ
(v)
IG
Question
15
15.
In the given figure, JKLM is a parallelogram
such that
N
and
O
are mid-points of sides
JK
&
LM
.
JO
meets
KM
at
T
and
LN
meets
KM
at
U
. Given
KM
=
17 cm
, find
TM
(i)
7.67 cm
(ii)
5.67 cm
(iii)
6.67 cm
(iv)
4.67 cm
(v)
3.67 cm
Question
16
16.
In the given figure, IJKL is a parallelogram such that Q is the mid-point of IJ and IJ = 2LI. Find ∠LQK
(i)
92°
(ii)
89°
(iii)
91°
(iv)
90°
(v)
88°
Question
17
17.
In the given figure, LMNO is a trapezium. P and Q are mid-points of LO and MN.Given NO = 8 cm and LM = 20 cm, find PQ
(i)
15.0 cm
(ii)
12.0 cm
(iii)
14.0 cm
(iv)
13.0 cm
(v)
16.0 cm
Question
18
18.
In the given figure, △DEF is a triangle.
G
,
H
&
I
are mid-points of
EF
,
FD
&
DE
respectively.
Given
GH = 10 cm
,
HI = 8 cm
&
IG = 10 cm
,
find the sides of the triangle.
(i)
20 cm
,
16 cm
&
20 cm
(ii)
21 cm
,
16 cm
&
20 cm
(iii)
20 cm
,
16 cm
&
23 cm
(iv)
18 cm
,
16 cm
&
20 cm
(v)
20 cm
,
15 cm
&
20 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 = 28 cm and FH = 15 cm, find the measure of the sides of PQRS.
(i)
14 cm
,
7.5 cm
,
14 cm
,
7.5 cm
(ii)
17 cm
,
7.5 cm
,
17 cm
,
7.5 cm
(iii)
14 cm
,
6 cm
,
14 cm
,
6 cm
(iv)
14 cm
,
5 cm
,
14 cm
,
5 cm
(v)
15 cm
,
7.5 cm
,
15 cm
,
7.5 cm
Assignment Key
1) (iv)
2) (i)
3) (i)
4) (iii)
5) (iii)
6) (v)
7) (v)
8) (v)
9) (v)
10) (v)
11) (iv)
12) (iii)
13) (iv)
14) (ii)
15) (ii)
16) (iv)
17) (iii)
18) (i)
19) (i)
