EduSahara™ Worksheet

Question 1

1.

(i)

5.76 cm
(ii)

6.76 cm
(iii)

4.76 cm
(iv)

3.76 cm
(v)

2.76 cm

Question 2

2.

In the given figure,
OP
∥
MN
.

(i)

4.18 cm
(ii)

5.18 cm
(iii)

7.18 cm
(iv)

8.18 cm
(v)

6.18 cm

Question 3

3.

In the given figure, RS ∥ FG and ER = 15 cm, EF = 25 cm and RS = 13.2 cm, find FG

(i)

22.0 cm
(ii)

23.0 cm
(iii)

24.0 cm
(iv)

20.0 cm
(v)

21.0 cm

Question 4

4.

In the given figure, △BCD is isosceles right-angled at C and CE ⟂ DB. ∠C =

(i)

∠D
(ii)

∠F
(iii)

∠E
(iv)

∠B
(v)

∠G

Question 5

5.

In the given figure, △JKL is isosceles right-angled at K and KM ⟂ LJ. ∠KMJ =

(i)

∠KLM
(ii)

∠MJK
(iii)

∠JKL
(iv)

∠MKL
(v)

∠JKM

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.

△ABH ∼

(i)

△FDA
(ii)

△ACF
(iii)

△DAE
(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.

∠FAC =

(i)

∠HFE
(ii)

∠FDA
(iii)

∠HAB
(iv)

∠FEH
(v)

∠AFD

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.

∠FDA =

(i)

∠DAF
(ii)

∠ABH
(iii)

∠EHF
(iv)

∠FEH
(v)

∠ACF

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.

∠BHA =

(i)

∠EHF
(ii)

∠AFD
(iii)

∠CFA
(iv)

∠DAF
(v)

∠HFE

Question 10

10.

In the given figure, EFGH is a trapezium in which

HI
=
(

2

x

+

18

)
cm, find the value of x

(i)

(

(
-7
2
)

,

26

)
(ii)

(

28

,

(
-7
2
)

)
(iii)

(

(
-9
2
)

,

26

)
(iv)

(

(
-17
4
)

,

27

)
(v)

(

(
-9
2
)

,

25

)

Question 11

11.

In the given figure, the altitudes RJ and KS of △IJK meet at Q. ∠KQJ =

(i)

∠QRS
(ii)

∠SQR
(iii)

∠QJK
(iv)

∠RSQ
(v)

∠JKQ

Question 12

12.

In the given figure, TU ∥ DE , and median CF bisects TU.

If CD = 16 cm, CF = 16.1 cm and CT = 8.89 cm, CG =

(i)

7.94 cm
(ii)

8.94 cm
(iii)

9.94 cm
(iv)

10.94 cm
(v)

6.94 cm

Question 13

13.

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

If GJ = 12.6 cm, GK = 7.56 cm and GQ = 9 cm, GI =

(i)

17.00 cm
(ii)

14.00 cm
(iii)

13.00 cm
(iv)

16.00 cm
(v)

15.00 cm

Question 14

14.

In the given figure, △BCD is a triangle in which BE is the internal bisector of ∠B and DF ∥ EB meeting CB produced at F . ∠BDF =

(i)

∠EDB
(ii)

∠DFB
(iii)

∠CEB
(iv)

∠FBD
(v)

∠BED

Question 15

15.

In the given figure, J and K are points on the sides GH and GI respectively of △GHI.For which of the following cases, JK ∥ HI

a)	GH = 15 cm, JH = 8.57 cm, GI = 16 cm and GK = 6.86 cm
b)	GH = 15 cm, GJ = 8.43 cm, GI = 16 cm and KI = 9.14 cm
c)	GH = 15 cm, JH = 8.57 cm, GK = 8.86 cm and GI = 16 cm
d)	GJ = 6.43 cm, JH = 8.57 cm, GK = 6.86 cm and KI = 9.14 cm

(i)

{b,a}
(ii)

{b,c,a}
(iii)

{c,d}
(iv)

{a,d}
(v)

{b,d,a}

Question 16

16.

In the given figure, the area of the △BCD is x sq.cm. E,F,G are the mid-points of the sides CD , DB and BC respectively. The area of the △EFG is

(i)
1
4

of area of △BCD
(ii)
3
4

of area of △BCD
(iii)
2
3

of area of △BCD
(iv)
1
2

of area of △BCD
(v)
1
3

of area of △BCD

Question 17

17.

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

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

(i)
thrice

the area of the triangle
(ii)
5
4

the area of the triangle
(iii)
twice

the area of the triangle
(iv)
4
3

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 I : J and the ratio of the corresponding heights is K : L , the ratio of their areas in the same order is

(i)

KL : IJ
(ii)

JK : IL
(iii)

IL : JK
(iv)

IK : JL
(v)

IJ : KL

Question 19

19.

In the given △IJK, LM ∥ JK. If IL : LJ = 6.86 cm : 9.14 cm and IK = 18 cm, MK =

(i)

9.29 cm
(ii)

12.29 cm
(iii)

11.29 cm
(iv)

8.29 cm
(v)

10.29 cm

Question 20

20.

In the given figure, given ∠JGH = ∠IGJ, x : y = 8.65 cm : 7.35 cm and p = 20 cm, find q =

(i)

19.00 cm
(ii)

16.00 cm
(iii)

18.00 cm
(iv)

17.00 cm
(v)

15.00 cm

Question 21

21.

In the given figure, given ∠JGH = ∠IGJ, p = 7.31 cm, q = 7.69 cm and HI = 15 cm, find JI =

(i)

7.69 cm
(ii)

6.69 cm
(iii)

9.69 cm
(iv)

5.69 cm
(v)

8.69 cm

Question 22

22.

In the given figure, BCDE is a trapezium where OB = 14 cm , OD = 5 cm and OE = 5 cm . Find OC =

(i)

14 cm
(ii)

12 cm
(iii)

16 cm
(iv)

15 cm
(v)

13 cm

Question 23

23.

In the given figure, ∠DAB = 43.89°, find the value of x =

(i)

48.11°
(ii)

45.11°
(iii)

47.11°
(iv)

44.11°
(v)

46.11°

Question 24

24.

In the given figure, ∠IJK = 36.87°, find the value of y =

(i)

51.13°
(ii)

54.13°
(iii)

53.13°
(iv)

52.13°
(v)

55.13°

Question 25

25.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. Which of the following are true?

a)

CD

2
=
CE
.
CF

b)

CD

2
=
EC
.
EF

c)

DE

2
=
CE
.
CF

d)

DE

2
=
EC
.
EF

e)

DF

2
=
CF
.
FE

(i)

{a,d,e}
(ii)

{b,a}
(iii)

{b,c,e}
(iv)

{b,a,d}
(v)

{c,d}

Question 26

26.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. If CD = 19 cm, DE = 17 cm, then find DF.

(i)

11.67 cm
(ii)

13.67 cm
(iii)

10.67 cm
(iv)

12.67 cm
(v)

14.67 cm

Question 27

27.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FI = 14.8 cm, IH = 12.1 cm, then find GI.

(i)

11.38 cm
(ii)

14.38 cm
(iii)

13.38 cm
(iv)

12.38 cm
(v)

15.38 cm

Question 28

28.

In the given figure, △ABC ∼ △PQR and AB = 14 cm, PQ = 19.6 cm.

(i)

181.02 sq.cm
(ii)

183.02 sq.cm
(iii)

180.02 sq.cm
(iv)

184.02 sq.cm
(v)

182.02 sq.cm

Question 29

29.

In the given figure, △DEF ∼ △OPQ and EF = 15 cm , PQ = 21 cm and

(i)

75.48 sq.cm
(ii)

73.48 sq.cm
(iii)

71.48 sq.cm
(iv)

72.48 sq.cm
(v)

74.48 sq.cm

Question 30

30.

In the given figure, △DEF & △PQR are similar triangles. If the ratio of the heights DG : PS = 10 : 14, then the ratio of their areas is

(i)

100

sq.cm

:

194

sq.cm
(ii)

99

sq.cm

:

196

sq.cm
(iii)

100

sq.cm

:

199

sq.cm
(iv)

101

sq.cm

:

196

sq.cm
(v)

100

sq.cm

:

196

sq.cm

Question 31

31.

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)

Area of trapezium NOQR is thrice the area of △MRQ

b)

c)

Area of △MNO = 4 times area of △PQR

d)

All four small triangles have equal areas

e)

(i)

{b,a,c}
(ii)

{a,c,d}
(iii)

{e,c}
(iv)

{b,a}
(v)

{b,e,d}

Question 32

32.

The perimeters of two similar triangles are 27 cm and 16 cm respectively. If one side of the first triangle is 9 cm, find the length of the corresponding side of the second triangle.

(i)

5.33 cm
(ii)

4.33 cm
(iii)

7.33 cm
(iv)

6.33 cm
(v)

3.33 cm

Question 33

33.

In the given figure, K is a point on side IJ of △HIJ such that ∠JHI = ∠HKJ = 107° , ∠KJH = 21°. Find ∠JHK

(i)

53°
(ii)

52°
(iii)

51°
(iv)

54°
(v)

50°

Question 34

34.

EFGH is a square and △EFI is an equilateral triangle. Also, △EGJ is an equilateral triangle. If area of △EFI is 'a' sq.units, then the area of △EGJ is

(i)
√

3

a sq.units
(ii)
2a sq.units
(iii)
1
2

a sq.units
(iv)
a

2

sq.units
(v)
1
2

√

3

a sq.units

Question 35

35.

EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 15 cm, find FG

(i)

16 cm
(ii)

15 cm
(iii)

17 cm
(iv)

14 cm
(v)

13 cm

Question 36

36.

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

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

Find the height of the tower.

(i)

111 m
(ii)

114 m
(iii)

110 m
(iv)

113 m
(v)

112 m

Question 37

37.

In the given figure, △ABC, QR ∥ BC such that

(i)

1
2

√

1
2
(ii)

1
2

4
√

2
(iii)

1
2

√

2
(iv)

1
2

√

5
(v)

1

Question 38

38.

In the given figure, △BDC is right-angled at D, DE ⟂ BC.

a)

b)

c)

ab
=
pc

d)

a

2
+
b

2
=
c

2

e)

1

a

2
+
1

b

2
=
1

p

2

(i)

{a,c,d}
(ii)

{c,d,e}
(iii)

{b,d}
(iv)

{a,b,e}
(v)

{a,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)
7 AD

2

=

9 AB

2
(iii)
3 AD

2

=

7 AB

2
(iv)
7 AD

2

=

3 AB

2

Question 40

40.

In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 18 cm, HJ = 8 cm and JI = 8 cm. Find GK

(i)

17.00 cm
(ii)

18.00 cm
(iii)

19.00 cm
(iv)

20.00 cm
(v)

16.00 cm

Question 41

41.

In the given figure, KM is the angular bisector of
∠K
&
∠M

(i)

23.00 cm
(ii)

20.00 cm
(iii)

22.00 cm
(iv)

24.00 cm
(v)

21.00 cm

Question 42

42.

In the given figure, BCD is a triangle and 'O' is a point inside △BCD. The angular bisector of ∠COB, ∠DOC & ∠BOD meet BC, CD & DB at E, F & G respectively . Then