EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

AAA Similarity

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SAS Similarity
(iii)

SSS Similarity
(iv)

not similar

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

SAS Similarity
(iii)

SSS Similarity
(iv)

AAA Similarity

Question 5

5.

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

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 6

6.

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

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

AAA Similarity

Question 7

7.

In the given figure, △NOP is isosceles right-angled at O and OQ ⟂ PN. ∠P =

(i)

∠S
(ii)

∠N
(iii)

∠Q
(iv)

∠O
(v)

∠R

Question 8

8.

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

(i)

∠KIJ
(ii)

∠KHI
(iii)

∠HIJ
(iv)

∠HIK
(v)

∠IJK

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)

△DCF
(ii)

△DAE
(iii)

△FEH
(iv)

△FDA
(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.

∠HAB =

(i)

∠FAC
(ii)

∠HFE
(iii)

∠FDA
(iv)

∠AFD
(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.

∠ABH =

(i)

∠DAF
(ii)

∠EHF
(iii)

∠ACF
(iv)

∠FEH
(v)

∠FDA

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.

∠EHF =

(i)

∠BHA
(ii)

∠AFD
(iii)

∠DAF
(iv)

∠CFA
(v)

∠HFE

Question 13

13.

In the given figure, CDEF is a trapezium in which

FG
=
(

5

x

+

3

)
cm, find the value of x

(i)

(

2

,

7

)
(ii)

(

5

,

-1

)
(iii)

(

5

,

0

)
(iv)

(

7

,

0

)
(v)

(

6

,

1

)

Question 14

14.

In the given figure, IJKL is a trapezium in which

(i)

△MIJ
(ii)

△MJK
(iii)

△LIJ
(iv)

△MLI
(v)

△JKL

Question 15

15.

In the given figure, the altitudes NH and IO of △GHI meet at M. △NIM ∼

(i)

△MHI
(ii)

△MON
(iii)

△OHM
(iv)

△NIH
(v)

△OHI

Question 16

16.

In the given figure, the altitudes RC and DS of △BCD meet at Q. ∠SCQ =

(i)

∠QDR
(ii)

∠CQS
(iii)

∠QSC
(iv)

∠DRQ
(v)

∠RQD

Question 17

17.

In the given figure, QR ∥ GH , and median FI bisects QR.
△FQJ ∼

(i)

△FGI
(ii)

△FJR
(iii)

△GHF
(iv)

△FGH
(v)

△FIH

Question 18

18.

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 . ∠PMN =

(i)

∠QMO
(ii)

∠OMP
(iii)

∠NPM
(iv)

∠POM
(v)

∠MPO

Question 19

19.

Which of the following are true?

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

(i)

{c,d,e}
(ii)

{e,f}
(iii)

{b,f}
(iv)

{a,e}
(v)

{a,f,e}

Question 20

20.

Which of the following are true?

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

(i)

{b,a}
(ii)

{a,c,e}
(iii)

{d,c}
(iv)

{b,d,e}
(v)

{b,a,c}

Question 21

21.

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

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

(i)

{c,d}
(ii)

{a,d}
(iii)

{b,c,a}
(iv)

{b,d,a}
(v)

{b,a}

Question 22

22.

Which of the following are true?

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

(i)

{c,a,b}
(ii)

{a,b,d}
(iii)

{c,b}
(iv)

{c,a}
(v)

{c,d}

Question 23

23.

Which of the following are true?

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

(i)

{d,a}
(ii)

{d,c}
(iii)

{a,b,c}
(iv)

{d,a,b}
(v)

{d,b}

Question 24

24.

In the given figure, the area of the △IJK is x sq.cm. L,M,N are the mid-points of the sides JK , KI and IJ respectively. The area of the △LMN is

(i)
3
4

of area of △IJK
(ii)
1
4

of area of △IJK
(iii)
2
3

of area of △IJK
(iv)
1
2

of area of △IJK
(v)
1
3

of area of △IJK

Question 25

25.

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

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

(i)
5
4

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
4
3

the area of the triangle
(iv)
thrice

the area of the triangle
(v)
twice

the area of the triangle

Question 26

26.

If the ratio of the bases of two triangles is C : D and the ratio of the corresponding heights is E : F , the ratio of their areas in the same order is

(i)

CE : DF
(ii)

CD : EF
(iii)

EF : CD
(iv)

CF : DE
(v)

DE : CF

Question 27

27.

In the given two similar triangles, if n = 16 cm, o = 16 cm, p = 19 cm, q = 9.6 cm, find r

(i)

11.60 cm
(ii)

7.60 cm
(iii)

9.60 cm
(iv)

10.60 cm
(v)

8.60 cm

Question 28

28.

In the given figure, given ∠KHI = ∠JHK, x : y = 9.21 cm : 9.79 cm and q = 17 cm, find p =

(i)

16.00 cm
(ii)

14.00 cm
(iii)

15.00 cm
(iv)

17.00 cm
(v)

18.00 cm

Question 29

29.

In the given figure, given ∠EBC = ∠DBE, p = 9.23 cm, q = 8.77 cm and CD = 18 cm, find ED =

(i)

9.77 cm
(ii)

7.77 cm
(iii)

6.77 cm
(iv)

10.77 cm
(v)

8.77 cm

Question 30

30.

In the given figure, HIJK is a trapezium where OH = 15 cm , OI = 15 cm and OK = 5 cm . Find OJ =

(i)

5 cm
(ii)

7 cm
(iii)

4 cm
(iv)

6 cm
(v)

3 cm

Question 31

31.

In the given figure, ∠IFG = 38.18°, find the value of x =

(i)

50.82°
(ii)

49.82°
(iii)

53.82°
(iv)

52.82°
(v)

51.82°

Question 32

32.

In the given figure, ∠CDE = 48.01°, find the value of y =

(i)

42.99°
(ii)

39.99°
(iii)

41.99°
(iv)

40.99°
(v)

43.99°

Question 33

33.

In the given figure, if FG ∥ HI then

(i)

△JGF ∼ △JIH
(ii)

△JFG ∼ △JHI
(iii)

△FGJ ∼ △IHJ
(iv)

△FGJ ∼ △JHI
(v)

△FGJ ∼ △JIH

Question 34

34.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. Which of the following are true?

a)

GH

2
=
HF
.
HI

b)

GH

2
=
FH
.
FI

c)

FG

2
=
HF
.
HI

d)

GI

2
=
FI
.
IH

e)

FG

2
=
FH
.
FI

(i)

{b,a,d}
(ii)

{b,a}
(iii)

{b,c,e}
(iv)

{c,d}
(v)

{a,d,e}

Question 35

35.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If HI = 19 cm, HJ = 13.77 cm, then find GH.

(i)

18.00 cm
(ii)

19.00 cm
(iii)

22.00 cm
(iv)

20.00 cm
(v)

21.00 cm

Question 36

36.

In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If ED = 12.1 cm, CE = 13.38 cm, then find BE.

(i)

15.80 cm
(ii)

16.80 cm
(iii)

13.80 cm
(iv)

12.80 cm
(v)

14.80 cm

Question 37

37.

In the given figure, △DEF ∼ △QRS and DE = 10 cm, QR = 14 cm.

(i)

112.71 sq.cm
(ii)

113.71 sq.cm
(iii)

111.71 sq.cm
(iv)

109.71 sq.cm
(v)

110.71 sq.cm

Question 38

38.

In the given figure, △DEF ∼ △MNO and EF = 15 cm , NO = 21 cm and

(i)

146.03 sq.cm
(ii)

142.03 sq.cm
(iii)

143.03 sq.cm
(iv)

144.03 sq.cm
(v)

145.03 sq.cm

Question 39

39.

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

(i)

99

sq.cm

:

196

sq.cm
(ii)

100

sq.cm

:

196

sq.cm
(iii)

101

sq.cm

:

196

sq.cm
(iv)

100

sq.cm

:

198

sq.cm
(v)

100

sq.cm

:

193

sq.cm

Question 40

40.

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)

b)

All four small triangles have equal areas

c)

d)

Area of △HIJ = 4 times area of △KLM

e)

Area of trapezium IJLM is thrice the area of △HML

(i)

{c,d}
(ii)

{a,c,e}
(iii)

{a,b,d}
(iv)

{a,b}
(v)

{b,d,e}

Question 41

41.

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

(i)

{b,c}
(ii)

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

{b,a}
(iv)

{b,d}
(v)

{b,e,a}

Question 42

42.

The perimeters of two similar triangles are 31 cm and 19 cm respectively. If one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.

(i)

5.35 cm
(ii)

7.35 cm
(iii)

8.35 cm
(iv)

6.35 cm
(v)

9.35 cm

Question 43

43.

In the given figure, F is a point on side DE of △CDE such that ∠ECD = ∠CFE = 108° , ∠FEC = 25°. Find ∠ECF

(i)

49°
(ii)

45°
(iii)

46°
(iv)

48°
(v)

47°

Question 44

44.

JKLM is a square and △JKN is an equilateral triangle. Also, △JLO is an equilateral triangle. If area of △JKN is 'a' sq.units, then the area of △JLO is

(i)
1
2

a sq.units
(ii)
1
2

√

3

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

2

sq.units
(v)
√

3

a sq.units

Question 45

45.

GHIJ is a cyclic trapezium. Diagonals HJ and GI intersect at K. If JG = 15 cm, find HI

(i)

17 cm
(ii)

14 cm
(iii)

13 cm
(iv)

16 cm
(v)

15 cm

Question 46

46.

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)

90 m
(iii)

87 m
(iv)

88 m
(v)

89 m

Question 47

47.

In the given figure, △CED is right-angled at E, EF ⟂ CD.

a)

ab
=
pc

b)

c)

a

2
+
b

2
=
c

2

d)

e)

1

a

2
+
1

b

2
=
1

p

2

(i)

{b,a,c}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{b,d,e}
(v)

{a,c,e}

Question 48

48.

In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 15 cm, HJ = 8 cm and JI = 10 cm. Find GK

(i)

18.75 cm
(ii)

16.75 cm
(iii)

17.75 cm
(iv)

20.75 cm
(v)

19.75 cm

Question 49

49.

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

(i)

21.00 cm
(ii)

22.00 cm
(iii)

24.00 cm
(iv)

25.00 cm
(v)

23.00 cm

Question 50

50.

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

:

10
.

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

(i)

8

:

10
(ii)

9

:

12
(iii)

10

:

9
(iv)

10

:

10
(v)

9

:

7

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)

10.32 cm
(ii)

12.32 cm
(iii)

13.32 cm
(iv)

11.32 cm
(v)

14.32 cm

Assignment Key