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)

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)

AAA Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 4

4.

In the given figure, △DEF and △RST 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, △HIJ and △QRS 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 6

6.

In the given figure, △FGH and △QRS 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)

7.60 cm
(ii)

5.60 cm
(iii)

6.60 cm
(iv)

9.60 cm
(v)

8.60 cm

Question 8

8.

In the given figure,
DE
∥
BC
.

(i)

5.84 cm
(ii)

7.84 cm
(iii)

6.84 cm
(iv)

8.84 cm
(v)

4.84 cm

Question 9

9.

In the given figure, PQ ∥ EF and DF = 20 cm, PQ = 12.6 cm and EF = 21 cm, find DQ

(i)

11.0 cm
(ii)

12.0 cm
(iii)

14.0 cm
(iv)

10.0 cm
(v)

13.0 cm

Question 10

10.

In the given figure, △OPQ is isosceles right-angled at P and PR ⟂ QO. ∠R =

(i)

∠S
(ii)

∠O
(iii)

∠T
(iv)

∠P
(v)

∠Q

Question 11

11.

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

(i)

∠FCD
(ii)

∠ECD
(iii)

∠CDF
(iv)

∠DFC
(v)

∠FDE

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.

△ABH ∼

(i)

△DAE
(ii)

△FDA
(iii)

△ACF
(iv)

△DCF
(v)

△FEH

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)

∠HFE
(ii)

∠FDA
(iii)

∠FEH
(iv)

∠AFD
(v)

∠FAC

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)

∠FDA
(ii)

∠EHF
(iii)

∠FEH
(iv)

∠DAF
(v)

∠ACF

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)

∠EHF
(ii)

∠AFD
(iii)

∠HFE
(iv)

∠BHA
(v)

∠DAF

Question 16

16.

In the given figure, KLMN is a trapezium in which

NO
=
(

x

+

16

)
cm, find the value of x

(i)

(

20

,

18

)
(ii)

(

20

,

20

)
(iii)

(

18

,

18

)
(iv)

(

19

,

19

)
(v)

(

18

,

17

)

Question 17

17.

In the given figure, FGHI is a trapezium in which

(i)

△GHI
(ii)

△JGH
(iii)

△IFG
(iv)

△JFG
(v)

△JIF

Question 18

18.

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

(i)

△SJR
(ii)

△TIR
(iii)

△SJI
(iv)

△RIJ
(v)

△RTS

Question 19

19.

In the given figure, the altitudes UE and FV of △DEF meet at T. ∠FTE =

(i)

∠EFT
(ii)

∠TEF
(iii)

∠TUV
(iv)

∠UVT
(v)

∠VTU

Question 20

20.

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

If GJ = 16.9 cm, GR = 8.5 cm and GK = 8.45 cm, GH =

(i)

16.00 cm
(ii)

19.00 cm
(iii)

17.00 cm
(iv)

18.00 cm
(v)

15.00 cm

Question 21

21.

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

If HK = 13.8 cm, HJ = 16 cm and HL = 9.2 cm, LK =

(i)

3.60 cm
(ii)

4.60 cm
(iii)

5.60 cm
(iv)

2.60 cm
(v)

6.60 cm

Question 22

22.

In the given figure, ST ∥ IJ , and median HK bisects ST.
△HLT ∼

(i)

△HIJ
(ii)

△HIK
(iii)

△IJH
(iv)

△HSL
(v)

△HKJ

Question 23

23.

In the given figure, △GHI is a triangle in which GJ is the internal bisector of ∠G and IK ∥ JG meeting HG produced at K . ∠JGH =

(i)

∠GJI
(ii)

∠KGI
(iii)

∠JIG
(iv)

∠IKG
(v)

∠HJG

Question 24

24.

In the given figure, F and G are points on the sides CD and CE respectively of △CDE.For which of the following cases, FG ∥ DE

a)	CF = 8.5 cm, FD = 8.5 cm, CG = 8 cm and GE = 8 cm
b)	CD = 17 cm, FD = 8.5 cm, CG = 10 cm and CE = 16 cm
c)	CD = 17 cm, FD = 8.5 cm, CE = 16 cm and CG = 8 cm
d)	CD = 17 cm, CF = 10.5 cm, CE = 16 cm and GE = 8 cm

(i)

{a,c}
(ii)

{b,a}
(iii)

{d,c}
(iv)

{b,c,a}
(v)

{b,d,a}

Question 25

25.

In the given figure, the area of the △GHI is x sq.cm. J,K,L are the mid-points of the sides HI , IG and GH respectively. The area of the △JKL is

(i)
1
2

of area of △GHI
(ii)
3
4

of area of △GHI
(iii)
1
4

of area of △GHI
(iv)
1
3

of area of △GHI
(v)
2
3

of area of △GHI

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)
3
2

the area of the triangle
(ii)
4
3

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 H : I and the ratio of the corresponding heights is J : K , the ratio of their areas in the same order is

(i)

IJ : HK
(ii)

HJ : IK
(iii)

JK : HI
(iv)

HI : JK
(v)

HK : IJ

Question 28

28.

In the given △FGH, IJ ∥ GH. If FI : IG = 8.5 cm : 8.5 cm and FH = 16 cm, FJ =

(i)

9.00 cm
(ii)

8.00 cm
(iii)

7.00 cm
(iv)

6.00 cm
(v)

10.00 cm

Question 29

29.

In the given two similar triangles, if c = 15 cm, d = 16 cm, e = 17 cm, h = 10.2 cm, find f

(i)

8.00 cm
(ii)

9.00 cm
(iii)

7.00 cm
(iv)

11.00 cm
(v)

10.00 cm

Question 30

30.

In the given figure, given ∠JGH = ∠IGJ, x : y = 8.26 cm : 7.74 cm and q = 15 cm, find p =

(i)

18.00 cm
(ii)

17.00 cm
(iii)

14.00 cm
(iv)

15.00 cm
(v)

16.00 cm

Question 31

31.

In the given figure, given ∠EBC = ∠DBE, p = 7.29 cm, q = 7.71 cm and CD = 15 cm, find CE =

(i)

7.29 cm
(ii)

5.29 cm
(iii)

9.29 cm
(iv)

6.29 cm
(v)

8.29 cm

Question 32

32.

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

(i)

2 cm
(ii)

6 cm
(iii)

5 cm
(iv)

3 cm
(v)

4 cm

Question 33

33.

In the given figure, ∠EBC = 42.93°, find the value of x =

(i)

47.07°
(ii)

45.07°
(iii)

48.07°
(iv)

46.07°
(v)

49.07°

Question 34

34.

In the given figure, ∠BCD = 41.7°, find the value of y =

(i)

49.30°
(ii)

50.30°
(iii)

48.30°
(iv)

46.30°
(v)

47.30°

Question 35

35.

In the given figure, if EF ∥ GH then

(i)

△IEF ∼ △IGH
(ii)

△IFE ∼ △IHG
(iii)

△EFI ∼ △HGI
(iv)

△EFI ∼ △IGH
(v)

△EFI ∼ △IHG

Question 36

36.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. Which of the following are true?

a)

EF

2
=
GE
.
GH

b)

FG

2
=
EG
.
EH

c)

FH

2
=
EH
.
HG

d)

EF

2
=
EG
.
EH

e)

FG

2
=
GE
.
GH

(i)

{a,c,d}
(ii)

{a,b,e}
(iii)

{a,c}
(iv)

{b,d}
(v)

{c,d,e}

Question 37

37.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. If DE = 19 cm, DF = 11.77 cm, then find CD.

(i)

17.00 cm
(ii)

15.00 cm
(iii)

14.00 cm
(iv)

16.00 cm
(v)

13.00 cm

Question 38

38.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FI = 11 cm, IH = 12.3 cm, then find GI.

(i)

9.63 cm
(ii)

10.63 cm
(iii)

13.63 cm
(iv)

11.63 cm
(v)

12.63 cm

Question 39

39.

In the given figure, △ABC ∼ △NOP and AB = 11 cm, NO = 15.4 cm.

(i)

105.10 sq.cm
(ii)

109.10 sq.cm
(iii)

106.10 sq.cm
(iv)

108.10 sq.cm
(v)

107.10 sq.cm

Question 40

40.

In the given figure, △DEF ∼ △NOP and EF = 15 cm , OP = 21 cm and

(i)

183.02 sq.cm
(ii)

181.02 sq.cm
(iii)

182.02 sq.cm
(iv)

184.02 sq.cm
(v)

180.02 sq.cm

Question 41

41.

In the given figure, △CDE & △PQR are similar triangles. If the ratio of the heights CF : PS = 10 : 14, then the ratio of their areas is

(i)

100

sq.cm

:

198

sq.cm
(ii)

100

sq.cm

:

194

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 F , G and H are the mid-points of sides DE, EC and CD of △CDE. Which of the following are true?

a)

All four small triangles have equal areas

b)

Area of △CDE = 4 times area of △FGH

c)

d)

Area of trapezium DEGH is thrice the area of △CHG

e)

(i)

{c,a,b}
(ii)

{a,b,d}
(iii)

{c,e,d}
(iv)

{c,a}
(v)

{e,b}

Question 43

43.

In the given figure, points D , E and F are the mid-points of sides BC, CA and AB of △ABC. Which of the following are true?

a)	△DFE ∼ △ABC
b)	△EDC ∼ △ABC
c)	△AFE ∼ △ABC
d)	△DEF ∼ △ABC
e)	△FBD ∼ △ABC

(i)

{a,e,b}
(ii)

{a,b}
(iii)

{a,d}
(iv)

{a,c}
(v)

{b,c,d,e}

Question 44

44.

The perimeters of two similar triangles are 33 cm and 22 cm respectively. If one side of the first triangle is 15 cm, find the length of the corresponding side of the second triangle.

(i)

10.00 cm
(ii)

8.00 cm
(iii)

9.00 cm
(iv)

12.00 cm
(v)

11.00 cm

Question 45

45.

In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 101° , ∠DCA = 26°. Find ∠CAD

(i)

52°
(ii)

55°
(iii)

53°
(iv)

51°
(v)

54°

Question 46

46.

MNOP is a square and △MNQ is an equilateral triangle. Also, △MOR is an equilateral triangle. If area of △MNQ is 'a' sq.units, then the area of △MOR is

(i)
1
2

√

3

a sq.units
(ii)
1
2

a sq.units
(iii)
√

3

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

2

sq.units

Question 47

47.

JKLM is a cyclic trapezium. Diagonals KM and JL intersect at N. If MJ = 15 cm, find KL

(i)

13 cm
(ii)

14 cm
(iii)

17 cm
(iv)

15 cm
(v)

16 cm

Question 48

48.

A vertical stick
13 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)

104 m
(ii)

106 m
(iii)

102 m
(iv)

103 m
(v)

105 m

Question 49

49.

In the given figure, △CDE, RS ∥ DE such that

(i)

1
2

4
√

2
(ii)

1
2

√

-1
(iii)

1
2

√

2
(iv)

1
(v)

1
2

√

5

Question 50

50.

In the given figure, ∠DAB = ∠CAD and AD ∥ EC and AB = 18 cm, BD = 8 cm and DC = 9 cm. Find AE

(i)

21.25 cm
(ii)

18.25 cm
(iii)

19.25 cm
(iv)

20.25 cm
(v)

22.25 cm

Question 51

51.

In the given figure, GI is the angular bisector of
∠G
&
∠I

(i)

22.00 cm
(ii)

20.00 cm
(iii)

19.00 cm
(iv)

23.00 cm
(v)

21.00 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