EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 5

5.

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

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 6

6.

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

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

SAS Similarity
(iii)

not similar
(iv)

SSS Similarity

Question 7

7.

(i)

4.60 cm
(ii)

5.60 cm
(iii)

3.60 cm
(iv)

2.60 cm
(v)

1.60 cm

Question 8

8.

In the given figure,
IJ
∥
GH
.

(i)

10.27 cm
(ii)

11.27 cm
(iii)

12.27 cm
(iv)

9.27 cm
(v)

8.27 cm

Question 9

9.

In the given figure, ST ∥ BC and AS = 14.4 cm, ST = 14.4 cm and BC = 24 cm, find AB

(i)

25.0 cm
(ii)

22.0 cm
(iii)

26.0 cm
(iv)

24.0 cm
(v)

23.0 cm

Question 10

10.

In the given figure, △LMN is isosceles right-angled at M and MO ⟂ NL. ∠L =

(i)

∠Q
(ii)

∠N
(iii)

∠M
(iv)

∠P
(v)

∠O

Question 11

11.

In the given figure, △JKL is isosceles right-angled at K and KM ⟂ LJ. ∠LMK =

(i)

∠MJK
(ii)

∠KLM
(iii)

∠JKM
(iv)

∠MKL
(v)

∠KMJ

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.

△ACF ∼

(i)

△FEH
(ii)

△FDA
(iii)

△DCF
(iv)

△DAE
(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.

∠HAB =

(i)

∠FEH
(ii)

∠HFE
(iii)

∠FAC
(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.

∠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.

∠BHA =

(i)

∠EHF
(ii)

∠CFA
(iii)

∠AFD
(iv)

∠HFE
(v)

∠DAF

Question 16

16.

In the given figure, KLMN is a trapezium in which

NO
=
(

2

x

+

20

)
cm, find the value of x

(i)

(

-14

,

70

)
(ii)

(

-16

,

71

)
(iii)

(

-17

,

69

)
(iv)

(

-17

,

70

)
(v)

(

72

,

-15

)

Question 17

17.

In the given figure, DEFG is a trapezium in which

(i)

△HGD
(ii)

△HDE
(iii)

△GDE
(iv)

△HEF
(v)

△EFG

Question 18

18.

In the given figure, the altitudes NF and GO of △EFG meet at M. △MON ∼

(i)

△OFM
(ii)

△MFG
(iii)

△NGF
(iv)

△NGM
(v)

△OFG

Question 19

19.

In the given figure, the altitudes QB and CR of △ABC meet at P. ∠CQP =

(i)

∠PRB
(ii)

∠RBP
(iii)

∠QPC
(iv)

∠BPR
(v)

∠PCQ

Question 20

20.

In the given figure, QR ∥ EF , and median DG bisects QR.

If DE = 15 cm, DQ = 8.57 cm and DH = 8.63 cm, DG =

(i)

13.10 cm
(ii)

14.10 cm
(iii)

15.10 cm
(iv)

16.10 cm
(v)

17.10 cm

Question 21

21.

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

If EH = 13.9 cm, EG = 15 cm and EI = 8.69 cm, SG =

(i)

4.62 cm
(ii)

3.62 cm
(iii)

7.62 cm
(iv)

6.62 cm
(v)

5.62 cm

Question 22

22.

In the given figure, QR ∥ BC , and median AD bisects QR.
△ADC ∼

(i)

△AQE
(ii)

△ABD
(iii)

△ABC
(iv)

△AER
(v)

△BCA

Question 23

23.

In the given figure, △MNO is a triangle in which MP is the internal bisector of ∠M and OQ ∥ PM meeting NM produced at Q . ∠OMP =

(i)

∠NPM
(ii)

∠MPO
(iii)

∠POM
(iv)

∠QMO
(v)

∠MOQ

Question 24

24.

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, NQ = 9.56 cm, NP = 17 cm and RP = 9.44 cm
b)	NQ = 7.56 cm, QO = 9.44 cm, NR = 7.56 cm and RP = 9.44 cm
c)	NO = 17 cm, QO = 9.44 cm, NP = 17 cm and NR = 7.56 cm
d)	NO = 17 cm, QO = 9.44 cm, NR = 9.56 cm and NP = 17 cm

(i)

{d,c}
(ii)

{a,b}
(iii)

{a,d,b}
(iv)

{b,c}
(v)

{a,c,b}

Question 25

25.

In the given figure, the area of the △HIJ is x sq.cm. K,L,M are the mid-points of the sides IJ , JH and HI respectively. The area of the △KLM is

(i)
3
4

of area of △HIJ
(ii)
1
3

of area of △HIJ
(iii)
1
4

of area of △HIJ
(iv)
1
2

of area of △HIJ
(v)
2
3

of area of △HIJ

Question 26

26.

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

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

(i)
twice

the area of the triangle
(ii)
thrice

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
3
2

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 E : F and the ratio of the corresponding heights is G : H , the ratio of their areas in the same order is

(i)

EG : FH
(ii)

GH : EF
(iii)

EF : GH
(iv)

FG : EH
(v)

EH : FG

Question 28

28.

In the given △EFG, HI ∥ FG. If EH : HF = 8.57 cm : 6.43 cm and EG = 20 cm, EI =

(i)

10.43 cm
(ii)

12.43 cm
(iii)

9.43 cm
(iv)

13.43 cm
(v)

11.43 cm

Question 29

29.

In the given two similar triangles, if f = 15 cm, g = 17 cm, h = 18 cm, j = 10.2 cm, find k

(i)

9.80 cm
(ii)

12.80 cm
(iii)

11.80 cm
(iv)

8.80 cm
(v)

10.80 cm

Question 30

30.

In the given figure, given ∠GDE = ∠FDG, x : y = 8.24 cm : 8.76 cm and p = 16 cm, find q =

(i)

17.00 cm
(ii)

18.00 cm
(iii)

15.00 cm
(iv)

16.00 cm
(v)

19.00 cm

Question 31

31.

In the given figure, given ∠JGH = ∠IGJ, p = 9 cm, q = 9 cm and HI = 18 cm, find JI =

(i)

8.00 cm
(ii)

10.00 cm
(iii)

11.00 cm
(iv)

9.00 cm
(v)

7.00 cm

Question 32

32.

In the given figure, DEFG is a trapezium where OD = 12 cm , OE = 12 cm and OF = 4 cm . Find OG =

(i)

3 cm
(ii)

4 cm
(iii)

5 cm
(iv)

6 cm
(v)

2 cm

Question 33

33.

In the given figure, ∠JGH = 46.98°, find the value of x =

(i)

45.02°
(ii)

42.02°
(iii)

44.02°
(iv)

41.02°
(v)

43.02°

Question 34

34.

In the given figure, ∠FDE = 48.62°, find the value of y =

(i)

39.38°
(ii)

41.38°
(iii)

40.38°
(iv)

42.38°
(v)

43.38°

Question 35

35.

In the given figure, if CD ∥ EF then

(i)

△GDC ∼ △GFE
(ii)

△CDG ∼ △FEG
(iii)

△CDG ∼ △GFE
(iv)

△CDG ∼ △GEF
(v)

△GCD ∼ △GEF

Question 36

36.

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)

GH

2
=
FH
.
FI

d)

GH

2
=
HF
.
HI

e)

GI

2
=
FI
.
IH

(i)

{b,a,d}
(ii)

{c,d}
(iii)

{b,c,e}
(iv)

{a,d,e}
(v)

{b,a}

Question 37

37.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. If CD = 20 cm, DF = 13.38 cm, then find DE.

(i)

20.00 cm
(ii)

17.00 cm
(iii)

19.00 cm
(iv)

16.00 cm
(v)

18.00 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)

12.38 cm
(ii)

14.38 cm
(iii)

11.38 cm
(iv)

13.38 cm
(v)

10.38 cm

Question 39

39.

In the given figure, △EFG ∼ △MNO and EF = 12 cm, MN = 16.8 cm.

(i)

153.70 sq.cm
(ii)

155.70 sq.cm
(iii)

154.70 sq.cm
(iv)

152.70 sq.cm
(v)

156.70 sq.cm

Question 40

40.

In the given figure, △BCD ∼ △OPQ and CD = 13 cm , PQ = 18.2 cm and

(i)

68.20 sq.cm
(ii)

70.20 sq.cm
(iii)

67.20 sq.cm
(iv)

71.20 sq.cm
(v)

69.20 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)

101

sq.cm

:

196

sq.cm
(ii)

100

sq.cm

:

193

sq.cm
(iii)

100

sq.cm

:

196

sq.cm
(iv)

99

sq.cm

:

196

sq.cm
(v)

100

sq.cm

:

199

sq.cm

Question 42

42.

In the given figure, points M , N and O are the mid-points of sides KL, LJ and JK of △JKL. Which of the following are true?

a)

All four small triangles have equal areas

b)

Area of △JKL = 4 times area of △MNO

c)

Area of trapezium KLNO is thrice the area of △JON

d)

e)

(i)

{d,a}
(ii)

{d,a,b}
(iii)

{e,b}
(iv)

{d,e,c}
(v)

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

(i)

{a,e,b}
(ii)

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

{a,d}
(iv)

{a,b}
(v)

{a,c}

Question 44

44.

The perimeters of two similar triangles are 30 cm and 15 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.

(i)

6.00 cm
(ii)

9.00 cm
(iii)

7.00 cm
(iv)

8.00 cm
(v)

10.00 cm

Question 45

45.

In the given figure, F is a point on side DE of △CDE such that ∠ECD = ∠CFE = 110° , ∠FEC = 26°. Find ∠ECF

(i)

44°
(ii)

45°
(iii)

46°
(iv)

42°
(v)

43°

Question 46

46.

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)
a

2

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

a sq.units
(v)
√

3

a sq.units

Question 47

47.

CDEF is a cyclic trapezium. Diagonals DF and CE intersect at G. If FC = 17 cm, find DE

(i)

17 cm
(ii)

16 cm
(iii)

15 cm
(iv)

19 cm
(v)

18 cm

Question 48

48.

A vertical stick
16 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)

130 m
(ii)

127 m
(iii)

126 m
(iv)

128 m
(v)

129 m

Question 49

49.

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

(i)

1
2

√

4
(ii)

1
(iii)

1
2

4
√

2
(iv)

1
2

√

1
2
(v)

1
2

√

2

Question 50

50.

In the given figure, ∠NKL = ∠MKN and KN ∥ OM and KL = 17 cm, LN = 9 cm and NM = 11 cm. Find KO

(i)

18.78 cm
(ii)

22.78 cm
(iii)

19.78 cm
(iv)

20.78 cm
(v)

21.78 cm

Question 51

51.

In the given figure, BD is the angular bisector of
∠B
&
∠D

(i)

20.00 cm
(ii)

18.00 cm
(iii)

19.00 cm
(iv)

21.00 cm
(v)

17.00 cm

Question 52

52.

In the given figure, ABC is a triangle and 'O' is a point inside △ABC. The angular bisector of ∠BOA, ∠COB & ∠AOC meet AB, BC & CA at D, E & F respectively . Then