EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Mid-Point and Intercept Theorems
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HK
=
(i)
HL
(ii)
IJ
(iii)
JH
2
(iv)
HI
2
(v)
IJ
2
Question
2
2.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DG
=
(i)
HF
(ii)
FD
(iii)
DE
(iv)
GE
(v)
DH
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.
∠ACF =
(i)
∠FDA
(ii)
∠ABH
(iii)
∠DAF
(iv)
∠FEH
(v)
∠EHF
Question
4
4.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HK
=
(i)
IJ
(ii)
HL
(iii)
JH
2
(iv)
HI
2
(v)
IJ
2
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)
1
4
of area of △ABC
(ii)
1
2
of area of △ABC
(iii)
3
4
of area of △ABC
(iv)
2
3
of area of △ABC
(v)
1
3
of area of △ABC
Question
6
6.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
IG
=
(i)
HF
(ii)
FI
(iii)
JH
(iv)
FG
(v)
FJ
Question
7
7.
In the given figure, ABCD is a parallelogram such that Q is the mid-point of AB and AB = 2DA. Find ∠DQC
(i)
88°
(ii)
89°
(iii)
90°
(iv)
91°
(v)
92°
Question
8
8.
ABCD is a quadrilateral. P, Q, R and S are mid-points of AB, BC, CD and DA respectively.If AC = 29 cm and BD = 17 cm, find the measure of the sides of PQRS.
(i)
15 cm
,
8.5 cm
,
15 cm
,
8.5 cm
(ii)
16 cm
,
8.5 cm
,
16 cm
,
8.5 cm
(iii)
14.5 cm
,
8.5 cm
,
14.5 cm
,
8.5 cm
(iv)
14.5 cm
,
5 cm
,
14.5 cm
,
5 cm
(v)
14.5 cm
,
7 cm
,
14.5 cm
,
7 cm
Question
9
9.
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)
△ABH
(ii)
△DAE
(iii)
△FDA
(iv)
△DCF
(v)
△ACF
Question
10
10.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
IM
=
(i)
MK
(ii)
IJ
(iii)
KI
(iv)
LJ
(v)
IL
Question
11
11.
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)
∠AFD
(ii)
∠HFE
(iii)
∠BHA
(iv)
∠EHF
(v)
∠CFA
Question
12
12.
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)
△FEH
(iii)
△ABH
(iv)
△DCF
(v)
△DAE
Question
13
13.
From the given figure and values, find x
(i)
(
-1
,
18
)
(ii)
(
1
,
19
)
(iii)
(
-1
,
19
)
(iv)
(
0
,
20
)
(v)
(
21
,
1
)
Question
14
14.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
KI
=
(i)
JH
(ii)
GJ
(iii)
IG
(iv)
GH
(v)
GK
Question
15
15.
In the given figure, ABCD is a parallelogram
such that
E
and
F
are mid-points of sides
AB
&
CD
.
AF
meets
BD
at
Q
and
CE
meets
BD
at
R
. Given
BD
=
20 cm
, find
BR
(i)
8.67 cm
(ii)
6.67 cm
(iii)
4.67 cm
(iv)
5.67 cm
(v)
7.67 cm
Question
16
16.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
BC
(ii)
BC
2
(iii)
AB
2
(iv)
AD
(v)
CA
2
Question
17
17.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 27 cm. Find AP
(i)
11.80 cm
(ii)
8.80 cm
(iii)
9.80 cm
(iv)
12.80 cm
(v)
10.80 cm
Question
18
18.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 23 cm. Find AP
(i)
7.20 cm
(ii)
11.20 cm
(iii)
8.20 cm
(iv)
9.20 cm
(v)
10.20 cm
Question
19
19.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
NL
=
(i)
JK
(ii)
JN
(iii)
JM
(iv)
MK
(v)
LJ
Question
20
20.
In the given figure, △FGH is a triangle.
I
,
J
&
K
are mid-points of
GH
,
HF
&
FG
respectively.
Given
IJ = 10 cm
,
JK = 9 cm
&
KI = 9 cm
,
find the sides of the triangle.
(i)
21 cm
,
18 cm
&
18 cm
(ii)
20 cm
,
17 cm
&
18 cm
(iii)
17 cm
,
18 cm
&
18 cm
(iv)
20 cm
,
18 cm
&
18 cm
(v)
20 cm
,
18 cm
&
20 cm
Question
21
21.
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)
∠AFD
(ii)
∠FAC
(iii)
∠FEH
(iv)
∠HFE
(v)
∠FDA
Question
22
22.
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)
Area of
△EFG
=
1
3
area of
△HIJ
b)
Area of △EFG = 4 times area of △HIJ
c)
Area of trapezium FGIJ is thrice the area of △EJI
d)
All four small triangles have equal areas
e)
Area of trapezium
FGIJ
is
1
4
the area of
△EFG
(i)
{b,c,d}
(ii)
{e,c}
(iii)
{a,b}
(iv)
{a,b,c}
(v)
{a,e,d}
Question
23
23.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
DB
=
(i)
CA
(ii)
AB
(iii)
AE
(iv)
EC
(v)
AD
Question
24
24.
In the given figure, KLMN is a trapezium. O and P are mid-points of KN and LM.Given MN = 9 cm and KL = 20 cm, find OP
(i)
16.5 cm
(ii)
14.5 cm
(iii)
12.5 cm
(iv)
13.5 cm
(v)
15.5 cm
Question
25
25.
In the given figure, points P , Q and R are the mid-points of sides NO, OM and MN of △MNO. Which of the following are true?
a)
All four small triangles have equal areas
b)
Area of trapezium NOQR is thrice the area of △MRQ
c)
Area of
△MNO
=
1
3
area of
△PQR
d)
Area of trapezium
NOQR
is
1
4
the area of
△MNO
e)
Area of △MNO = 4 times area of △PQR
(i)
{c,a}
(ii)
{d,b}
(iii)
{a,b,e}
(iv)
{c,d,e}
(v)
{c,a,b}
Assignment Key
1) (iv)
2) (iv)
3) (ii)
4) (iv)
5) (i)
6) (ii)
7) (iii)
8) (iii)
9) (iii)
10) (i)
11) (iv)
12) (ii)
13) (iii)
14) (v)
15) (ii)
16) (v)
17) (v)
18) (iv)
19) (ii)
20) (iv)
21) (ii)
22) (i)
23) (v)
24) (ii)
25) (iii)
