EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SAS Similarity
(iii)

SSS Similarity
(iv)

not similar

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

AAA Similarity

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

not similar
(iv)

SAS Similarity

Question 5

5.

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

Identify the property by which the two triangles are similar

(i)

SAS Similarity
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 6

6.

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

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

AAA Similarity
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 7

7.

(i)

3.07 cm
(ii)

6.07 cm
(iii)

7.07 cm
(iv)

5.07 cm
(v)

4.07 cm

Question 8

8.

In the given figure,
ST
∥
QR
.

(i)

10.18 cm
(ii)

7.18 cm
(iii)

9.18 cm
(iv)

11.18 cm
(v)

8.18 cm

Question 9

9.

In the given figure, ST ∥ BC and AB = 24 cm, ST = 12 cm and BC = 20 cm, find AS

(i)

13.4 cm
(ii)

16.4 cm
(iii)

12.4 cm
(iv)

14.4 cm
(v)

15.4 cm

Question 10

10.

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

(i)

∠C
(ii)

∠H
(iii)

∠D
(iv)

∠F
(v)

∠G

Question 11

11.

In the given figure, △IJK is isosceles right-angled at J and JL ⟂ KI. ∠KLJ =

(i)

∠JKL
(ii)

∠LIJ
(iii)

∠LJK
(iv)

∠IJL
(v)

∠JLI

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.

∠HFE =

(i)

∠HAB
(ii)

∠AFD
(iii)

∠FEH
(iv)

∠FAC
(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.

∠ABH =

(i)

∠ACF
(ii)

∠FDA
(iii)

∠EHF
(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)

∠DAF
(ii)

∠EHF
(iii)

∠BHA
(iv)

∠AFD
(v)

∠HFE

Question 16

16.

In the given figure, DEFG is a trapezium in which

GH
=
(

2

x

+

8

)
cm, find the value of x

(i)

(

13

,

(
-2
5
)

)
(ii)

(

7
3

,

14

)
(iii)

(

14

,

(
-2
3
)

)
(iv)

(

12

,

-2

)
(v)

(

12

,

(
-2
3
)

)

Question 17

17.

In the given figure, BCDE is a trapezium in which

(i)

△CDE
(ii)

△EBC
(iii)

△FEB
(iv)

△FCD
(v)

△FBC

Question 18

18.

In the given figure, the altitudes SI and JT of △HIJ meet at R. △TIJ ∼

(i)

△RIJ
(ii)

△TIR
(iii)

△SJI
(iv)

△SJR
(v)

△RTS

Question 19

19.

In the given figure, the altitudes SB and CT of △ABC meet at R. ∠BRT =

(i)

∠RCS
(ii)

∠TBR
(iii)

∠SRC
(iv)

∠RTB
(v)

∠CSR

Question 20

20.

In the given figure, TU ∥ BC , and median AD bisects TU.

If AB = 17 cm, AT = 8.5 cm and AE = 8.5 cm, AD =

(i)

19.00 cm
(ii)

15.00 cm
(iii)

17.00 cm
(iv)

18.00 cm
(v)

16.00 cm

Question 21

21.

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

If GJ = 16.2 cm, GI = 17 cm and GQ = 7.29 cm, GK =

(i)

5.94 cm
(ii)

7.94 cm
(iii)

6.94 cm
(iv)

8.94 cm
(v)

4.94 cm

Question 22

22.

In the given figure, QR ∥ CD , and median BE bisects QR.
△BED ∼

(i)

△BFR
(ii)

△CDB
(iii)

△BCE
(iv)

△BQF
(v)

△BCD

Question 23

23.

In the given figure, △OPQ is a triangle in which OR is the internal bisector of ∠O and QS ∥ RO meeting PO produced at S . ∠QOR =

(i)

∠PRO
(ii)

∠SOQ
(iii)

∠ORQ
(iv)

∠RQO
(v)

∠ROP

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 = 16 cm, EH = 10.89 cm, EG = 18 cm and IG = 8 cm
b)	EF = 16 cm, HF = 7.11 cm, EG = 18 cm and EI = 10 cm
c)	EH = 8.89 cm, HF = 7.11 cm, EI = 10 cm and IG = 8 cm
d)	EF = 16 cm, HF = 7.11 cm, EI = 12 cm and EG = 18 cm

(i)

{a,d,b}
(ii)

{a,c,b}
(iii)

{d,c}
(iv)

{a,b}
(v)

{b,c}

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)
1
3

of area of △KLM
(ii)
2
3

of area of △KLM
(iii)
1
2

of area of △KLM
(iv)
1
4

of area of △KLM
(v)
3
4

of area of △KLM

Question 26

26.

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

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

(i)
5
4

the area of the triangle
(ii)
thrice

the area of the triangle
(iii)
4
3

the area of the triangle
(iv)
3
2

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

(i)

EH : FG
(ii)

EF : GH
(iii)

GH : EF
(iv)

FG : EH
(v)

EG : FH

Question 28

28.

In the given △GHI, JK ∥ HI. If GJ : JH = 8.64 cm : 10.36 cm and GI = 20 cm, KI =

(i)

9.91 cm
(ii)

11.91 cm
(iii)

10.91 cm
(iv)

12.91 cm
(v)

8.91 cm

Question 29

29.

In the given two similar triangles, if b = 20 cm, c = 15 cm, d = 17 cm, g = 10.2 cm, find e

(i)

10.00 cm
(ii)

13.00 cm
(iii)

12.00 cm
(iv)

14.00 cm
(v)

11.00 cm

Question 30

30.

In the given figure, given ∠KHI = ∠JHK, x : y = 9 cm : 9 cm and p = 18 cm, find q =

(i)

20.00 cm
(ii)

16.00 cm
(iii)

19.00 cm
(iv)

18.00 cm
(v)

17.00 cm

Question 31

31.

In the given figure, given ∠GDE = ∠FDG, p = 9.77 cm, q = 9.23 cm and EF = 19 cm, find GF =

(i)

10.23 cm
(ii)

9.23 cm
(iii)

7.23 cm
(iv)

8.23 cm
(v)

11.23 cm

Question 32

32.

In the given figure, DEFG is a trapezium where OE = 13 cm , OF = 4 cm and OG = 4 cm . Find OD =

(i)

11 cm
(ii)

13 cm
(iii)

12 cm
(iv)

14 cm
(v)

15 cm

Question 33

33.

In the given figure, ∠HEF = 48.45°, find the value of x =

(i)

43.55°
(ii)

40.55°
(iii)

39.55°
(iv)

42.55°
(v)

41.55°

Question 34

34.

In the given figure, ∠JKL = 42.93°, find the value of y =

(i)

47.07°
(ii)

45.07°
(iii)

48.07°
(iv)

49.07°
(v)

46.07°

Question 35

35.

In the given figure, if FG ∥ HI then

(i)

△JFG ∼ △JHI
(ii)

△FGJ ∼ △JIH
(iii)

△JGF ∼ △JIH
(iv)

△FGJ ∼ △IHJ
(v)

△FGJ ∼ △JHI

Question 36

36.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. Which of the following are true?

a)

HI

2
=
IG
.
IJ

b)

GH

2
=
GI
.
GJ

c)

GH

2
=
IG
.
IJ

d)

HI

2
=
GI
.
GJ

e)

HJ

2
=
GJ
.
JI

(i)

{a,b,e}
(ii)

{c,d,e}
(iii)

{c,a}
(iv)

{c,a,b}
(v)

{d,b}

Question 37

37.

In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If HI = 17 cm, IJ = 20 cm, then find IK.

(i)

13.95 cm
(ii)

12.95 cm
(iii)

14.95 cm
(iv)

11.95 cm
(v)

10.95 cm

Question 38

38.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If GJ = 9 cm, HJ = 12 cm, then find JI.

(i)

14.00 cm
(ii)

18.00 cm
(iii)

17.00 cm
(iv)

16.00 cm
(v)

15.00 cm

Question 39

39.

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

(i)

63.39 sq.cm
(ii)

60.39 sq.cm
(iii)

62.39 sq.cm
(iv)

64.39 sq.cm
(v)

61.39 sq.cm

Question 40

40.

In the given figure, △BCD ∼ △PQR and CD = 13 cm , QR = 18.2 cm and

(i)

76.68 sq.cm
(ii)

74.68 sq.cm
(iii)

78.68 sq.cm
(iv)

75.68 sq.cm
(v)

77.68 sq.cm

Question 41

41.

In the given figure, △ABC & △OPQ are similar triangles. If the ratio of the heights AD : OR = 13 : 18, then the ratio of their areas is

(i)

169

sq.cm

:

324

sq.cm
(ii)

169

sq.cm

:

321

sq.cm
(iii)

168

sq.cm

:

324

sq.cm
(iv)

169

sq.cm

:

327

sq.cm
(v)

170

sq.cm

:

324

sq.cm

Question 42

42.

In the given figure, points K , L and M are the mid-points of sides IJ, JH and HI of △HIJ. Which of the following are true?

a)

Area of △HIJ = 4 times area of △KLM

b)

c)

d)

Area of trapezium IJLM is thrice the area of △HML

e)

All four small triangles have equal areas

(i)

{a,d,e}
(ii)

{b,a,d}
(iii)

{b,a}
(iv)

{b,c,e}
(v)

{c,d}

Question 43

43.

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)	△QMO ∼ △LMN
b)	△LQP ∼ △LMN
c)	△OQP ∼ △LMN
d)	△OPQ ∼ △LMN
e)	△PON ∼ △LMN

(i)

{c,e,a}
(ii)

{c,b}
(iii)

{c,d}
(iv)

{a,b,d,e}
(v)

{c,a}

Question 44

44.

The perimeters of two similar triangles are 31 cm and 23 cm respectively. If one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.

(i)

9.90 cm
(ii)

10.90 cm
(iii)

6.90 cm
(iv)

8.90 cm
(v)

7.90 cm

Question 45

45.

In the given figure, J is a point on side HI of △GHI such that ∠IGH = ∠GJI = 109° , ∠JIG = 22°. Find ∠IGJ

(i)

49°
(ii)

48°
(iii)

51°
(iv)

47°
(v)

50°

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)
2a sq.units
(iii)
1
2

a sq.units
(iv)
1
2

√

3

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 = 15 cm, find DE

(i)

14 cm
(ii)

17 cm
(iii)

16 cm
(iv)

13 cm
(v)

15 cm

Question 48

48.

A vertical stick
14 m
long casts a shadow of
15 m
long on the ground.

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

Find the height of the tower.

(i)

112 m
(ii)

114 m
(iii)

113 m
(iv)

111 m
(v)

110 m

Question 49

49.

In the given figure, △ABC, RS ∥ BC such that

(i)

1
2

√

1
2
(ii)

1
2

√

2
(iii)

1
2

√

4
(iv)

1
2

4
√

2
(v)

1

Question 50

50.

In the given figure, ∠EBC = ∠DBE and BE ∥ FD and BC = 19 cm, CE = 7 cm and ED = 8 cm. Find BF

(i)

21.71 cm
(ii)

19.71 cm
(iii)

23.71 cm
(iv)

20.71 cm
(v)

22.71 cm

Question 51

51.

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

(i)

19.00 cm
(ii)

15.00 cm
(iii)

18.00 cm
(iv)

16.00 cm
(v)

17.00 cm

Question 52

52.

In the given figure, BCD is a triangle and 'O' is a point inside △BCD. The angular bisector of ∠COB, ∠DOC & ∠BOD meet BC, CD & DB at E, F & G respectively . Then