EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

SAS 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)

AAA Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

SAS Similarity
(ii)

AAA Similarity
(iii)

SSS Similarity
(iv)

not similar

Question 5

5.

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

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 6

6.

In the given figure, △HIJ and △TUV 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 7

7.

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

(i)

∠A
(ii)

∠F
(iii)

∠E
(iv)

∠B
(v)

∠D

Question 8

8.

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

(i)

∠IKH
(ii)

∠HIK
(iii)

∠KIJ
(iv)

∠IJK
(v)

∠KHI

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.

△ACF ∼

(i)

△FEH
(ii)

△FDA
(iii)

△ABH
(iv)

△DCF
(v)

△DAE

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.

∠FAC =

(i)

∠HAB
(ii)

∠FEH
(iii)

∠AFD
(iv)

∠HFE
(v)

∠FDA

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.

∠ACF =

(i)

∠EHF
(ii)

∠DAF
(iii)

∠FEH
(iv)

∠FDA
(v)

∠ABH

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)

∠CFA
(iii)

∠HFE
(iv)

∠AFD
(v)

∠EHF

Question 13

13.

In the given figure, NOPQ is a trapezium in which

QR
=
(

5

x

+

1

)
cm, find the value of x

(i)

(

1

,

8

)
(ii)

(

2

,

7

)
(iii)

(

9

,

2

)
(iv)

(

0

,

7

)
(v)

(

0

,

6

)

Question 14

14.

In the given figure, IJKL is a trapezium in which

(i)

△MKL
(ii)

△JKL
(iii)

△MLI
(iv)

△MJK
(v)

△LIJ

Question 15

15.

In the given figure, the altitudes OE and FP of △DEF meet at N. △NEF ∼

(i)

△OFN
(ii)

△PEF
(iii)

△PEN
(iv)

△OFE
(v)

△NPO

Question 16

16.

In the given figure, the altitudes OC and DP of △BCD meet at N. ∠NDO =

(i)

∠DON
(ii)

∠CNP
(iii)

∠NPC
(iv)

∠PCN
(v)

∠OND

Question 17

17.

In the given figure, ST ∥ FG , and median EH bisects ST.
△EFH ∼

(i)

△EHG
(ii)

△EIT
(iii)

△ESI
(iv)

△FGE
(v)

△EFG

Question 18

18.

In the given figure, △DEF is a triangle in which DG is the internal bisector of ∠D and FH ∥ GD meeting ED produced at H . ∠GDE =

(i)

∠HDF
(ii)

∠EGD
(iii)

∠DGF
(iv)

∠GFD
(v)

∠FHD

Question 19

19.

Which of the following are true?

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

(i)

{d,e,b}
(ii)

{a,f,b}
(iii)

{b,f}
(iv)

{a,b}
(v)

{c,f}

Question 20

20.

Which of the following are true?

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

(i)

{d,a}
(ii)

{e,b}
(iii)

{d,a,b}
(iv)

{a,b,c}
(v)

{d,e,c}

Question 21

21.

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

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

(i)

{c,a}
(ii)

{d,b}
(iii)

{c,b,a}
(iv)

{a,b}
(v)

{c,d,a}

Question 22

22.

Which of the following are true?

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

(i)

{b,d}
(ii)

{b,a}
(iii)

{b,c}
(iv)

{b,a,c}
(v)

{a,c,d}

Question 23

23.

Which of the following are true?

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

(i)

{c,b}
(ii)

{a,b,d}
(iii)

{c,d}
(iv)

{c,a}
(v)

{c,a,b}

Question 24

24.

In the given figure, the area of the △FGH is x sq.cm. I,J,K are the mid-points of the sides GH , HF and FG respectively. The area of the △IJK is

(i)
1
2

of area of △FGH
(ii)
3
4

of area of △FGH
(iii)
1
3

of area of △FGH
(iv)
2
3

of area of △FGH
(v)
1
4

of area of △FGH

Question 25

25.

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

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

(i)
thrice

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
twice

the area of the triangle
(v)
4
3

the area of the triangle

Question 26

26.

If the ratio of the bases of two triangles is K : L and the ratio of the corresponding heights is M : N , the ratio of their areas in the same order is

(i)

KN : LM
(ii)

KM : LN
(iii)

KL : MN
(iv)

MN : KL
(v)

LM : KN

Question 27

27.

In the given two similar triangles, if a = 18 cm, b = 15 cm, c = 20 cm, f = 12 cm, find d

(i)

8.80 cm
(ii)

11.80 cm
(iii)

10.80 cm
(iv)

9.80 cm
(v)

12.80 cm

Question 28

28.

In the given figure, given ∠DAB = ∠CAD, x : y = 7.97 cm : 9.03 cm and q = 17 cm, find p =

(i)

16.00 cm
(ii)

15.00 cm
(iii)

14.00 cm
(iv)

13.00 cm
(v)

17.00 cm

Question 29

29.

In the given figure, given ∠GDE = ∠FDG, p = 10.62 cm, q = 8.38 cm and EF = 19 cm, find GF =

(i)

10.38 cm
(ii)

8.38 cm
(iii)

7.38 cm
(iv)

6.38 cm
(v)

9.38 cm

Question 30

30.

In the given figure, FGHI is a trapezium where OF = 15 cm , OG = 15 cm and OH = 5 cm . Find OI =

(i)

6 cm
(ii)

3 cm
(iii)

4 cm
(iv)

5 cm
(v)

7 cm

Question 31

31.

In the given figure, ∠HIK = 50.01°, find the value of x =

(i)

40.99°
(ii)

39.99°
(iii)

37.99°
(iv)

38.99°
(v)

41.99°

Question 32

32.

In the given figure, ∠LJK = 42.27°, find the value of y =

(i)

46.73°
(ii)

48.73°
(iii)

47.73°
(iv)

45.73°
(v)

49.73°

Question 33

33.

In the given figure, if DE ∥ FG then

(i)

△DEH ∼ △HGF
(ii)

△DEH ∼ △GFH
(iii)

△HDE ∼ △HFG
(iv)

△HED ∼ △HGF
(v)

△DEH ∼ △HFG

Question 34

34.

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)

FG

2
=
GE
.
GH

c)

FG

2
=
EG
.
EH

d)

EF

2
=
EG
.
EH

e)

EF

2
=
GE
.
GH

(i)

{c,a}
(ii)

{a,b,d}
(iii)

{e,b}
(iv)

{c,e,d}
(v)

{c,a,b}

Question 35

35.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FG = 15 cm, GI = 10.94 cm, then find GH.

(i)

18.00 cm
(ii)

14.00 cm
(iii)

16.00 cm
(iv)

15.00 cm
(v)

17.00 cm

Question 36

36.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. If HG = 12.1 cm, FH = 13.38 cm, then find EH.

(i)

14.80 cm
(ii)

12.80 cm
(iii)

13.80 cm
(iv)

16.80 cm
(v)

15.80 cm

Question 37

37.

In the given figure, △CDE ∼ △NOP and CD = 14 cm, NO = 19.6 cm.

(i)

128.15 sq.cm
(ii)

127.15 sq.cm
(iii)

130.15 sq.cm
(iv)

126.15 sq.cm
(v)

129.15 sq.cm

Question 38

38.

In the given figure, △ABC ∼ △PQR and BC = 11 cm , QR = 15.4 cm and

(i)

98.02 sq.cm
(ii)

95.02 sq.cm
(iii)

97.02 sq.cm
(iv)

96.02 sq.cm
(v)

94.02 sq.cm

Question 39

39.

In the given figure, △EFG & △QRS are similar triangles. If the ratio of the heights EH : QT = 8 : 11, then the ratio of their areas is

(i)

63

sq.cm

:

121

sq.cm
(ii)

64

sq.cm

:

118

sq.cm
(iii)

64

sq.cm

:

123

sq.cm
(iv)

64

sq.cm

:

121

sq.cm
(v)

65

sq.cm

:

121

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)

Area of trapezium EFHI is thrice the area of △DIH

c)

d)

e)

All four small triangles have equal areas

(i)

{c,a,b}
(ii)

{c,a}
(iii)

{a,b,e}
(iv)

{c,d,e}
(v)

{d,b}

Question 41

41.

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)	△FHG ∼ △CDE
b)	△FGH ∼ △CDE
c)	△HDF ∼ △CDE
d)	△GFE ∼ △CDE
e)	△CHG ∼ △CDE

(i)

{a,e,b}
(ii)

{a,d}
(iii)

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

{a,b}
(v)

{a,c}

Question 42

42.

The perimeters of two similar triangles are 28 cm and 25 cm respectively. If one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.

(i)

10.71 cm
(ii)

12.71 cm
(iii)

11.71 cm
(iv)

9.71 cm
(v)

8.71 cm

Question 43

43.

In the given figure, J is a point on side HI of △GHI such that ∠IGH = ∠GJI = 105° , ∠JIG = 23°. Find ∠IGJ

(i)

51°
(ii)

50°
(iii)

53°
(iv)

54°
(v)

52°

Question 44

44.

DEFG is a square and △DEH is an equilateral triangle. Also, △DFI is an equilateral triangle. If area of △DEH is 'a' sq.units, then the area of △DFI is

(i)
a

2

sq.units
(ii)
√

3

a sq.units
(iii)
1
2

√

3

a sq.units
(iv)
2a sq.units
(v)
1
2

a sq.units

Question 45

45.

EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 17 cm, find FG

(i)

18 cm
(ii)

19 cm
(iii)

15 cm
(iv)

16 cm
(v)

17 cm

Question 46

46.

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

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

Find the height of the tower.

(i)

130 m
(ii)

129 m
(iii)

128 m
(iv)

126 m
(v)

127 m

Question 47

47.

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

a)

ab
=
pc

b)

1

a

2
+
1

b

2
=
1

p

2

c)

a

2
+
b

2
=
c

2

d)

e)

(i)

{d,e,c}
(ii)

{e,b}
(iii)

{d,a}
(iv)

{d,a,b}
(v)

{a,b,c}

Question 48

48.

In the given figure, ∠NKL = ∠MKN and KN ∥ OM and KL = 19 cm, LN = 8 cm and NM = 8 cm. Find KO

(i)

18.00 cm
(ii)

21.00 cm
(iii)

17.00 cm
(iv)

19.00 cm
(v)

20.00 cm

Question 49

49.

In the given figure, CE is the angular bisector of
∠C
&
∠E

(i)

22.00 cm
(ii)

21.00 cm
(iii)

25.00 cm
(iv)

23.00 cm
(v)

24.00 cm

Question 50

50.

The ratio of the bases of two triangles ABC and DEF is
5

:

6
.

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

(i)

4

:

6
(ii)

6

:

6
(iii)

5

:

4
(iv)

5

:

8
(v)

6

:

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)

11.78 cm
(ii)

9.78 cm
(iii)

10.78 cm
(iv)

13.78 cm
(v)

12.78 cm

Assignment Key