EduSahara™ Worksheet

Question 1

1.

(i)

2.80 cm
(ii)

1.80 cm
(iii)

5.80 cm
(iv)

4.80 cm
(v)

3.80 cm

Question 2

2.

In the given figure,
FG
∥
DE
.

(i)

7.31 cm
(ii)

4.31 cm
(iii)

6.31 cm
(iv)

5.31 cm
(v)

3.31 cm

Question 3

3.

In the given figure, PQ ∥ DE and CD = 24 cm, PQ = 13.2 cm and DE = 22 cm, find CP

(i)

12.4 cm
(ii)

15.4 cm
(iii)

16.4 cm
(iv)

14.4 cm
(v)

13.4 cm

Question 4

4.

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

(i)

∠F
(ii)

∠E
(iii)

∠D
(iv)

∠G
(v)

∠C

Question 5

5.

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

(i)

∠MNO
(ii)

∠PMN
(iii)

∠MNP
(iv)

∠OMN
(v)

∠PNO

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)

△FEH
(ii)

△DAE
(iii)

△DCF
(iv)

△ABH
(v)

△FDA

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.

∠HFE =

(i)

∠HAB
(ii)

∠FDA
(iii)

∠FEH
(iv)

∠AFD
(v)

∠FAC

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)

∠EHF
(ii)

∠FEH
(iii)

∠DAF
(iv)

∠FDA
(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.

∠EHF =

(i)

∠AFD
(ii)

∠BHA
(iii)

∠CFA
(iv)

∠DAF
(v)

∠HFE

Question 10

10.

In the given figure, IJKL is a trapezium in which

LM
=
(

x

+

24

)
cm, find the value of x

(i)

(

8

,

28

)
(ii)

(

26

,

6

)
(iii)

(

27

,

7

)
(iv)

(

29

,

6

)
(v)

(

26

,

5

)

Question 11

11.

In the given figure, the altitudes QI and JR of △HIJ meet at P. ∠RIP =

(i)

∠QPJ
(ii)

∠JQP
(iii)

∠PJQ
(iv)

∠PRI
(v)

∠IPR

Question 12

12.

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

If BE = 18 cm, BS = 9 cm and BF = 9 cm, BC =

(i)

18.00 cm
(ii)

16.00 cm
(iii)

17.00 cm
(iv)

19.00 cm
(v)

20.00 cm

Question 13

13.

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

If IL = 16.4 cm, IK = 17 cm and IU = 8.5 cm, IM =

(i)

7.20 cm
(ii)

9.20 cm
(iii)

10.20 cm
(iv)

8.20 cm
(v)

6.20 cm

Question 14

14.

In the given figure, △LMN is a triangle in which LO is the internal bisector of ∠L and NP ∥ OL meeting ML produced at P . ∠OLM =

(i)

∠MOL
(ii)

∠PLN
(iii)

∠NLO
(iv)

∠ONL
(v)

∠LON

Question 15

15.

In the given figure, D and E are points on the sides AB and AC respectively of △ABC.For which of the following cases, DE ∥ BC

a)	AB = 16 cm, DB = 9.14 cm, AE = 8.43 cm and AC = 15 cm
b)	AB = 16 cm, AD = 8.86 cm, AC = 15 cm and EC = 8.57 cm
c)	AD = 6.86 cm, DB = 9.14 cm, AE = 6.43 cm and EC = 8.57 cm
d)	AB = 16 cm, DB = 9.14 cm, AC = 15 cm and AE = 6.43 cm

(i)

{a,b,c}
(ii)

{a,d,c}
(iii)

{b,d}
(iv)

{c,d}
(v)

{a,c}

Question 16

16.

In the given figure, the area of the △IJK is x sq.cm. L,M,N are the mid-points of the sides JK , KI and IJ respectively. The area of the △LMN is

(i)
1
4

of area of △IJK
(ii)
2
3

of area of △IJK
(iii)
1
3

of area of △IJK
(iv)
3
4

of area of △IJK
(v)
1
2

of area of △IJK

Question 17

17.

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

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

(i)
3
2

the area of the triangle
(ii)
5
4

the area of the triangle
(iii)
twice

the area of the triangle
(iv)
thrice

the area of the triangle
(v)
4
3

the area of the triangle

Question 18

18.

If the ratio of the bases of two triangles is M : N and the ratio of the corresponding heights is O : P , the ratio of their areas in the same order is

(i)

OP : MN
(ii)

NO : MP
(iii)

MP : NO
(iv)

MN : OP
(v)

MO : NP

Question 19

19.

In the given △EFG, HI ∥ FG. If EH : HF = 10.62 cm : 6.38 cm and EG = 20 cm, IG =

(i)

8.50 cm
(ii)

5.50 cm
(iii)

7.50 cm
(iv)

9.50 cm
(v)

6.50 cm

Question 20

20.

In the given figure, given ∠HEF = ∠GEH, x : y = 9.19 cm : 9.81 cm and q = 16 cm, find p =

(i)

17.00 cm
(ii)

16.00 cm
(iii)

15.00 cm
(iv)

14.00 cm
(v)

13.00 cm

Question 21

21.

In the given figure, given ∠KHI = ∠JHK, p = 7.31 cm, q = 8.69 cm and IJ = 16 cm, find KJ =

(i)

10.69 cm
(ii)

7.69 cm
(iii)

8.69 cm
(iv)

9.69 cm
(v)

6.69 cm

Question 22

22.

In the given figure, IJKL is a trapezium where OI = 12 cm , OK = 4 cm and OL = 4 cm . Find OJ =

(i)

10 cm
(ii)

13 cm
(iii)

14 cm
(iv)

11 cm
(v)

12 cm

Question 23

23.

In the given figure, ∠DAB = 48.02°, find the value of x =

(i)

43.98°
(ii)

41.98°
(iii)

39.98°
(iv)

40.98°
(v)

42.98°

Question 24

24.

In the given figure, ∠HFG = 47.73°, find the value of y =

(i)

40.27°
(ii)

42.27°
(iii)

44.27°
(iv)

43.27°
(v)

41.27°

Question 25

25.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. Which of the following are true?

a)

FG

2
=
FH
.
FI

b)

FG

2
=
HF
.
HI

c)

GI

2
=
FI
.
IH

d)

GH

2
=
HF
.
HI

e)

GH

2
=
FH
.
FI

(i)

{b,a}
(ii)

{b,a,c}
(iii)

{e,c}
(iv)

{a,c,d}
(v)

{b,e,d}

Question 26

26.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. If CD = 16 cm, DF = 10.94 cm, then find DE.

(i)

13.00 cm
(ii)

17.00 cm
(iii)

15.00 cm
(iv)

16.00 cm
(v)

14.00 cm

Question 27

27.

In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If HK = 10.2 cm, IK = 10.92 cm, then find KJ.

(i)

11.70 cm
(ii)

13.70 cm
(iii)

12.70 cm
(iv)

10.70 cm
(v)

9.70 cm

Question 28

28.

In the given figure, △EFG ∼ △OPQ and EF = 12 cm, OP = 16.8 cm.

(i)

56.66 sq.cm
(ii)

59.66 sq.cm
(iii)

60.66 sq.cm
(iv)

57.66 sq.cm
(v)

58.66 sq.cm

Question 29

29.

In the given figure, △DEF ∼ △MNO and EF = 15 cm , NO = 21 cm and

(i)

139.59 sq.cm
(ii)

137.59 sq.cm
(iii)

136.59 sq.cm
(iv)

140.59 sq.cm
(v)

138.59 sq.cm

Question 30

30.

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

(i)

80

sq.cm

:

169

sq.cm
(ii)

81

sq.cm

:

169

sq.cm
(iii)

81

sq.cm

:

171

sq.cm
(iv)

82

sq.cm

:

169

sq.cm
(v)

81

sq.cm

:

166

sq.cm

Question 31

31.

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)

b)

Area of trapezium EFHI is thrice the area of △DIH

c)

All four small triangles have equal areas

d)

Area of △DEF = 4 times area of △GHI

e)

(i)

{e,c}
(ii)

{a,b}
(iii)

{a,b,c}
(iv)

{a,e,d}
(v)

{b,c,d}

Question 32

32.

The perimeters of two similar triangles are 32 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)

9.31 cm
(ii)

10.31 cm
(iii)

12.31 cm
(iv)

11.31 cm
(v)

8.31 cm

Question 33

33.

In the given figure, J is a point on side HI of △GHI such that ∠IGH = ∠GJI = 109° , ∠JIG = 23°. Find ∠IGJ

(i)

48°
(ii)

46°
(iii)

49°
(iv)

50°
(v)

47°

Question 34

34.

JKLM is a square and △JKN is an equilateral triangle. Also, △JLO is an equilateral triangle. If area of △JKN is 'a' sq.units, then the area of △JLO is

(i)
1
2

√

3

a sq.units
(ii)
a

2

sq.units
(iii)
2a sq.units
(iv)
√

3

a sq.units
(v)
1
2

a sq.units

Question 35

35.

EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 18 cm, find FG

(i)

19 cm
(ii)

18 cm
(iii)

16 cm
(iv)

20 cm
(v)

17 cm

Question 36

36.

A vertical stick
16 m
long casts a shadow of
11 m
long on the ground.

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

Find the height of the tower.

(i)

126 m
(ii)

127 m
(iii)

130 m
(iv)

128 m
(v)

129 m

Question 37

37.

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

(i)

1
2

√

4
(ii)

1
2

√

2
(iii)

1
(iv)

1
2

4
√

2
(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)

c)

d)

1

a

2
+
1

b

2
=
1

p

2

e)

ab
=
pc

(i)

{a,d,e}
(ii)

{b,a,d}
(iii)

{c,d}
(iv)

{b,c,e}
(v)

{b,a}

Question 39

39.

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

(i)
7 AD

2

=

3 AB

2
(ii)
9 AD

2

=

7 AB

2
(iii)
7 AD

2

=

9 AB

2
(iv)
3 AD

2

=

7 AB

2

Question 40

40.

In the given figure, ∠NKL = ∠MKN and KN ∥ OM and KL = 19 cm, LN = 10 cm and NM = 10 cm. Find KO

(i)

21.00 cm
(ii)

17.00 cm
(iii)

19.00 cm
(iv)

18.00 cm
(v)

20.00 cm

Question 41

41.

In the given figure, JL is the angular bisector of
∠J
&
∠L

(i)

20.00 cm
(ii)

21.00 cm
(iii)

23.00 cm
(iv)

24.00 cm
(v)

22.00 cm

Question 42

42.

In the given figure, FGH is a triangle and 'O' is a point inside △FGH. The angular bisector of ∠GOF, ∠HOG & ∠FOH meet FG, GH & HF at I, J & K respectively . Then