EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

not similar
(iv)

AAA Similarity

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 4

4.

In the given figure, △EFG and △TUV are such that

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

AAA Similarity

Question 5

5.

In the given figure, △CDE and △TUV are such that

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 6

6.

In the given figure, △FGH and △QRS are such that

Identify the property by which the two triangles are similar

(i)

SAS Similarity
(ii)

SSS Similarity
(iii)

not similar
(iv)

AAA Similarity

Question 7

7.

(i)

11.43 cm
(ii)

9.43 cm
(iii)

10.43 cm
(iv)

12.43 cm
(v)

8.43 cm

Question 8

8.

In the given figure,
ST
∥
QR
.

(i)

10.69 cm
(ii)

8.69 cm
(iii)

9.69 cm
(iv)

6.69 cm
(v)

7.69 cm

Question 9

9.

In the given figure, TU ∥ CD and BU = 12 cm, BD = 20 cm and CD = 20 cm, find TU

(i)

10.0 cm
(ii)

14.0 cm
(iii)

12.0 cm
(iv)

11.0 cm
(v)

13.0 cm

Question 10

10.

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

(i)

∠L
(ii)

∠H
(iii)

∠J
(iv)

∠M
(v)

∠I

Question 11

11.

In the given figure, △CDE is isosceles right-angled at D and DF ⟂ EC. ∠EFD =

(i)

∠FDE
(ii)

∠CDE
(iii)

∠FCD
(iv)

∠DEF
(v)

∠CDF

Question 12

12.

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)

△FDA
(ii)

△ACF
(iii)

△DAE
(iv)

△DCF
(v)

△ABH

Question 13

13.

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)

∠FAC
(ii)

∠FDA
(iii)

∠HAB
(iv)

∠FEH
(v)

∠AFD

Question 14

14.

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)

∠FDA
(iv)

∠ABH
(v)

∠DAF

Question 15

15.

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)

∠BHA
(iii)

∠DAF
(iv)

∠EHF
(v)

∠AFD

Question 16

16.

In the given figure, KLMN is a trapezium in which

NO
=
(

7

x

+

1

)
cm, find the value of x

(i)

(

6

,

(
-1
7
)

)
(ii)

(

5

,

(
-1
3
)

)
(iii)

(

4
5

,

7

)
(iv)

(

5

,

(
-1
5
)

)
(v)

(

8

,

(
-1
5
)

)

Question 17

17.

In the given figure, HIJK is a trapezium in which

(i)

△LHI
(ii)

△KHI
(iii)

△LKH
(iv)

△LIJ
(v)

△IJK

Question 18

18.

In the given figure, the altitudes QG and HR of △FGH meet at P. △QHP ∼

(i)

△RGP
(ii)

△RGH
(iii)

△QHG
(iv)

△PRQ
(v)

△PGH

Question 19

19.

In the given figure, the altitudes TD and EU of △CDE meet at S. ∠UDS =

(i)

∠ETS
(ii)

∠SUD
(iii)

∠DSU
(iv)

∠SET
(v)

∠TSE

Question 20

20.

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

If GH = 20 cm, GR = 12.5 cm and GK = 12.5 cm, GJ =

(i)

19.00 cm
(ii)

18.00 cm
(iii)

20.00 cm
(iv)

22.00 cm
(v)

21.00 cm

Question 21

21.

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

If IL = 15.9 cm, IK = 16 cm and IM = 9.54 cm, IT =

(i)

7.60 cm
(ii)

10.60 cm
(iii)

9.60 cm
(iv)

11.60 cm
(v)

8.60 cm

Question 22

22.

In the given figure, PQ ∥ JK , and median IL bisects PQ.
△IJL ∼

(i)

△ILK
(ii)

△IMQ
(iii)

△IPM
(iv)

△JKI
(v)

△IJK

Question 23

23.

In the given figure, △NOP is a triangle in which NQ is the internal bisector of ∠N and PR ∥ QN meeting ON produced at R . ∠PNQ =

(i)

∠RNP
(ii)

∠OQN
(iii)

∠NQP
(iv)

∠QPN
(v)

∠PRN

Question 24

24.

In the given figure, P and Q are points on the sides MN and MO respectively of △MNO.For which of the following cases, PQ ∥ NO

a)	MN = 18 cm, PN = 9 cm, MQ = 9.5 cm and MO = 15 cm
b)	MN = 18 cm, PN = 9 cm, MO = 15 cm and MQ = 7.5 cm
c)	MN = 18 cm, MP = 11 cm, MO = 15 cm and QO = 7.5 cm
d)	MP = 9 cm, PN = 9 cm, MQ = 7.5 cm and QO = 7.5 cm

(i)

{a,d,b}
(ii)

{a,b}
(iii)

{b,d}
(iv)

{a,c,b}
(v)

{c,d}

Question 25

25.

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
2

of area of △IJK
(iv)
1
3

of area of △IJK
(v)
3
4

of area of △IJK

Question 26

26.

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)
thrice

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
4
3

the area of the triangle
(v)
twice

the area of the triangle

Question 27

27.

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)

IL : JK
(ii)

IK : JL
(iii)

JK : IL
(iv)

KL : IJ
(v)

IJ : KL

Question 28

28.

In the given △HIJ, KL ∥ IJ. If HK : KI = 12.5 cm : 7.5 cm and HJ = 16 cm, LJ =

(i)

5.00 cm
(ii)

6.00 cm
(iii)

7.00 cm
(iv)

4.00 cm
(v)

8.00 cm

Question 29

29.

In the given two similar triangles, if o = 19 cm, p = 20 cm, q = 18 cm, s = 12 cm, find t

(i)

12.80 cm
(ii)

9.80 cm
(iii)

8.80 cm
(iv)

10.80 cm
(v)

11.80 cm

Question 30

30.

In the given figure, given ∠JGH = ∠IGJ, x : y = 7.5 cm : 7.5 cm and p = 17 cm, find q =

(i)

15.00 cm
(ii)

17.00 cm
(iii)

16.00 cm
(iv)

18.00 cm
(v)

19.00 cm

Question 31

31.

In the given figure, given ∠JGH = ∠IGJ, p = 7.5 cm, q = 7.5 cm and HI = 15 cm, find HJ =

(i)

6.50 cm
(ii)

9.50 cm
(iii)

7.50 cm
(iv)

8.50 cm
(v)

5.50 cm

Question 32

32.

In the given figure, DEFG is a trapezium where OE = 14 cm , OF = 5 cm and OG = 5 cm . Find OD =

(i)

15 cm
(ii)

14 cm
(iii)

13 cm
(iv)

16 cm
(v)

12 cm

Question 33

33.

In the given figure, ∠EBC = 44.07°, find the value of x =

(i)

45.93°
(ii)

44.93°
(iii)

43.93°
(iv)

47.93°
(v)

46.93°

Question 34

34.

In the given figure, ∠DEF = 43.68°, find the value of y =

(i)

44.32°
(ii)

48.32°
(iii)

45.32°
(iv)

47.32°
(v)

46.32°

Question 35

35.

In the given figure, if HI ∥ JK then

(i)

△HIL ∼ △LKJ
(ii)

△LIH ∼ △LKJ
(iii)

△HIL ∼ △KJL
(iv)

△LHI ∼ △LJK
(v)

△HIL ∼ △LJK

Question 36

36.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. Which of the following are true?

a)

DE

2
=
FD
.
FG

b)

EF

2
=
FD
.
FG

c)

EF

2
=
DF
.
DG

d)

EG

2
=
DG
.
GF

e)

DE

2
=
DF
.
DG

(i)

{a,b}
(ii)

{c,d}
(iii)

{b,d,e}
(iv)

{a,b,d}
(v)

{a,c,e}

Question 37

37.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. If EF = 18 cm, FG = 20 cm, then find FH.

(i)

12.38 cm
(ii)

14.38 cm
(iii)

13.38 cm
(iv)

11.38 cm
(v)

15.38 cm

Question 38

38.

In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If BE = 13.1 cm, ED = 11.7 cm, then find CE.

(i)

13.38 cm
(ii)

11.38 cm
(iii)

12.38 cm
(iv)

10.38 cm
(v)

14.38 cm

Question 39

39.

In the given figure, △ABC ∼ △MNO and AB = 12 cm, MN = 16.8 cm.

(i)

116.97 sq.cm
(ii)

114.97 sq.cm
(iii)

115.97 sq.cm
(iv)

113.97 sq.cm
(v)

112.97 sq.cm

Question 40

40.

In the given figure, △ABC ∼ △PQR and BC = 15 cm , QR = 21 cm and

(i)

86.87 sq.cm
(ii)

87.87 sq.cm
(iii)

85.87 sq.cm
(iv)

89.87 sq.cm
(v)

88.87 sq.cm

Question 41

41.

In the given figure, △EFG & △QRS are similar triangles. If the ratio of the heights EH : QT = 10 : 15, then the ratio of their areas is

(i)

99

sq.cm

:

225

sq.cm
(ii)

100

sq.cm

:

225

sq.cm
(iii)

100

sq.cm

:

223

sq.cm
(iv)

101

sq.cm

:

225

sq.cm
(v)

100

sq.cm

:

227

sq.cm

Question 42

42.

In the given figure, points E , F and G are the mid-points of sides CD, DB and BC of △BCD. Which of the following are true?

a)

b)

Area of trapezium CDFG is thrice the area of △BGF

c)

All four small triangles have equal areas

d)

e)

Area of △BCD = 4 times area of △EFG

(i)

{a,d,e}
(ii)

{a,b,c}
(iii)

{d,c}
(iv)

{b,c,e}
(v)

{a,b}

Question 43

43.

In the given figure, points N , O and P are the mid-points of sides LM, MK and KL of △KLM. Which of the following are true?

a)	△NPO ∼ △KLM
b)	△ONM ∼ △KLM
c)	△PLN ∼ △KLM
d)	△KPO ∼ △KLM
e)	△NOP ∼ △KLM

(i)

{b,c,d,e}
(ii)

{a,d}
(iii)

{a,b}
(iv)

{a,c}
(v)

{a,e,b}

Question 44

44.

The perimeters of two similar triangles are 28 cm and 25 cm respectively. If one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.

(i)

9.71 cm
(ii)

10.71 cm
(iii)

11.71 cm
(iv)

12.71 cm
(v)

8.71 cm

Question 45

45.

In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 102° , ∠DCA = 28°. Find ∠CAD

(i)

50°
(ii)

52°
(iii)

48°
(iv)

49°
(v)

51°

Question 46

46.

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)
1
2

a sq.units
(ii)
2a sq.units
(iii)
√

3

a sq.units
(iv)
1
2

√

3

a sq.units
(v)
a

2

sq.units

Question 47

47.

ABCD is a cyclic trapezium. Diagonals BD and AC intersect at E. If DA = 15 cm, find BC

(i)

17 cm
(ii)

13 cm
(iii)

16 cm
(iv)

15 cm
(v)

14 cm

Question 48

48.

A vertical stick
12 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)

95 m
(ii)

94 m
(iii)

96 m
(iv)

97 m
(v)

98 m

Question 49

49.

In the given figure, △DEF, ST ∥ EF such that

(i)

1
2

√

-1
(ii)

1
2

√

2
(iii)

1
(iv)

1
2

√

5
(v)

1
2

4
√

2

Question 50

50.

In the given figure, ∠GDE = ∠FDG and DG ∥ HF and DE = 17 cm, EG = 9 cm and GF = 9 cm. Find DH

(i)

17.00 cm
(ii)

16.00 cm
(iii)

18.00 cm
(iv)

19.00 cm
(v)

15.00 cm

Question 51

51.

In the given figure, CE is the angular bisector of
∠C
&
∠E

(i)

22.00 cm
(ii)

21.00 cm
(iii)

24.00 cm
(iv)

23.00 cm
(v)

20.00 cm

Question 52

52.

In the given figure, CDE is a triangle and 'O' is a point inside △CDE. The angular bisector of ∠DOC, ∠EOD & ∠COE meet CD, DE & EC at F, G & H respectively . Then