EduSahara™ Worksheet

Question 1

1.

(i)

4.45 cm
(ii)

5.45 cm
(iii)

8.45 cm
(iv)

7.45 cm
(v)

6.45 cm

Question 2

2.

In the given figure,
NO
∥
LM
.

(i)

5.40 cm
(ii)

8.40 cm
(iii)

7.40 cm
(iv)

9.40 cm
(v)

6.40 cm

Question 3

3.

In the given figure, RS ∥ BC and AC = 20 cm, RS = 12.6 cm and BC = 21 cm, find AS

(i)

11.0 cm
(ii)

10.0 cm
(iii)

13.0 cm
(iv)

12.0 cm
(v)

14.0 cm

Question 4

4.

In the given figure, △KLM is isosceles right-angled at L and LN ⟂ MK. ∠L =

(i)

∠O
(ii)

∠M
(iii)

∠K
(iv)

∠N
(v)

∠P

Question 5

5.

In the given figure, △MNO is isosceles right-angled at N and NP ⟂ OM. ∠MNO =

(i)

∠PNO
(ii)

∠MNP
(iii)

∠PMN
(iv)

∠NOP
(v)

∠NPM

Question 6

6.

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)

△DAE
(iii)

△ABH
(iv)

△FEH
(v)

△DCF

Question 7

7.

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)

∠FEH
(iv)

∠HAB
(v)

∠HFE

Question 8

8.

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)

∠FDA
(ii)

∠ACF
(iii)

∠FEH
(iv)

∠DAF
(v)

∠EHF

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.

∠CFA =

(i)

∠HFE
(ii)

∠AFD
(iii)

∠BHA
(iv)

∠DAF
(v)

∠EHF

Question 10

10.

In the given figure, NOPQ is a trapezium in which

QR
=
(

4

x

+

2

)
cm, find the value of x

(i)

(

(
-1
4
)

,

10

)
(ii)

(

(
-1
2
)

,

8

)
(iii)

(

1
2

,

9

)
(iv)

(

(
-1
2
)

,

9

)
(v)

(

11

,

3
2

)

Question 11

11.

In the given figure, the altitudes MF and GN of △EFG meet at L. ∠FLN =

(i)

∠LNF
(ii)

∠LGM
(iii)

∠GML
(iv)

∠MLG
(v)

∠NFL

Question 12

12.

In the given figure, RS ∥ HI , and median GJ bisects RS.

If GJ = 19 cm, GR = 9.5 cm and GK = 9.5 cm, GH =

(i)

19.00 cm
(ii)

20.00 cm
(iii)

21.00 cm
(iv)

18.00 cm
(v)

17.00 cm

Question 13

13.

In the given figure, QR ∥ GH , and median FI bisects QR.

If FI = 12.5 cm, FJ = 7.14 cm and FR = 9.14 cm, FH =

(i)

14.00 cm
(ii)

16.00 cm
(iii)

17.00 cm
(iv)

15.00 cm
(v)

18.00 cm

Question 14

14.

In the given figure, △GHI is a triangle in which GJ is the internal bisector of ∠G and IK ∥ JG meeting HG produced at K . ∠GIK =

(i)

∠HJG
(ii)

∠KGI
(iii)

∠JIG
(iv)

∠IGJ
(v)

∠GJI

Question 15

15.

In the given figure, K and L are points on the sides HI and HJ respectively of △HIJ.For which of the following cases, KL ∥ IJ

a)	HI = 17 cm, HK = 10.5 cm, HJ = 16 cm and LJ = 8 cm
b)	HI = 17 cm, KI = 8.5 cm, HJ = 16 cm and HL = 8 cm
c)	HI = 17 cm, KI = 8.5 cm, HL = 10 cm and HJ = 16 cm
d)	HK = 8.5 cm, KI = 8.5 cm, HL = 8 cm and LJ = 8 cm

(i)

{a,b}
(ii)

{c,d}
(iii)

{a,c,b}
(iv)

{a,d,b}
(v)

{b,d}

Question 16

16.

In the given figure, the area of the △MNO is x sq.cm. P,Q,R are the mid-points of the sides NO , OM and MN respectively. The area of the △PQR is

(i)
2
3

of area of △MNO
(ii)
1
3

of area of △MNO
(iii)
1
4

of area of △MNO
(iv)
1
2

of area of △MNO
(v)
3
4

of area of △MNO

Question 17

17.

In the given figure, the parallelogram EFGH and the triangle △IEF are on the same bases and between the same parallels.

The area of the
△IEF
is x sq.cm. The area of the parallelogram is

(i)
4
3

the area of the triangle
(ii)
twice

the area of the triangle
(iii)
thrice

the area of the triangle
(iv)
5
4

the area of the triangle
(v)
3
2

the area of the triangle

Question 18

18.

If the ratio of the bases of two triangles is D : E and the ratio of the corresponding heights is F : G , the ratio of their areas in the same order is

(i)

DG : EF
(ii)

FG : DE
(iii)

EF : DG
(iv)

DE : FG
(v)

DF : EG

Question 19

19.

In the given △KLM, NO ∥ LM. If KN : NL = 9.27 cm : 7.73 cm and KM = 20 cm, KO =

(i)

12.91 cm
(ii)

10.91 cm
(iii)

11.91 cm
(iv)

9.91 cm
(v)

8.91 cm

Question 20

20.

In the given figure, given ∠DAB = ∠CAD, x : y = 6.82 cm : 8.18 cm and q = 18 cm, find p =

(i)

14.00 cm
(ii)

16.00 cm
(iii)

15.00 cm
(iv)

13.00 cm
(v)

17.00 cm

Question 21

21.

In the given figure, given ∠EBC = ∠DBE, p = 10.06 cm, q = 8.94 cm and CD = 19 cm, find CE =

(i)

9.06 cm
(ii)

8.06 cm
(iii)

12.06 cm
(iv)

10.06 cm
(v)

11.06 cm

Question 22

22.

In the given figure, DEFG is a trapezium where OD = 15 cm , OE = 15 cm and OG = 5 cm . Find OF =

(i)

6 cm
(ii)

7 cm
(iii)

3 cm
(iv)

4 cm
(v)

5 cm

Question 23

23.

In the given figure, ∠HIK = 43.38°, find the value of x =

(i)

48.62°
(ii)

46.62°
(iii)

45.62°
(iv)

44.62°
(v)

47.62°

Question 24

24.

In the given figure, ∠IGH = 50.01°, find the value of y =

(i)

38.99°
(ii)

39.99°
(iii)

37.99°
(iv)

41.99°
(v)

40.99°

Question 25

25.

In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. Which of the following are true?

a)

IJ

2
=
KI
.
KL

b)

JK

2
=
IK
.
IL

c)

JK

2
=
KI
.
KL

d)

IJ

2
=
IK
.
IL

e)

JL

2
=
IL
.
LK

(i)

{a,c,d}
(ii)

{a,b,e}
(iii)

{a,c}
(iv)

{b,d}
(v)

{c,d,e}

Question 26

26.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. If EF = 18 cm, FH = 13.07 cm, then find FG.

(i)

20.00 cm
(ii)

21.00 cm
(iii)

17.00 cm
(iv)

18.00 cm
(v)

19.00 cm

Question 27

27.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AD = 9.3 cm, DC = 14.9 cm, then find BD.

(i)

11.77 cm
(ii)

12.77 cm
(iii)

9.77 cm
(iv)

13.77 cm
(v)

10.77 cm

Question 28

28.

In the given figure, △EFG ∼ △MNO and EF = 15 cm, MN = 21 cm.

(i)

74.83 sq.cm
(ii)

73.83 sq.cm
(iii)

72.83 sq.cm
(iv)

75.83 sq.cm
(v)

76.83 sq.cm

Question 29

29.

In the given figure, △CDE ∼ △OPQ and DE = 10 cm , PQ = 14 cm and

(i)

113.71 sq.cm
(ii)

111.71 sq.cm
(iii)

110.71 sq.cm
(iv)

109.71 sq.cm
(v)

112.71 sq.cm

Question 30

30.

In the given figure, △EFG & △PQR are similar triangles. If the ratio of the heights EH : PS = 9 : 13, then the ratio of their areas is

(i)

81

sq.cm

:

169

sq.cm
(ii)

82

sq.cm

:

169

sq.cm
(iii)

81

sq.cm

:

167

sq.cm
(iv)

81

sq.cm

:

172

sq.cm
(v)

80

sq.cm

:

169

sq.cm

Question 31

31.

In the given figure, points J , K and L are the mid-points of sides HI, IG and GH of △GHI. Which of the following are true?

a)

Area of △GHI = 4 times area of △JKL

b)

All four small triangles have equal areas

c)

Area of trapezium HIKL is thrice the area of △GLK

d)

e)

(i)

{e,b}
(ii)

{d,a}
(iii)

{d,e,c}
(iv)

{a,b,c}
(v)

{d,a,b}

Question 32

32.

The perimeters of two similar triangles are 27 cm and 22 cm respectively. If one side of the first triangle is 15 cm, find the length of the corresponding side of the second triangle.

(i)

11.22 cm
(ii)

12.22 cm
(iii)

14.22 cm
(iv)

10.22 cm
(v)

13.22 cm

Question 33

33.

In the given figure, K is a point on side IJ of △HIJ such that ∠JHI = ∠HKJ = 107° , ∠KJH = 25°. Find ∠JHK

(i)

50°
(ii)

49°
(iii)

47°
(iv)

46°
(v)

48°

Question 34

34.

KLMN is a square and △KLO is an equilateral triangle. Also, △KMP is an equilateral triangle. If area of △KLO is 'a' sq.units, then the area of △KMP is

(i)
a

2

sq.units
(ii)
2a sq.units
(iii)
√

3

a sq.units
(iv)
1
2

√

3

a sq.units
(v)
1
2

a sq.units

Question 35

35.

DEFG is a cyclic trapezium. Diagonals EG and DF intersect at H. If GD = 15 cm, find EF

(i)

16 cm
(ii)

17 cm
(iii)

15 cm
(iv)

14 cm
(v)

13 cm

Question 36

36.

A vertical stick
13 m
long casts a shadow of
14 m
long on the ground.

At the same time, a tower casts the shadow
112 m
long on the ground.

Find the height of the tower.

(i)

102 m
(ii)

106 m
(iii)

105 m
(iv)

103 m
(v)

104 m

Question 37

37.

In the given figure, △BCD, RS ∥ CD such that

(i)

1
2

4
√

2
(ii)

1
2

√

2
(iii)

1
2

√

5
(iv)

1
(v)

1
2

√

-1

Question 38

38.

In the given figure, △DFE is right-angled at F, FG ⟂ DE.

a)

a

2
+
b

2
=
c

2

b)

1

a

2
+
1

b

2
=
1

p

2

c)

ab
=
pc

d)

e)

(i)

{d,e,c}
(ii)

{d,a,b}
(iii)

{d,a}
(iv)

{e,b}
(v)

{a,b,c}

Question 39

39.

In an equilateral triangle ABC, the side BC is trisected at D. Then

(i)
9 AD

2

=

7 AB

2
(ii)
3 AD

2

=

7 AB

2
(iii)
7 AD

2

=

9 AB

2
(iv)
7 AD

2

=

3 AB

2

Question 40

40.

In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 15 cm, HJ = 6 cm and JI = 9 cm. Find GK

(i)

21.50 cm
(ii)

22.50 cm
(iii)

20.50 cm
(iv)

24.50 cm
(v)

23.50 cm

Question 41

41.

In the given figure, DF is the angular bisector of
∠D
&
∠F

(i)

19.00 cm
(ii)

18.00 cm
(iii)

17.00 cm
(iv)

21.00 cm
(v)

20.00 cm

Question 42

42.

In the given figure, ABC is a triangle and 'O' is a point inside △ABC. The angular bisector of ∠BOA, ∠COB & ∠AOC meet AB, BC & CA at D, E & F respectively . Then