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)

not similar
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 4

4.

In the given figure, △HIJ and △RST 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 5

5.

In the given figure, △ABC and △PQR 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, △IJK and △PQR 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 7

7.

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

(i)

∠M
(ii)

∠J
(iii)

∠O
(iv)

∠N
(v)

∠K

Question 8

8.

In the given figure, △HIJ is isosceles right-angled at I and IK ⟂ JH. ∠HIK ≠

(i)

∠IJK
(ii)

∠KHI
(iii)

∠HIJ
(iv)

∠JHI
(v)

∠KIJ

Question 9

9.

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)

△FEH
(iii)

△DAE
(iv)

△DCF
(v)

△ACF

Question 10

10.

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.

∠AFD =

(i)

∠HFE
(ii)

∠FDA
(iii)

∠HAB
(iv)

∠FAC
(v)

∠FEH

Question 11

11.

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)

∠FEH
(iii)

∠ABH
(iv)

∠DAF
(v)

∠ACF

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.

∠BHA =

(i)

∠DAF
(ii)

∠EHF
(iii)

∠HFE
(iv)

∠CFA
(v)

∠AFD

Question 13

13.

In the given figure, FGHI is a trapezium in which

IJ
=
(

2

x

+

2

)
cm, find the value of x

(i)

(

13

,

0

)
(ii)

(

12

,

-1

)
(iii)

(

1

,

14

)
(iv)

(

12

,

-2

)
(v)

(

14

,

-1

)

Question 14

14.

In the given figure, NOPQ is a trapezium in which

(i)

△OPQ
(ii)

△RQN
(iii)

△RPQ
(iv)

△QNO
(v)

△ROP

Question 15

15.

In the given figure, the altitudes OC and DP of △BCD meet at N. △NPO ∼

(i)

△ODC
(ii)

△NCD
(iii)

△ODN
(iv)

△PCN
(v)

△PCD

Question 16

16.

In the given figure, the altitudes QF and GR of △EFG meet at P. ∠QPG =

(i)

∠GQP
(ii)

∠RFP
(iii)

∠FPR
(iv)

∠PGQ
(v)

∠PRF

Question 17

17.

In the given figure, QR ∥ DE , and median CF bisects QR.
△CQG ∼

(i)

△CFE
(ii)

△DEC
(iii)

△CDE
(iv)

△CGR
(v)

△CDF

Question 18

18.

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 . ∠GIK =

(i)

∠JIG
(ii)

∠GJI
(iii)

∠JGH
(iv)

∠HJG
(v)

∠KGI

Question 19

19.

Which of the following are true?

a)	Any two squares are similar.
b)	Any two circles are similar.
c)	Any two triangles are congruent.
d)	Any two squares are congruent.
e)	Any two triangles are similar.
f)	Any two circles are congruent.

(i)

{c,b,a}
(ii)

{e,f,a}
(iii)

{a,b}
(iv)

{c,a}
(v)

{d,b}

Question 20

20.

Which of the following are true?

a)	If two figures are congruent, then they are similar too.
b)	Similar figures have same area.
c)	If two figures are similar, then they are congruent too.
d)	Similar and congruent are not synonymous.
e)	Congruent figures have same area.

(i)

{b,c,e}
(ii)

{b,a,d}
(iii)

{c,d}
(iv)

{b,a}
(v)

{a,d,e}

Question 21

21.

Which of the following are necessary conditions for similarity of two polygons ?

a)	The corresponding sides are proportional.
b)	The corresponding angles are proportional.
c)	The corresponding angles are equal.
d)	The corresponding sides are equal.

(i)

{a,c}
(ii)

{b,a}
(iii)

{b,c,a}
(iv)

{d,c}
(v)

{b,d,a}

Question 22

22.

Which of the following are true?

a)	Similarity is reflexive.
b)	Similarity is symmetric.
c)	Similarity is transitive.
d)	Similarity is anti symmetric.

(i)

{d,a}
(ii)

{d,b}
(iii)

{a,b,c}
(iv)

{d,c}
(v)

{d,a,b}

Question 23

23.

Which of the following are true?

a)	Any two triangles are similar if the corresponding sides are proportional.
b)	Any two triangles are similar if the corresponding angles are equal.
c)	Any two quadrilaterals are similar if the corresponding angles are equal.
d)	Any two quadrilaterals are similar if the corresponding sides are proportional.

(i)

{c,b}
(ii)

{c,a,b}
(iii)

{a,b,d}
(iv)

{c,a}
(v)

{c,d}

Question 24

24.

In the given figure, the area of the △ABC is x sq.cm. D,E,F are the mid-points of the sides BC , CA and AB respectively. The area of the △DEF is

(i)
3
4

of area of △ABC
(ii)
2
3

of area of △ABC
(iii)
1
2

of area of △ABC
(iv)
1
4

of area of △ABC
(v)
1
3

of area of △ABC

Question 25

25.

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

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

(i)
5
4

the area of the triangle
(ii)
4
3

the area of the triangle
(iii)
thrice

the area of the triangle
(iv)
twice

the area of the triangle
(v)
3
2

the area of the triangle

Question 26

26.

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)

MP : NO
(ii)

MO : NP
(iii)

MN : OP
(iv)

NO : MP
(v)

OP : MN

Question 27

27.

In the given two similar triangles, if c = 20 cm, d = 16 cm, e = 19 cm, g = 9.6 cm, find h

(i)

12.40 cm
(ii)

11.40 cm
(iii)

13.40 cm
(iv)

9.40 cm
(v)

10.40 cm

Question 28

28.

In the given figure, given ∠DAB = ∠CAD, x : y = 8.89 cm : 7.11 cm and q = 16 cm, find p =

(i)

18.00 cm
(ii)

19.00 cm
(iii)

21.00 cm
(iv)

22.00 cm
(v)

20.00 cm

Question 29

29.

In the given figure, given ∠IFG = ∠HFI, p = 7.78 cm, q = 8.22 cm and GH = 16 cm, find GI =

(i)

8.78 cm
(ii)

9.78 cm
(iii)

5.78 cm
(iv)

7.78 cm
(v)

6.78 cm

Question 30

30.

In the given figure, IJKL is a trapezium where OJ = 12 cm , OK = 4 cm and OL = 4 cm . Find OI =

(i)

10 cm
(ii)

12 cm
(iii)

13 cm
(iv)

11 cm
(v)

14 cm

Question 31

31.

In the given figure, ∠CDF = 38.43°, find the value of x =

(i)

53.57°
(ii)

51.57°
(iii)

49.57°
(iv)

50.57°
(v)

52.57°

Question 32

32.

In the given figure, ∠GEF = 49.35°, find the value of y =

(i)

38.65°
(ii)

41.65°
(iii)

39.65°
(iv)

40.65°
(v)

42.65°

Question 33

33.

In the given figure, if GH ∥ IJ then

(i)

△GHK ∼ △KJI
(ii)

△KHG ∼ △KJI
(iii)

△GHK ∼ △JIK
(iv)

△GHK ∼ △KIJ
(v)

△KGH ∼ △KIJ

Question 34

34.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. Which of the following are true?

a)

BC

2
=
CA
.
CD

b)

BC

2
=
AC
.
AD

c)

BD

2
=
AD
.
DC

d)

AB

2
=
CA
.
CD

e)

AB

2
=
AC
.
AD

(i)

{b,d,e}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{b,a,c}
(v)

{a,c,e}

Question 35

35.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If DE = 18 cm, EG = 13.38 cm, then find EF.

(i)

22.00 cm
(ii)

18.00 cm
(iii)

21.00 cm
(iv)

20.00 cm
(v)

19.00 cm

Question 36

36.

In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If HK = 10.6 cm, KJ = 13.5 cm, then find IK.

(i)

12.96 cm
(ii)

10.96 cm
(iii)

9.96 cm
(iv)

11.96 cm
(v)

13.96 cm

Question 37

37.

In the given figure, △ABC ∼ △MNO and AB = 14 cm, MN = 19.6 cm.

(i)

64.38 sq.cm
(ii)

65.38 sq.cm
(iii)

66.38 sq.cm
(iv)

63.38 sq.cm
(v)

67.38 sq.cm

Question 38

38.

In the given figure, △DEF ∼ △PQR and EF = 12 cm , QR = 16.8 cm and

(i)

123.21 sq.cm
(ii)

121.21 sq.cm
(iii)

120.21 sq.cm
(iv)

124.21 sq.cm
(v)

122.21 sq.cm

Question 39

39.

In the given figure, △ABC & △OPQ are similar triangles. If the ratio of the heights AD : OR = 9 : 13, then the ratio of their areas is

(i)

80

sq.cm

:

169

sq.cm
(ii)

82

sq.cm

:

169

sq.cm
(iii)

81

sq.cm

:

167

sq.cm
(iv)

81

sq.cm

:

169

sq.cm
(v)

81

sq.cm

:

171

sq.cm

Question 40

40.

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)

Area of △DEF = 4 times area of △GHI

b)

c)

Area of trapezium EFHI is thrice the area of △DIH

d)

e)

All four small triangles have equal areas

(i)

{b,a,c}
(ii)

{b,a}
(iii)

{a,c,e}
(iv)

{b,d,e}
(v)

{d,c}

Question 41

41.

In the given figure, points N , O and P are the mid-points of sides LM, MK and KL of △KLM. Which of the following are true?

a)	△ONM ∼ △KLM
b)	△KPO ∼ △KLM
c)	△NPO ∼ △KLM
d)	△PLN ∼ △KLM
e)	△NOP ∼ △KLM

(i)

{c,b}
(ii)

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

{c,e,a}
(iv)

{c,a}
(v)

{c,d}

Question 42

42.

The perimeters of two similar triangles are 25 cm and 24 cm respectively. If one side of the first triangle is 9 cm, find the length of the corresponding side of the second triangle.

(i)

9.64 cm
(ii)

8.64 cm
(iii)

10.64 cm
(iv)

7.64 cm
(v)

6.64 cm

Question 43

43.

In the given figure, J is a point on side HI of △GHI such that ∠IGH = ∠GJI = 103° , ∠JIG = 22°. Find ∠IGJ

(i)

53°
(ii)

55°
(iii)

56°
(iv)

54°
(v)

57°

Question 44

44.

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)
√

3

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

√

3

a sq.units
(iv)
1
2

a sq.units
(v)
a

2

sq.units

Question 45

45.

CDEF is a cyclic trapezium. Diagonals DF and CE intersect at G. If FC = 15 cm, find DE

(i)

15 cm
(ii)

16 cm
(iii)

13 cm
(iv)

14 cm
(v)

17 cm

Question 46

46.

A vertical stick
15 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)

119 m
(ii)

122 m
(iii)

118 m
(iv)

120 m
(v)

121 m

Question 47

47.

In the given figure, △DFE is right-angled at F, FG ⟂ DE.

a)

a

2
+
b

2
=
c

2

b)

c)

ab
=
pc

d)

1

a

2
+
1

b

2
=
1

p

2

e)

(i)

{e,c}
(ii)

{b,e,d}
(iii)

{b,a,c}
(iv)

{b,a}
(v)

{a,c,d}

Question 48

48.

In the given figure, ∠IFG = ∠HFI and FI ∥ JH and FG = 19 cm, GI = 8 cm and IH = 7 cm. Find FJ

(i)

15.62 cm
(ii)

14.62 cm
(iii)

16.62 cm
(iv)

17.62 cm
(v)

18.62 cm

Question 49

49.

In the given figure, MO is the angular bisector of
∠M
&
∠O

(i)

22.00 cm
(ii)

24.00 cm
(iii)

23.00 cm
(iv)

25.00 cm
(v)

26.00 cm

Question 50

50.

The ratio of the bases of two triangles ABC and DEF is
9

:

7
.

If the triangles are equal in area, then the ratio of their heights is

(i)

8

:

7
(ii)

9

:

9
(iii)

7

:

9
(iv)

10

:

7
(v)

9

:

5

Question 51

51.

In the given figure, the two circles touch each other internally.

Diameter
OB
passes through the centre of the smaller circle.

Find the radius of the outer circle.

(i)

12.83 cm
(ii)

14.83 cm
(iii)

10.83 cm
(iv)

13.83 cm
(v)

11.83 cm

Assignment Key