EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

AAA Similarity

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 5

5.

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

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

not similar
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 6

6.

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

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 7

7.

(i)

3.73 cm
(ii)

5.73 cm
(iii)

2.73 cm
(iv)

1.73 cm
(v)

4.73 cm

Question 8

8.

In the given figure,
PQ
∥
NO
.

(i)

11.50 cm
(ii)

10.50 cm
(iii)

8.50 cm
(iv)

9.50 cm
(v)

7.50 cm

Question 9

9.

In the given figure, PQ ∥ DE and CD = 21 cm, PQ = 14.4 cm and DE = 24 cm, find CP

(i)

14.6 cm
(ii)

10.6 cm
(iii)

13.6 cm
(iv)

12.6 cm
(v)

11.6 cm

Question 10

10.

In the given figure, △FGH is isosceles right-angled at G and GI ⟂ HF. ∠H =

(i)

∠I
(ii)

∠J
(iii)

∠K
(iv)

∠G
(v)

∠F

Question 11

11.

In the given figure, △NOP is isosceles right-angled at O and OQ ⟂ PN. ∠PQO =

(i)

∠NOQ
(ii)

∠QNO
(iii)

∠OPQ
(iv)

∠QOP
(v)

∠OQN

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)

△DAE
(ii)

△ABH
(iii)

△DCF
(iv)

△FDA
(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.

∠HFE =

(i)

∠FAC
(ii)

∠FEH
(iii)

∠HAB
(iv)

∠AFD
(v)

∠FDA

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.

∠FDA =

(i)

∠ABH
(ii)

∠DAF
(iii)

∠FEH
(iv)

∠ACF
(v)

∠EHF

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.

∠DAF =

(i)

∠BHA
(ii)

∠HFE
(iii)

∠CFA
(iv)

∠EHF
(v)

∠AFD

Question 16

16.

In the given figure, GHIJ is a trapezium in which

JK
=
(

x

+

37

)
cm, find the value of x

(i)

(

40

,

-2

)
(ii)

(

-1

,

38

)
(iii)

(

-4

,

37

)
(iv)

(

-3

,

39

)
(v)

(

-4

,

38

)

Question 17

17.

In the given figure, DEFG is a trapezium in which

(i)

△HFG
(ii)

△HEF
(iii)

△HGD
(iv)

△GDE
(v)

△EFG

Question 18

18.

In the given figure, the altitudes OE and FP of △DEF meet at N. △PEN ∼

(i)

△PEF
(ii)

△NPO
(iii)

△OFN
(iv)

△OFE
(v)

△NEF

Question 19

19.

In the given figure, the altitudes UG and HV of △FGH meet at T. ∠GTV =

(i)

∠UTH
(ii)

∠TVG
(iii)

∠HUT
(iv)

∠VGT
(v)

∠THU

Question 20

20.

In the given figure, PQ ∥ FG , and median EH bisects PQ.

If EF = 15 cm, EH = 15 cm and EP = 10 cm, IH =

(i)

4.00 cm
(ii)

7.00 cm
(iii)

6.00 cm
(iv)

3.00 cm
(v)

5.00 cm

Question 21

21.

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

If BE = 14.8 cm, BD = 20 cm and BS = 11.11 cm, BF =

(i)

6.22 cm
(ii)

10.22 cm
(iii)

7.22 cm
(iv)

9.22 cm
(v)

8.22 cm

Question 22

22.

In the given figure, PQ ∥ IJ , and median HK bisects PQ.
△HIK ∼

(i)

△HPL
(ii)

△HLQ
(iii)

△HIJ
(iv)

△IJH
(v)

△HKJ

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 . ∠NPR =

(i)

∠OQN
(ii)

∠PRN
(iii)

∠QPN
(iv)

∠RNP
(v)

∠NQP

Question 24

24.

In the given figure, H and I are points on the sides EF and EG respectively of △EFG.For which of the following cases, HI ∥ FG

a)	EF = 20 cm, HF = 10 cm, EG = 18 cm and EI = 9 cm
b)	EH = 10 cm, HF = 10 cm, EI = 9 cm and IG = 9 cm
c)	EF = 20 cm, HF = 10 cm, EI = 11 cm and EG = 18 cm
d)	EF = 20 cm, EH = 12 cm, EG = 18 cm and IG = 9 cm

(i)

{c,a}
(ii)

{c,d,a}
(iii)

{c,b,a}
(iv)

{d,b}
(v)

{a,b}

Question 25

25.

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)
2
3

of area of △BCD
(iii)
1
2

of area of △BCD
(iv)
3
4

of area of △BCD
(v)
1
3

of area of △BCD

Question 26

26.

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

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

(i)
4
3

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
twice

the area of the triangle
(iv)
5
4

the area of the triangle
(v)
thrice

the area of the triangle

Question 27

27.

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)

MO : NP
(ii)

NO : MP
(iii)

MN : OP
(iv)

MP : NO
(v)

OP : MN

Question 28

28.

In the given △DEF, GH ∥ EF. If DG : GE = 5.33 cm : 10.67 cm and DF = 15 cm, DH =

(i)

4.00 cm
(ii)

6.00 cm
(iii)

5.00 cm
(iv)

3.00 cm
(v)

7.00 cm

Question 29

29.

In the given two similar triangles, if n = 18 cm, o = 19 cm, p = 19 cm, s = 11.4 cm, find q

(i)

8.80 cm
(ii)

10.80 cm
(iii)

12.80 cm
(iv)

9.80 cm
(v)

11.80 cm

Question 30

30.

In the given figure, given ∠KHI = ∠JHK, x : y = 9.71 cm : 7.29 cm and p = 20 cm, find q =

(i)

17.00 cm
(ii)

15.00 cm
(iii)

16.00 cm
(iv)

14.00 cm
(v)

13.00 cm

Question 31

31.

In the given figure, given ∠GDE = ∠FDG, p = 10.31 cm, q = 8.69 cm and EF = 19 cm, find EG =

(i)

9.31 cm
(ii)

12.31 cm
(iii)

11.31 cm
(iv)

10.31 cm
(v)

8.31 cm

Question 32

32.

In the given figure, FGHI is a trapezium where OF = 12 cm , OH = 4 cm and OI = 4 cm . Find OG =

(i)

11 cm
(ii)

14 cm
(iii)

10 cm
(iv)

13 cm
(v)

12 cm

Question 33

33.

In the given figure, ∠LIJ = 41.98°, find the value of x =

(i)

49.02°
(ii)

48.02°
(iii)

46.02°
(iv)

47.02°
(v)

50.02°

Question 34

34.

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

(i)

53.13°
(ii)

51.13°
(iii)

52.13°
(iv)

55.13°
(v)

54.13°

Question 35

35.

In the given figure, if AB ∥ CD then

(i)

△ABE ∼ △DCE
(ii)

△EBA ∼ △EDC
(iii)

△EAB ∼ △ECD
(iv)

△ABE ∼ △ECD
(v)

△ABE ∼ △EDC

Question 36

36.

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

a)

DE

2
=
CE
.
CF

b)

DE

2
=
EC
.
EF

c)

CD

2
=
EC
.
EF

d)

CD

2
=
CE
.
CF

e)

DF

2
=
CF
.
FE

(i)

{c,d}
(ii)

{b,d,e}
(iii)

{a,b}
(iv)

{a,b,d}
(v)

{a,c,e}

Question 37

37.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If GH = 18 cm, GI = 13.07 cm, then find FG.

(i)

18.00 cm
(ii)

21.00 cm
(iii)

20.00 cm
(iv)

19.00 cm
(v)

17.00 cm

Question 38

38.

In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. If LK = 14.6 cm, JL = 13.78 cm, then find IL.

(i)

13.00 cm
(ii)

12.00 cm
(iii)

14.00 cm
(iv)

15.00 cm
(v)

11.00 cm

Question 39

39.

In the given figure, △ABC ∼ △MNO and AB = 11 cm, MN = 15.4 cm.

(i)

65.71 sq.cm
(ii)

61.71 sq.cm
(iii)

62.71 sq.cm
(iv)

63.71 sq.cm
(v)

64.71 sq.cm

Question 40

40.

In the given figure, △ABC ∼ △NOP and BC = 13 cm , OP = 18.2 cm and

(i)

105.75 sq.cm
(ii)

106.75 sq.cm
(iii)

104.75 sq.cm
(iv)

102.75 sq.cm
(v)

103.75 sq.cm

Question 41

41.

In the given figure, △ABC & △NOP are similar triangles. If the ratio of the heights AD : NQ = 11 : 15, then the ratio of their areas is

(i)

120

sq.cm

:

225

sq.cm
(ii)

121

sq.cm

:

227

sq.cm
(iii)

121

sq.cm

:

225

sq.cm
(iv)

121

sq.cm

:

223

sq.cm
(v)

122

sq.cm

:

225

sq.cm

Question 42

42.

In the given figure, points L , M and N are the mid-points of sides JK, KI and IJ of △IJK. Which of the following are true?

a)

Area of trapezium JKMN is thrice the area of △INM

b)

Area of △IJK = 4 times area of △LMN

c)

d)

e)

All four small triangles have equal areas

(i)

{a,b,e}
(ii)

{c,d,e}
(iii)

{d,b}
(iv)

{c,a,b}
(v)

{c,a}

Question 43

43.

In the given figure, points J , K and L are the mid-points of sides HI, IG and GH of △GHI. Which of the following are true?

a)	△LHJ ∼ △GHI
b)	△JKL ∼ △GHI
c)	△JLK ∼ △GHI
d)	△GLK ∼ △GHI
e)	△KJI ∼ △GHI

(i)

{c,e,a}
(ii)

{c,d}
(iii)

{c,b}
(iv)

{c,a}
(v)

{a,b,d,e}

Question 44

44.

The perimeters of two similar triangles are 34 cm and 25 cm respectively. If one side of the first triangle is 9 cm, find the length of the corresponding side of the second triangle.

(i)

7.62 cm
(ii)

8.62 cm
(iii)

4.62 cm
(iv)

6.62 cm
(v)

5.62 cm

Question 45

45.

In the given figure, K is a point on side IJ of △HIJ such that ∠JHI = ∠HKJ = 101° , ∠KJH = 20°. Find ∠JHK

(i)

61°
(ii)

57°
(iii)

60°
(iv)

58°
(v)

59°

Question 46

46.

IJKL is a square and △IJM is an equilateral triangle. Also, △IKN is an equilateral triangle. If area of △IJM is 'a' sq.units, then the area of △IKN is

(i)
1
2

√

3

a sq.units
(ii)
1
2

a sq.units
(iii)
a

2

sq.units
(iv)
2a sq.units
(v)
√

3

a sq.units

Question 47

47.

GHIJ is a cyclic trapezium. Diagonals HJ and GI intersect at K. If JG = 15 cm, find HI

(i)

14 cm
(ii)

15 cm
(iii)

16 cm
(iv)

13 cm
(v)

17 cm

Question 48

48.

A vertical stick
14 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)

112 m
(ii)

113 m
(iii)

114 m
(iv)

111 m
(v)

110 m

Question 49

49.

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

(i)

1
2

√

2
(ii)

1
2

√

1
2
(iii)

1
2

√

5
(iv)

1
(v)

1
2

4
√

2

Question 50

50.

In the given figure, ∠LIJ = ∠KIL and IL ∥ MK and IJ = 16 cm, JL = 9 cm and LK = 9 cm. Find IM

(i)

17.00 cm
(ii)

14.00 cm
(iii)

15.00 cm
(iv)

18.00 cm
(v)

16.00 cm

Question 51

51.

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

(i)

24.00 cm
(ii)

25.00 cm
(iii)

22.00 cm
(iv)

23.00 cm
(v)

26.00 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