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.
△FEH ∼
(i)
△DAE
(ii)
△FDA
(iii)
△ACF
(iv)
△ABH
(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.
∠HFE =
(i)
∠AFD
(ii)
∠HAB
(iii)
∠FEH
(iv)
∠FDA
(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)
∠ACF
(ii)
∠EHF
(iii)
∠FEH
(iv)
∠DAF
(v)
∠FDA
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.
∠EHF =
(i)
∠HFE
(ii)
∠AFD
(iii)
∠DAF
(iv)
∠CFA
(v)
∠BHA
Question
5
5.
In the given figure, the area of the △HIJ is x sq.cm. K,L,M are the mid-points of the sides IJ , JH and HI respectively. The area of the △KLM is
(i)
3
4
of area of △HIJ
(ii)
2
3
of area of △HIJ
(iii)
1
4
of area of △HIJ
(iv)
1
3
of area of △HIJ
(v)
1
2
of area of △HIJ
Question
6
6.
In the given figure, points G , H and I are the mid-points of sides EF, FD and DE of △DEF. Which of the following are true?
a)
Area of trapezium EFHI is thrice the area of △DIH
b)
Area of
△DEF
=
1
3
area of
△GHI
c)
Area of trapezium
EFHI
is
1
4
the area of
△DEF
d)
All four small triangles have equal areas
e)
Area of △DEF = 4 times area of △GHI
(i)
{c,d}
(ii)
{b,c,e}
(iii)
{a,d,e}
(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 = 25 cm. Find AP
(i)
8.00 cm
(ii)
9.00 cm
(iii)
10.00 cm
(iv)
12.00 cm
(v)
11.00 cm
Question
8
8.
From the given figure and values, find x
(i)
(
18
,
-3
)
(ii)
(
19
,
(
-9
4
)
)
(iii)
(
(
-1
2
)
,
20
)
(iv)
(
20
,
(
-5
2
)
)
(v)
(
18
,
(
-5
2
)
)
Question
9
9.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HL
=
(i)
IJ
(ii)
HK
(iii)
HI
2
(iv)
IJ
2
(v)
JH
2
Question
10
10.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
AB
2
(ii)
CA
2
(iii)
BC
2
(iv)
BC
(v)
AE
Question
11
11.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FI
=
(i)
IG
(ii)
JH
(iii)
HF
(iv)
FJ
(v)
FG
Question
12
12.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
DB
=
(i)
AE
(ii)
EC
(iii)
AD
(iv)
AB
(v)
CA
Question
13
13.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HL
=
(i)
HK
(ii)
KI
(iii)
JH
(iv)
HI
(v)
LJ
Question
14
14.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
FD
=
(i)
BE
(ii)
DB
(iii)
EC
(iv)
BF
(v)
BC
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
U
and
GI
meets
FH
at
V
. Given
FH
=
16 cm
, find
UH
(i)
7.33 cm
(ii)
6.33 cm
(iii)
3.33 cm
(iv)
4.33 cm
(v)
5.33 cm
Question
16
16.
In the given figure, FGHI is a parallelogram such that Q is the mid-point of FG and FG = 2IF. Find ∠IQH
(i)
88°
(ii)
90°
(iii)
91°
(iv)
89°
(v)
92°
Question
17
17.
In the given figure, FGHI is a trapezium. J and K are mid-points of FI and GH.Given FG = 19 cm and JK = 14 cm, find HI
(i)
8.0 cm
(ii)
11.0 cm
(iii)
9.0 cm
(iv)
10.0 cm
(v)
7.0 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 = 8 cm
,
find the sides of the triangle.
(i)
20 cm
,
18 cm
&
16 cm
(ii)
21 cm
,
18 cm
&
16 cm
(iii)
20 cm
,
17 cm
&
16 cm
(iv)
17 cm
,
18 cm
&
16 cm
(v)
20 cm
,
18 cm
&
18 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 = 31 cm and FH = 15 cm, find the measure of the sides of RSTU.
(i)
15.5 cm
,
6 cm
,
15.5 cm
,
6 cm
(ii)
16 cm
,
7.5 cm
,
16 cm
,
7.5 cm
(iii)
18 cm
,
7.5 cm
,
18 cm
,
7.5 cm
(iv)
15.5 cm
,
5 cm
,
15.5 cm
,
5 cm
(v)
15.5 cm
,
7.5 cm
,
15.5 cm
,
7.5 cm
Assignment Key
1) (ii)
2) (i)
3) (i)
4) (iii)
5) (iii)
6) (iii)
7) (iii)
8) (v)
9) (v)
10) (i)
11) (i)
12) (iii)
13) (v)
14) (iv)
15) (v)
16) (ii)
17) (iii)
18) (i)
19) (v)
