EduSahara™ Worksheet

Question 1

1.

(i)

8.08 cm
(ii)

5.08 cm
(iii)

6.08 cm
(iv)

7.08 cm
(v)

9.08 cm

Question 2

2.

In the given figure,
PQ
∥
NO
.

(i)

9.32 cm
(ii)

5.32 cm
(iii)

8.32 cm
(iv)

7.32 cm
(v)

6.32 cm

Question 3

3.

In the given figure, ST ∥ FG and EG = 22 cm, ST = 13.2 cm and FG = 22 cm, find ET

(i)

11.2 cm
(ii)

14.2 cm
(iii)

13.2 cm
(iv)

15.2 cm
(v)

12.2 cm

Question 4

4.

In the given figure, △HIJ is isosceles right-angled at I and IK ⟂ JH. ∠I =

(i)

∠L
(ii)

∠J
(iii)

∠H
(iv)

∠M
(v)

∠K

Question 5

5.

In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠SQR ≠

(i)

∠RPQ
(ii)

∠PQS
(iii)

∠QRS
(iv)

∠SPQ
(v)

∠RSQ

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.

△FDA ∼

(i)

△ACF
(ii)

△FEH
(iii)

△ABH
(iv)

△DAE
(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)

∠FEH
(ii)

∠FAC
(iii)

∠FDA
(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.

∠ACF =

(i)

∠EHF
(ii)

∠FEH
(iii)

∠DAF
(iv)

∠ABH
(v)

∠FDA

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.

∠DAF =

(i)

∠EHF
(ii)

∠HFE
(iii)

∠AFD
(iv)

∠CFA
(v)

∠BHA

Question 10

10.

In the given figure, LMNO is a trapezium in which

OP
=
(

8

x

+

4

)
cm, find the value of x

(i)

(

6

,

0

)
(ii)

(

6

,

-1

)
(iii)

(

8

,

0

)
(iv)

(

7

,

1

)
(v)

(

2

,

8

)

Question 11

11.

In the given figure, the altitudes PF and GQ of △EFG meet at O. ∠GOF =

(i)

∠OFG
(ii)

∠QOP
(iii)

∠PQO
(iv)

∠OPQ
(v)

∠FGO

Question 12

12.

In the given figure, ST ∥ CD , and median BE bisects ST.

If BC = 16 cm, BS = 9.14 cm and BF = 9.14 cm, BE =

(i)

14.00 cm
(ii)

18.00 cm
(iii)

16.00 cm
(iv)

15.00 cm
(v)

17.00 cm

Question 13

13.

In the given figure, ST ∥ JK , and median IL bisects ST.

If IL = 14.9 cm, IK = 17 cm and IT = 10.62 cm, IM =

(i)

8.31 cm
(ii)

7.31 cm
(iii)

10.31 cm
(iv)

11.31 cm
(v)

9.31 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)

∠KGI
(ii)

∠HJG
(iii)

∠JGH
(iv)

∠GJI
(v)

∠JIG

Question 15

15.

In the given figure, Q and R are points on the sides NO and NP respectively of △NOP.For which of the following cases, QR ∥ OP

a)	NO = 17 cm, QO = 9.71 cm, NR = 10.14 cm and NP = 19 cm
b)	NQ = 7.29 cm, QO = 9.71 cm, NR = 8.14 cm and RP = 10.86 cm
c)	NO = 17 cm, NQ = 9.29 cm, NP = 19 cm and RP = 10.86 cm
d)	NO = 17 cm, QO = 9.71 cm, NP = 19 cm and NR = 8.14 cm

(i)

{c,d}
(ii)

{a,c,b}
(iii)

{a,d,b}
(iv)

{b,d}
(v)

{a,b}

Question 16

16.

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)
1
3

of area of △ABC
(v)
2
3

of area of △ABC

Question 17

17.

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

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

(i)
twice

the area of the triangle
(ii)
5
4

the area of the triangle
(iii)
3
2

the area of the triangle
(iv)
4
3

the area of the triangle
(v)
thrice

the area of the triangle

Question 18

18.

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

(i)

HI : FG
(ii)

GH : FI
(iii)

FG : HI
(iv)

FH : GI
(v)

FI : GH

Question 19

19.

In the given △BCD, EF ∥ CD. If BE : EC = 6.67 cm : 13.33 cm and BD = 16 cm, BF =

(i)

5.33 cm
(ii)

3.33 cm
(iii)

4.33 cm
(iv)

7.33 cm
(v)

6.33 cm

Question 20

20.

In the given figure, given ∠IFG = ∠HFI, x : y = 8.26 cm : 7.74 cm and p = 16 cm, find q =

(i)

16.00 cm
(ii)

15.00 cm
(iii)

13.00 cm
(iv)

14.00 cm
(v)

17.00 cm

Question 21

21.

In the given figure, given ∠EBC = ∠DBE, p = 10.29 cm, q = 7.71 cm and CD = 18 cm, find CE =

(i)

8.29 cm
(ii)

10.29 cm
(iii)

9.29 cm
(iv)

11.29 cm
(v)

12.29 cm

Question 22

22.

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

(i)

5 cm
(ii)

3 cm
(iii)

4 cm
(iv)

6 cm
(v)

7 cm

Question 23

23.

In the given figure, ∠HEF = 50.5°, find the value of x =

(i)

39.50°
(ii)

37.50°
(iii)

38.50°
(iv)

40.50°
(v)

41.50°

Question 24

24.

In the given figure, ∠KIJ = 43.38°, find the value of y =

(i)

44.62°
(ii)

45.62°
(iii)

47.62°
(iv)

46.62°
(v)

48.62°

Question 25

25.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. Which of the following are true?

a)

EF

2
=
EG
.
EH

b)

FH

2
=
EH
.
HG

c)

FG

2
=
EG
.
EH

d)

EF

2
=
GE
.
GH

e)

FG

2
=
GE
.
GH

(i)

{c,a}
(ii)

{c,a,b}
(iii)

{d,b}
(iv)

{c,d,e}
(v)

{a,b,e}

Question 26

26.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If GH = 20 cm, HJ = 12.49 cm, then find HI.

(i)

17.00 cm
(ii)

14.00 cm
(iii)

18.00 cm
(iv)

15.00 cm
(v)

16.00 cm

Question 27

27.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FI = 14.2 cm, GI = 12.67 cm, then find IH.

(i)

10.30 cm
(ii)

9.30 cm
(iii)

13.30 cm
(iv)

12.30 cm
(v)

11.30 cm

Question 28

28.

In the given figure, △DEF ∼ △PQR and DE = 11 cm, PQ = 15.4 cm.

(i)

57.68 sq.cm
(ii)

58.68 sq.cm
(iii)

55.68 sq.cm
(iv)

59.68 sq.cm
(v)

56.68 sq.cm

Question 29

29.

In the given figure, △ABC ∼ △OPQ and BC = 14 cm , PQ = 19.6 cm and

(i)

70.81 sq.cm
(ii)

69.81 sq.cm
(iii)

71.81 sq.cm
(iv)

72.81 sq.cm
(v)

68.81 sq.cm

Question 30

30.

In the given figure, △CDE & △MNO are similar triangles. If the ratio of the heights CF : MP = 10 : 14, then the ratio of their areas is

(i)

100

sq.cm

:

198

sq.cm
(ii)

99

sq.cm

:

196

sq.cm
(iii)

100

sq.cm

:

196

sq.cm
(iv)

101

sq.cm

:

196

sq.cm
(v)

100

sq.cm

:

194

sq.cm

Question 31

31.

In the given figure, points I , J and K are the mid-points of sides GH, HF and FG of △FGH. Which of the following are true?

a)

b)

Area of trapezium GHJK is thrice the area of △FKJ

c)

Area of △FGH = 4 times area of △IJK

d)

e)

All four small triangles have equal areas

(i)

{b,c,e}
(ii)

{a,d,e}
(iii)

{a,b,c}
(iv)

{a,b}
(v)

{d,c}

Question 32

32.

The perimeters of two similar triangles are 26 cm and 24 cm respectively. If one side of the first triangle is 14 cm, find the length of the corresponding side of the second triangle.

(i)

10.92 cm
(ii)

11.92 cm
(iii)

14.92 cm
(iv)

13.92 cm
(v)

12.92 cm

Question 33

33.

In the given figure, I is a point on side GH of △FGH such that ∠HFG = ∠FIH = 107° , ∠IHF = 28°. Find ∠HFI

(i)

44°
(ii)

47°
(iii)

46°
(iv)

45°
(v)

43°

Question 34

34.

LMNO is a square and △LMP is an equilateral triangle. Also, △LNQ is an equilateral triangle. If area of △LMP is 'a' sq.units, then the area of △LNQ is

(i)
1
2

√

3

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

a sq.units
(iv)
a

2

sq.units
(v)
√

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)

17 cm
(ii)

16 cm
(iii)

14 cm
(iv)

15 cm
(v)

13 cm

Question 36

36.

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

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

Find the height of the tower.

(i)

105 m
(ii)

103 m
(iii)

104 m
(iv)

106 m
(v)

102 m

Question 37

37.

In the given figure, △GHI, QR ∥ HI such that

(i)

1
2

√

2
(ii)

1
(iii)

1
2

√

1
2
(iv)

1
2

4
√

2
(v)

1
2

√

5

Question 38

38.

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

a)

ab
=
pc

b)

1

a

2
+
1

b

2
=
1

p

2

c)

d)

e)

a

2
+
b

2
=
c

2

(i)

{c,d,e}
(ii)

{d,b}
(iii)

{c,a}
(iv)

{c,a,b}
(v)

{a,b,e}

Question 39

39.

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

(i)
3 AD

2

=

7 AB

2
(ii)
9 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, ∠KHI = ∠JHK and HK ∥ LJ and HI = 17 cm, IK = 7 cm and KJ = 8 cm. Find HL

(i)

21.43 cm
(ii)

19.43 cm
(iii)

18.43 cm
(iv)

17.43 cm
(v)

20.43 cm

Question 41

41.

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

(i)

24.00 cm
(ii)

23.00 cm
(iii)

22.00 cm
(iv)

25.00 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