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)

not similar
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

AAA Similarity

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

AAA Similarity
(iii)

SSS Similarity
(iv)

not similar

Question 4

4.

In the given figure, △CDE and △UVW 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, △IJK and △UVW are such that

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 6

6.

In the given figure, △FGH and △RST are such that

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 7

7.

In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠J =

(i)

∠L
(ii)

∠H
(iii)

∠I
(iv)

∠G
(v)

∠K

Question 8

8.

In the given figure, △FGH is isosceles right-angled at G and GI ⟂ HF. ∠GHF ≠

(i)

∠HIG
(ii)

∠GHI
(iii)

∠IGH
(iv)

∠IFG
(v)

∠FGI

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.

△FDA ∼

(i)

△FEH
(ii)

△ABH
(iii)

△DAE
(iv)

△ACF
(v)

△DCF

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.

∠HFE =

(i)

∠FDA
(ii)

∠FEH
(iii)

∠FAC
(iv)

∠AFD
(v)

∠HAB

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.

∠FEH =

(i)

∠EHF
(ii)

∠FDA
(iii)

∠ACF
(iv)

∠DAF
(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.

∠CFA =

(i)

∠BHA
(ii)

∠EHF
(iii)

∠AFD
(iv)

∠DAF
(v)

∠HFE

Question 13

13.

In the given figure, HIJK is a trapezium in which

KL
=
(

2

x

+

1

)
cm, find the value of x

(i)

(

27

,

(
-3
2
)

)
(ii)

(

(
-1
2
)

,

27

)
(iii)

(

26

,

(
-5
4
)

)
(iv)

(

25

,

(
-3
2
)

)
(v)

(

25

,

-2

)

Question 14

14.

In the given figure, ABCD is a trapezium in which

(i)

△EDA
(ii)

△EBC
(iii)

△EAB
(iv)

△DAB
(v)

△BCD

Question 15

15.

In the given figure, the altitudes TE and FU of △DEF meet at S. △SUT ∼

(i)

△SEF
(ii)

△UEF
(iii)

△TFS
(iv)

△UES
(v)

△TFE

Question 16

16.

In the given figure, the altitudes RI and JS of △HIJ meet at Q. ∠JQI =

(i)

∠QRS
(ii)

∠QIJ
(iii)

∠IJQ
(iv)

∠SQR
(v)

∠RSQ

Question 17

17.

In the given figure, PQ ∥ HI , and median GJ bisects PQ.
△GJI ∼

(i)

△GKQ
(ii)

△HIG
(iii)

△GHJ
(iv)

△GPK
(v)

△GHI

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 . ∠OMP =

(i)

∠POM
(ii)

∠NPM
(iii)

∠MOQ
(iv)

∠QMO
(v)

∠MPO

Question 19

19.

Which of the following are true?

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

(i)

{c,e}
(ii)

{d,f,c}
(iii)

{a,c}
(iv)

{b,e}
(v)

{a,e,c}

Question 20

20.

Which of the following are true?

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

(i)

{a,d,e}
(ii)

{a,b,c}
(iii)

{b,c,e}
(iv)

{d,c}
(v)

{a,b}

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

(i)

{d,b}
(ii)

{a,b}
(iii)

{c,d,a}
(iv)

{c,a}
(v)

{c,b,a}

Question 22

22.

Which of the following are true?

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

(i)

{b,c}
(ii)

{a,c,d}
(iii)

{b,a,c}
(iv)

{b,d}
(v)

{b,a}

Question 23

23.

Which of the following are true?

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

(i)

{a,b}
(ii)

{a,d}
(iii)

{a,c}
(iv)

{a,b,c}
(v)

{b,c,d}

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)
2
3

of area of △FGH
(iii)
1
4

of area of △FGH
(iv)
1
3

of area of △FGH
(v)
3
4

of area of △FGH

Question 25

25.

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)
twice

the area of the triangle
(iii)
thrice

the area of the triangle
(iv)
4
3

the area of the triangle
(v)
5
4

the area of the triangle

Question 26

26.

If the ratio of the bases of two triangles is F : G and the ratio of the corresponding heights is H : I , the ratio of their areas in the same order is

(i)

FG : HI
(ii)

GH : FI
(iii)

FH : GI
(iv)

FI : GH
(v)

HI : FG

Question 27

27.

In the given two similar triangles, if a = 18 cm, b = 17 cm, c = 20 cm, d = 10.8 cm, find e

(i)

12.20 cm
(ii)

9.20 cm
(iii)

8.20 cm
(iv)

11.20 cm
(v)

10.20 cm

Question 28

28.

In the given figure, given ∠DAB = ∠CAD, x : y = 10 cm : 9 cm and p = 20 cm, find q =

(i)

17.00 cm
(ii)

20.00 cm
(iii)

16.00 cm
(iv)

19.00 cm
(v)

18.00 cm

Question 29

29.

In the given figure, given ∠GDE = ∠FDG, p = 9.5 cm, q = 9.5 cm and EF = 19 cm, find EG =

(i)

10.50 cm
(ii)

9.50 cm
(iii)

8.50 cm
(iv)

7.50 cm
(v)

11.50 cm

Question 30

30.

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

(i)

13 cm
(ii)

15 cm
(iii)

16 cm
(iv)

12 cm
(v)

14 cm

Question 31

31.

In the given figure, ∠EFH = 46.75°, find the value of x =

(i)

41.25°
(ii)

43.25°
(iii)

44.25°
(iv)

42.25°
(v)

45.25°

Question 32

32.

In the given figure, ∠IJK = 50.13°, find the value of y =

(i)

40.87°
(ii)

38.87°
(iii)

39.87°
(iv)

37.87°
(v)

41.87°

Question 33

33.

In the given figure, if IJ ∥ KL then

(i)

△MIJ ∼ △MKL
(ii)

△MJI ∼ △MLK
(iii)

△IJM ∼ △MLK
(iv)

△IJM ∼ △LKM
(v)

△IJM ∼ △MKL

Question 34

34.

In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. Which of the following are true?

a)

BC

2
=
BD
.
BE

b)

BC

2
=
DB
.
DE

c)

CE

2
=
BE
.
ED

d)

CD

2
=
BD
.
BE

e)

CD

2
=
DB
.
DE

(i)

{b,d,e}
(ii)

{b,a,c}
(iii)

{b,a}
(iv)

{a,c,e}
(v)

{d,c}

Question 35

35.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If EF = 16 cm, EG = 12.49 cm, then find DE.

(i)

19.00 cm
(ii)

20.00 cm
(iii)

18.00 cm
(iv)

22.00 cm
(v)

21.00 cm

Question 36

36.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If DC = 9.9 cm, BD = 11.26 cm, then find AD.

(i)

13.80 cm
(ii)

12.80 cm
(iii)

11.80 cm
(iv)

14.80 cm
(v)

10.80 cm

Question 37

37.

In the given figure, △DEF ∼ △OPQ and DE = 13 cm, OP = 18.2 cm.

(i)

133.35 sq.cm
(ii)

132.35 sq.cm
(iii)

134.35 sq.cm
(iv)

131.35 sq.cm
(v)

130.35 sq.cm

Question 38

38.

In the given figure, △DEF ∼ △QRS and EF = 15 cm , RS = 21 cm and

(i)

63.24 sq.cm
(ii)

66.24 sq.cm
(iii)

65.24 sq.cm
(iv)

64.24 sq.cm
(v)

67.24 sq.cm

Question 39

39.

In the given figure, △DEF & △PQR are similar triangles. If the ratio of the heights DG : PS = 11 : 16, then the ratio of their areas is

(i)

121

sq.cm

:

256

sq.cm
(ii)

121

sq.cm

:

258

sq.cm
(iii)

120

sq.cm

:

256

sq.cm
(iv)

121

sq.cm

:

254

sq.cm
(v)

122

sq.cm

:

256

sq.cm

Question 40

40.

In the given figure, points P , Q and R are the mid-points of sides NO, OM and MN of △MNO. Which of the following are true?

a)

Area of △MNO = 4 times area of △PQR

b)

All four small triangles have equal areas

c)

Area of trapezium NOQR is thrice the area of △MRQ

d)

e)

(i)

{a,b,c}
(ii)

{e,b}
(iii)

{d,a}
(iv)

{d,e,c}
(v)

{d,a,b}

Question 41

41.

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)	△INM ∼ △IJK
b)	△LMN ∼ △IJK
c)	△LNM ∼ △IJK
d)	△NJL ∼ △IJK
e)	△MLK ∼ △IJK

(i)

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

{c,a}
(iii)

{c,b}
(iv)

{c,e,a}
(v)

{c,d}

Question 42

42.

The perimeters of two similar triangles are 29 cm and 24 cm respectively. If one side of the first triangle is 15 cm, find the length of the corresponding side of the second triangle.

(i)

11.41 cm
(ii)

14.41 cm
(iii)

13.41 cm
(iv)

12.41 cm
(v)

10.41 cm

Question 43

43.

In the given figure, J is a point on side HI of △GHI such that ∠IGH = ∠GJI = 100° , ∠JIG = 23°. Find ∠IGJ

(i)

56°
(ii)

58°
(iii)

55°
(iv)

57°
(v)

59°

Question 44

44.

CDEF is a square and △CDG is an equilateral triangle. Also, △CEH is an equilateral triangle. If area of △CDG is 'a' sq.units, then the area of △CEH is

(i)
a

2

sq.units
(ii)
1
2

a sq.units
(iii)
1
2

√

3

a sq.units
(iv)
2a sq.units
(v)
√

3

a sq.units

Question 45

45.

BCDE is a cyclic trapezium. Diagonals CE and BD intersect at F. If EB = 18 cm, find CD

(i)

20 cm
(ii)

18 cm
(iii)

19 cm
(iv)

17 cm
(v)

16 cm

Question 46

46.

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

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

Find the height of the tower.

(i)

122 m
(ii)

119 m
(iii)

118 m
(iv)

120 m
(v)

121 m

Question 47

47.

In the given figure, △EGF is right-angled at G, GH ⟂ EF.

a)

1

a

2
+
1

b

2
=
1

p

2

b)

c)

d)

a

2
+
b

2
=
c

2

e)

ab
=
pc

(i)

{b,a}
(ii)

{c,d}
(iii)

{a,d,e}
(iv)

{b,a,d}
(v)

{b,c,e}

Question 48

48.

In the given figure, ∠IFG = ∠HFI and FI ∥ JH and FG = 20 cm, GI = 10 cm and IH = 8 cm. Find FJ

(i)

15.00 cm
(ii)

18.00 cm
(iii)

16.00 cm
(iv)

14.00 cm
(v)

17.00 cm

Question 49

49.

In the given figure, DF is the angular bisector of
∠D
&
∠F

(i)

20.00 cm
(ii)

19.00 cm
(iii)

22.00 cm
(iv)

23.00 cm
(v)

21.00 cm

Question 50

50.

The ratio of the bases of two triangles ABC and DEF is
10

:

9
.

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

(i)

10

:

7
(ii)

10

:

12
(iii)

11

:

9
(iv)

9

:

9
(v)

9

:

10

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)

12.26 cm
(ii)

13.26 cm
(iii)

16.26 cm
(iv)

15.26 cm
(v)

14.26 cm

Assignment Key