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)
△DAE
(iv)
△DCF
(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.
∠HAB =
(i)
∠FAC
(ii)
∠HFE
(iii)
∠FEH
(iv)
∠AFD
(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.
∠FDA =
(i)
∠ABH
(ii)
∠DAF
(iii)
∠FEH
(iv)
∠EHF
(v)
∠ACF
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.
∠CFA =
(i)
∠HFE
(ii)
∠EHF
(iii)
∠DAF
(iv)
∠BHA
(v)
∠AFD
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)
1
3
of area of △KLM
(ii)
1
2
of area of △KLM
(iii)
1
4
of area of △KLM
(iv)
3
4
of area of △KLM
(v)
2
3
of area of △KLM
Question
6
6.
In the given figure, points D , E and F are the mid-points of sides BC, CA and AB of △ABC. Which of the following are true?
a)
Area of
△ABC
=
1
3
area of
△DEF
b)
Area of △ABC = 4 times area of △DEF
c)
Area of trapezium
BCEF
is
1
4
the area of
△ABC
d)
Area of trapezium BCEF is thrice the area of △AFE
e)
All four small triangles have equal areas
(i)
{a,b}
(ii)
{a,b,d}
(iii)
{b,d,e}
(iv)
{c,d}
(v)
{a,c,e}
Question
7
7.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 24 cm and AP = 10 cm. Find PB
(i)
15.00 cm
(ii)
16.00 cm
(iii)
13.00 cm
(iv)
14.00 cm
(v)
12.00 cm
Question
8
8.
From the given figure and values, find x
(i)
(
18
,
0
)
(ii)
(
2
,
17
)
(iii)
(
15
,
0
)
(iv)
(
16
,
1
)
(v)
(
15
,
-1
)
Question
9
9.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
BC
2
(ii)
CA
2
(iii)
BC
(iv)
AB
2
(v)
AD
Question
10
10.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GJ
=
(i)
GH
2
(ii)
GK
(iii)
IG
2
(iv)
HI
(v)
HI
2
Question
11
11.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DG
=
(i)
DE
(ii)
GE
(iii)
DH
(iv)
HF
(v)
FD
Question
12
12.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
FD
=
(i)
CG
(ii)
CD
(iii)
GE
(iv)
EC
(v)
CF
Question
13
13.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BF
=
(i)
BC
(ii)
DB
(iii)
FD
(iv)
BE
(v)
EC
Question
14
14.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
IG
=
(i)
EI
(ii)
HF
(iii)
EH
(iv)
GE
(v)
EF
Question
15
15.
In the given figure, EFGH is a parallelogram
such that
I
and
J
are mid-points of sides
EF
&
GH
.
EJ
meets
FH
at
S
and
GI
meets
FH
at
T
. Given
FH
=
15 cm
, find
SH
(i)
5.00 cm
(ii)
4.00 cm
(iii)
7.00 cm
(iv)
3.00 cm
(v)
6.00 cm
Question
16
16.
In the given figure, GHIJ is a parallelogram such that R is the mid-point of GH and GH = 2JG. Find ∠JRI
(i)
88°
(ii)
89°
(iii)
91°
(iv)
90°
(v)
92°
Question
17
17.
In the given figure, HIJK is a trapezium. L and M are mid-points of HK and IJ.Given LM = 14 cm and HI = 19 cm, find JK
(i)
9.0 cm
(ii)
7.0 cm
(iii)
8.0 cm
(iv)
11.0 cm
(v)
10.0 cm
Question
18
18.
In the given figure, △ABC is a triangle.
D
,
E
&
F
are mid-points of
BC
,
CA
&
AB
respectively.
Given
DE = 10 cm
,
EF = 8 cm
&
FD = 10 cm
,
find the sides of the triangle.
(i)
20 cm
,
16 cm
&
22 cm
(ii)
20 cm
,
16 cm
&
20 cm
(iii)
17 cm
,
16 cm
&
20 cm
(iv)
21 cm
,
16 cm
&
20 cm
(v)
20 cm
,
15 cm
&
20 cm
Question
19
19.
EFGH is a quadrilateral. R, S, T and U are mid-points of EF, FG, GH and HE respectively.If EG = 30 cm and FH = 15 cm, find the measure of the sides of RSTU.
(i)
15 cm
,
7.5 cm
,
15 cm
,
7.5 cm
(ii)
15 cm
,
5 cm
,
15 cm
,
5 cm
(iii)
16 cm
,
7.5 cm
,
16 cm
,
7.5 cm
(iv)
17 cm
,
7.5 cm
,
17 cm
,
7.5 cm
(v)
15 cm
,
6 cm
,
15 cm
,
6 cm
Assignment Key
1) (v)
2) (i)
3) (iii)
4) (iv)
5) (iii)
6) (iii)
7) (iv)
8) (iii)
9) (ii)
10) (i)
11) (ii)
12) (v)
13) (iii)
14) (i)
15) (i)
16) (iv)
17) (i)
18) (ii)
19) (i)
