EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

SSS Similarity
(iii)

not similar
(iv)

AAA Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 5

5.

In the given figure, △ABC and △PQR are such that

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 6

6.

In the given figure, △FGH and △UVW 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 7

7.

(i)

8.09 cm
(ii)

4.09 cm
(iii)

6.09 cm
(iv)

5.09 cm
(v)

7.09 cm

Question 8

8.

In the given figure,
HI
∥
FG
.

(i)

8.65 cm
(ii)

6.65 cm
(iii)

7.65 cm
(iv)

4.65 cm
(v)

5.65 cm

Question 9

9.

In the given figure, PQ ∥ EF and DQ = 13.2 cm, PQ = 12 cm and EF = 20 cm, find DF

(i)

23.0 cm
(ii)

21.0 cm
(iii)

22.0 cm
(iv)

20.0 cm
(v)

24.0 cm

Question 10

10.

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

(i)

∠B
(ii)

∠C
(iii)

∠G
(iv)

∠F
(v)

∠D

Question 11

11.

In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠HJG =

(i)

∠JHI
(ii)

∠HIJ
(iii)

∠GHI
(iv)

∠GHJ
(v)

∠JGH

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.

△FDA ∼

(i)

△ABH
(ii)

△DAE
(iii)

△FEH
(iv)

△DCF
(v)

△ACF

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.

∠AFD =

(i)

∠FDA
(ii)

∠HFE
(iii)

∠FAC
(iv)

∠FEH
(v)

∠HAB

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)

∠FDA
(ii)

∠EHF
(iii)

∠ABH
(iv)

∠FEH
(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)

∠BHA
(ii)

∠EHF
(iii)

∠DAF
(iv)

∠HFE
(v)

∠AFD

Question 16

16.

In the given figure, MNOP is a trapezium in which

PQ
=
(

x

+

1

)
cm, find the value of x

(i)

(

67

,

66

)
(ii)

(

70

,

67

)
(iii)

(

68

,

68

)
(iv)

(

69

,

69

)
(v)

(

67

,

67

)

Question 17

17.

In the given figure, FGHI is a trapezium in which

(i)

△JGH
(ii)

△JFG
(iii)

△JIF
(iv)

△GHI
(v)

△IFG

Question 18

18.

In the given figure, the altitudes PH and IQ of △GHI meet at O. △QHI ∼

(i)

△OHI
(ii)

△QHO
(iii)

△PIO
(iv)

△PIH
(v)

△OQP

Question 19

19.

In the given figure, the altitudes ND and EO of △CDE meet at M. ∠MEN =

(i)

∠ENM
(ii)

∠DMO
(iii)

∠ODM
(iv)

∠NME
(v)

∠MOD

Question 20

20.

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

If GJ = 18.1 cm, GR = 9 cm and GK = 9.05 cm, GH =

(i)

19.00 cm
(ii)

20.00 cm
(iii)

16.00 cm
(iv)

17.00 cm
(v)

18.00 cm

Question 21

21.

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

If IL = 13.8 cm, IK = 17 cm and IM = 4.6 cm, IS =

(i)

3.67 cm
(ii)

5.67 cm
(iii)

6.67 cm
(iv)

7.67 cm
(v)

4.67 cm

Question 22

22.

In the given figure, RS ∥ IJ , and median HK bisects RS.
△HLS ∼

(i)

△HKJ
(ii)

△IJH
(iii)

△HIJ
(iv)

△HIK
(v)

△HRL

Question 23

23.

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)

∠FBD
(iii)

∠BED
(iv)

∠CEB
(v)

∠DFB

Question 24

24.

In the given figure, I and J are points on the sides FG and FH respectively of △FGH.For which of the following cases, IJ ∥ GH

a)	FI = 10 cm, IG = 8 cm, FJ = 10 cm and JH = 8 cm
b)	FG = 18 cm, IG = 8 cm, FJ = 12 cm and FH = 18 cm
c)	FG = 18 cm, FI = 12 cm, FH = 18 cm and JH = 8 cm
d)	FG = 18 cm, IG = 8 cm, FH = 18 cm and FJ = 10 cm

(i)

{a,d}
(ii)

{b,d,a}
(iii)

{b,c,a}
(iv)

{c,d}
(v)

{b,a}

Question 25

25.

In the given figure, the area of the △KLM is x sq.cm. N,O,P are the mid-points of the sides LM , MK and KL respectively. The area of the △NOP is

(i)
3
4

of area of △KLM
(ii)
1
2

of area of △KLM
(iii)
2
3

of area of △KLM
(iv)
1
3

of area of △KLM
(v)
1
4

of area of △KLM

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)
5
4

the area of the triangle
(ii)
twice

the area of the triangle
(iii)
3
2

the area of the triangle
(iv)
thrice

the area of the triangle
(v)
4
3

the area of the triangle

Question 27

27.

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

(i)

EF : CD
(ii)

CD : EF
(iii)

CF : DE
(iv)

DE : CF
(v)

CE : DF

Question 28

28.

In the given △GHI, JK ∥ HI. If GJ : JH = 7.71 cm : 10.29 cm and GI = 18 cm, KI =

(i)

12.29 cm
(ii)

9.29 cm
(iii)

11.29 cm
(iv)

10.29 cm
(v)

8.29 cm

Question 29

29.

In the given two similar triangles, if d = 19 cm, e = 18 cm, f = 20 cm, h = 10.8 cm, find i

(i)

11.00 cm
(ii)

12.00 cm
(iii)

14.00 cm
(iv)

10.00 cm
(v)

13.00 cm

Question 30

30.

In the given figure, given ∠IFG = ∠HFI, x : y = 10.31 cm : 8.69 cm and p = 19 cm, find q =

(i)

16.00 cm
(ii)

18.00 cm
(iii)

17.00 cm
(iv)

15.00 cm
(v)

14.00 cm

Question 31

31.

In the given figure, given ∠DAB = ∠CAD, p = 10.81 cm, q = 9.19 cm and BC = 20 cm, find BD =

(i)

9.81 cm
(ii)

8.81 cm
(iii)

12.81 cm
(iv)

10.81 cm
(v)

11.81 cm

Question 32

32.

In the given figure, ABCD is a trapezium where OB = 13 cm , OC = 4 cm and OD = 4 cm . Find OA =

(i)

12 cm
(ii)

14 cm
(iii)

11 cm
(iv)

15 cm
(v)

13 cm

Question 33

33.

In the given figure, ∠IFG = 51.52°, find the value of x =

(i)

39.48°
(ii)

36.48°
(iii)

40.48°
(iv)

38.48°
(v)

37.48°

Question 34

34.

In the given figure, ∠GHI = 43.83°, find the value of y =

(i)

46.17°
(ii)

48.17°
(iii)

45.17°
(iv)

44.17°
(v)

47.17°

Question 35

35.

In the given figure, if IJ ∥ KL then

(i)

△IJM ∼ △LKM
(ii)

△IJM ∼ △MLK
(iii)

△MIJ ∼ △MKL
(iv)

△MJI ∼ △MLK
(v)

△IJM ∼ △MKL

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
=
DF
.
DG

b)

EF

2
=
FD
.
FG

c)

DE

2
=
FD
.
FG

d)

EG

2
=
DG
.
GF

e)

EF

2
=
DF
.
DG

(i)

{a,b,d}
(ii)

{c,a,b}
(iii)

{c,a}
(iv)

{c,e,d}
(v)

{e,b}

Question 37

37.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If GH = 15 cm, HI = 18 cm, then find HJ.

(i)

12.52 cm
(ii)

11.52 cm
(iii)

13.52 cm
(iv)

10.52 cm
(v)

9.52 cm

Question 38

38.

In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If BE = 13 cm, ED = 14.6 cm, then find CE.

(i)

15.78 cm
(ii)

13.78 cm
(iii)

11.78 cm
(iv)

12.78 cm
(v)

14.78 cm

Question 39

39.

In the given figure, △DEF ∼ △MNO and DE = 13 cm, MN = 18.2 cm.

(i)

53.44 sq.cm
(ii)

55.44 sq.cm
(iii)

52.44 sq.cm
(iv)

54.44 sq.cm
(v)

51.44 sq.cm

Question 40

40.

In the given figure, △ABC ∼ △OPQ and BC = 10 cm , PQ = 14 cm and

(i)

121.28 sq.cm
(ii)

122.28 sq.cm
(iii)

123.28 sq.cm
(iv)

120.28 sq.cm
(v)

124.28 sq.cm

Question 41

41.

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

(i)

100

sq.cm

:

193

sq.cm
(ii)

100

sq.cm

:

198

sq.cm
(iii)

99

sq.cm

:

196

sq.cm
(iv)

101

sq.cm

:

196

sq.cm
(v)

100

sq.cm

:

196

sq.cm

Question 42

42.

In the given figure, points O , P and Q are the mid-points of sides MN, NL and LM of △LMN. Which of the following are true?

a)

Area of trapezium MNPQ is thrice the area of △LQP

b)

c)

All four small triangles have equal areas

d)

Area of △LMN = 4 times area of △OPQ

e)

(i)

{a,c,d}
(ii)

{b,a,c}
(iii)

{b,e,d}
(iv)

{b,a}
(v)

{e,c}

Question 43

43.

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)	△IEG ∼ △DEF
b)	△HGF ∼ △DEF
c)	△GHI ∼ △DEF
d)	△DIH ∼ △DEF
e)	△GIH ∼ △DEF

(i)

{e,c}
(ii)

{e,d,a}
(iii)

{a,b,c,d}
(iv)

{e,b}
(v)

{e,a}

Question 44

44.

The perimeters of two similar triangles are 30 cm and 23 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.

(i)

14.27 cm
(ii)

10.27 cm
(iii)

12.27 cm
(iv)

11.27 cm
(v)

13.27 cm

Question 45

45.

In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 100° , ∠DCA = 22°. Find ∠CAD

(i)

57°
(ii)

56°
(iii)

60°
(iv)

58°
(v)

59°

Question 46

46.

HIJK is a square and △HIL is an equilateral triangle. Also, △HJM is an equilateral triangle. If area of △HIL is 'a' sq.units, then the area of △HJM is

(i)
a

2

sq.units
(ii)
1
2

√

3

a sq.units
(iii)
√

3

a sq.units
(iv)
1
2

a sq.units
(v)
2a sq.units

Question 47

47.

ABCD is a cyclic trapezium. Diagonals BD and AC intersect at E. If DA = 16 cm, find BC

(i)

15 cm
(ii)

18 cm
(iii)

14 cm
(iv)

16 cm
(v)

17 cm

Question 48

48.

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

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

Find the height of the tower.

(i)

88 m
(ii)

90 m
(iii)

87 m
(iv)

86 m
(v)

89 m

Question 49

49.

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

(i)

1
2

√

2
(ii)

1
2

√

4
(iii)

1
2

√

1
2
(iv)

1
2

4
√

2
(v)

1

Question 50

50.

In the given figure, ∠FCD = ∠ECF and CF ∥ GE and CD = 20 cm, DF = 10 cm and FE = 9 cm. Find CG

(i)

20.00 cm
(ii)

17.00 cm
(iii)

18.00 cm
(iv)

19.00 cm
(v)

16.00 cm

Question 51

51.

In the given figure, IK is the angular bisector of
∠I
&
∠K

(i)

22.76 cm
(ii)

23.76 cm
(iii)

25.76 cm
(iv)

26.76 cm
(v)

24.76 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