EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

not similar
(iv)

SAS Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SSS 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)

not similar
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 5

5.

In the given figure, △GHI 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 6

6.

In the given figure, △GHI and △QRS 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)

10.94 cm
(ii)

8.94 cm
(iii)

6.94 cm
(iv)

7.94 cm
(v)

9.94 cm

Question 8

8.

In the given figure,
EF
∥
CD
.

(i)

4.53 cm
(ii)

3.53 cm
(iii)

5.53 cm
(iv)

2.53 cm
(v)

6.53 cm

Question 9

9.

In the given figure, TU ∥ HI and GT = 12 cm, GH = 20 cm and TU = 15 cm, find HI

(i)

23.0 cm
(ii)

27.0 cm
(iii)

26.0 cm
(iv)

24.0 cm
(v)

25.0 cm

Question 10

10.

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

(i)

∠L
(ii)

∠O
(iii)

∠Q
(iv)

∠M
(v)

∠P

Question 11

11.

In the given figure, △ABC is isosceles right-angled at B and BD ⟂ CA. ∠BDA =

(i)

∠DAB
(ii)

∠ABD
(iii)

∠ABC
(iv)

∠BCD
(v)

∠DBC

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)

△ACF
(ii)

△DAE
(iii)

△FDA
(iv)

△ABH
(v)

△DCF

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.

∠FAC =

(i)

∠AFD
(ii)

∠HAB
(iii)

∠HFE
(iv)

∠FDA
(v)

∠FEH

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)

∠EHF
(ii)

∠ABH
(iii)

∠ACF
(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)

∠DAF
(ii)

∠EHF
(iii)

∠AFD
(iv)

∠HFE
(v)

∠CFA

Question 16

16.

In the given figure, HIJK is a trapezium in which

KL
=
(

2

x

+

22

)
cm, find the value of x

(i)

(

-6

,

36

)
(ii)

(

34

,

-8

)
(iii)

(

37

,

-8

)
(iv)

(

35

,

-7

)
(v)

(

34

,

-9

)

Question 17

17.

In the given figure, DEFG is a trapezium in which

(i)

△HGD
(ii)

△HEF
(iii)

△GDE
(iv)

△HFG
(v)

△EFG

Question 18

18.

In the given figure, the altitudes TH and IU of △GHI meet at S. △TIH ∼

(i)

△UHS
(ii)

△UHI
(iii)

△TIS
(iv)

△SHI
(v)

△SUT

Question 19

19.

In the given figure, the altitudes NH and IO of △GHI meet at M. ∠NMI =

(i)

∠MOH
(ii)

∠MIN
(iii)

∠OHM
(iv)

∠HMO
(v)

∠INM

Question 20

20.

In the given figure, PQ ∥ GH , and median FI bisects PQ.

If FG = 17 cm, FI = 16.9 cm and FP = 7.73 cm, PG =

(i)

10.27 cm
(ii)

8.27 cm
(iii)

11.27 cm
(iv)

7.27 cm
(v)

9.27 cm

Question 21

21.

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

If HK = 16.5 cm, HJ = 20 cm and HL = 9.43 cm, HQ =

(i)

9.43 cm
(ii)

13.43 cm
(iii)

12.43 cm
(iv)

10.43 cm
(v)

11.43 cm

Question 22

22.

In the given figure, TU ∥ HI , and median GJ bisects TU.
△GTK ∼

(i)

△GKU
(ii)

△GJI
(iii)

△GHJ
(iv)

△GHI
(v)

△HIG

Question 23

23.

In the given figure, △FGH is a triangle in which FI is the internal bisector of ∠F and HJ ∥ IF meeting GF produced at J . ∠HJF =

(i)

∠IHF
(ii)

∠IFG
(iii)

∠JFH
(iv)

∠GIF
(v)

∠FIH

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)	CD = 20 cm, FD = 8.57 cm, CG = 13.43 cm and CE = 20 cm
b)	CD = 20 cm, FD = 8.57 cm, CE = 20 cm and CG = 11.43 cm
c)	CF = 11.43 cm, FD = 8.57 cm, CG = 11.43 cm and GE = 8.57 cm
d)	CD = 20 cm, CF = 13.43 cm, CE = 20 cm and GE = 8.57 cm

(i)

{d,c}
(ii)

{a,b}
(iii)

{a,c,b}
(iv)

{a,d,b}
(v)

{b,c}

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
3

of area of △GHI
(ii)
2
3

of area of △GHI
(iii)
1
4

of area of △GHI
(iv)
3
4

of area of △GHI
(v)
1
2

of area of △GHI

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)
thrice

the area of the triangle
(ii)
4
3

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
twice

the area of the triangle
(v)
3
2

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)

HI : JK
(ii)

JK : HI
(iii)

HJ : IK
(iv)

IJ : HK
(v)

HK : IJ

Question 28

28.

In the given △ABC, DE ∥ BC. If AD : DB = 11.43 cm : 8.57 cm and AC = 16 cm, AE =

(i)

11.14 cm
(ii)

10.14 cm
(iii)

8.14 cm
(iv)

7.14 cm
(v)

9.14 cm

Question 29

29.

In the given two similar triangles, if m = 20 cm, n = 19 cm, o = 20 cm, r = 12 cm, find p

(i)

13.00 cm
(ii)

10.00 cm
(iii)

14.00 cm
(iv)

12.00 cm
(v)

11.00 cm

Question 30

30.

In the given figure, given ∠GDE = ∠FDG, x : y = 8.18 cm : 9.82 cm and q = 18 cm, find p =

(i)

16.00 cm
(ii)

15.00 cm
(iii)

17.00 cm
(iv)

13.00 cm
(v)

14.00 cm

Question 31

31.

In the given figure, given ∠JGH = ∠IGJ, p = 7.76 cm, q = 8.24 cm and HI = 16 cm, find JI =

(i)

8.24 cm
(ii)

6.24 cm
(iii)

7.24 cm
(iv)

10.24 cm
(v)

9.24 cm

Question 32

32.

In the given figure, BCDE is a trapezium where OB = 14 cm , OC = 14 cm and OD = 5 cm . Find OE =

(i)

7 cm
(ii)

3 cm
(iii)

4 cm
(iv)

6 cm
(v)

5 cm

Question 33

33.

In the given figure, ∠EFH = 47.23°, find the value of x =

(i)

41.77°
(ii)

44.77°
(iii)

42.77°
(iv)

43.77°
(v)

40.77°

Question 34

34.

In the given figure, ∠DEF = 48.46°, find the value of y =

(i)

39.54°
(ii)

41.54°
(iii)

42.54°
(iv)

43.54°
(v)

40.54°

Question 35

35.

In the given figure, if CD ∥ EF then

(i)

△GDC ∼ △GFE
(ii)

△CDG ∼ △GEF
(iii)

△CDG ∼ △GFE
(iv)

△GCD ∼ △GEF
(v)

△CDG ∼ △FEG

Question 36

36.

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

a)

FH

2
=
EH
.
HG

b)

EF

2
=
GE
.
GH

c)

EF

2
=
EG
.
EH

d)

FG

2
=
GE
.
GH

e)

FG

2
=
EG
.
EH

(i)

{b,a}
(ii)

{b,a,c}
(iii)

{a,c,d}
(iv)

{e,c}
(v)

{b,e,d}

Question 37

37.

In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. If IJ = 17 cm, JL = 12.95 cm, then find JK.

(i)

20.00 cm
(ii)

19.00 cm
(iii)

21.00 cm
(iv)

18.00 cm
(v)

22.00 cm

Question 38

38.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AD = 12.1 cm, BD = 13.38 cm, then find DC.

(i)

16.80 cm
(ii)

14.80 cm
(iii)

13.80 cm
(iv)

12.80 cm
(v)

15.80 cm

Question 39

39.

In the given figure, △ABC ∼ △NOP and AB = 12 cm, NO = 16.8 cm.

(i)

47.00 sq.cm
(ii)

48.00 sq.cm
(iii)

46.00 sq.cm
(iv)

50.00 sq.cm
(v)

49.00 sq.cm

Question 40

40.

In the given figure, △ABC ∼ △NOP and BC = 15 cm , OP = 21 cm and

(i)

162.64 sq.cm
(ii)

164.64 sq.cm
(iii)

163.64 sq.cm
(iv)

166.64 sq.cm
(v)

165.64 sq.cm

Question 41

41.

In the given figure, △DEF & △OPQ are similar triangles. If the ratio of the heights DG : OR = 10 : 13, then the ratio of their areas is

(i)

101

sq.cm

:

169

sq.cm
(ii)

100

sq.cm

:

172

sq.cm
(iii)

100

sq.cm

:

169

sq.cm
(iv)

100

sq.cm

:

166

sq.cm
(v)

99

sq.cm

:

169

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)

b)

All four small triangles have equal areas

c)

Area of △IJK = 4 times area of △LMN

d)

e)

Area of trapezium JKMN is thrice the area of △INM

(i)

{b,c,e}
(ii)

{a,b,c}
(iii)

{d,c}
(iv)

{a,b}
(v)

{a,d,e}

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

(i)

{d,e,a}
(ii)

{d,a}
(iii)

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

{d,c}
(v)

{d,b}

Question 44

44.

The perimeters of two similar triangles are 26 cm and 22 cm respectively. If one side of the first triangle is 13 cm, find the length of the corresponding side of the second triangle.

(i)

10.00 cm
(ii)

11.00 cm
(iii)

9.00 cm
(iv)

13.00 cm
(v)

12.00 cm

Question 45

45.

In the given figure, L is a point on side JK of △IJK such that ∠KIJ = ∠ILK = 102° , ∠LKI = 29°. Find ∠KIL

(i)

47°
(ii)

48°
(iii)

51°
(iv)

50°
(v)

49°

Question 46

46.

ABCD is a square and △ABE is an equilateral triangle. Also, △ACF is an equilateral triangle. If area of △ABE is 'a' sq.units, then the area of △ACF is

(i)
1
2

√

3

a sq.units
(ii)
1
2

a sq.units
(iii)
2a sq.units
(iv)
√

3

a sq.units
(v)
a

2

sq.units

Question 47

47.

DEFG is a cyclic trapezium. Diagonals EG and DF intersect at H. If GD = 17 cm, find EF

(i)

18 cm
(ii)

17 cm
(iii)

16 cm
(iv)

19 cm
(v)

15 cm

Question 48

48.

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

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

Find the height of the tower.

(i)

86 m
(ii)

88 m
(iii)

87 m
(iv)

90 m
(v)

89 m

Question 49

49.

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

(i)

1
2

√

1
2
(ii)

1
2

√

2
(iii)

1
(iv)

1
2

√

5
(v)

1
2

4
√

2

Question 50

50.

In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 15 cm, HJ = 7 cm and JI = 9 cm. Find GK

(i)

17.29 cm
(ii)

20.29 cm
(iii)

21.29 cm
(iv)

18.29 cm
(v)

19.29 cm

Question 51

51.

In the given figure, HJ is the angular bisector of
∠H
&
∠J

(i)

18.00 cm
(ii)

19.00 cm
(iii)

20.00 cm
(iv)

21.00 cm
(v)

17.00 cm

Question 52

52.

In the given figure, DEF is a triangle and 'O' is a point inside △DEF. The angular bisector of ∠EOD, ∠FOE & ∠DOF meet DE, EF & FD at G, H & I respectively . Then