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)

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)

SSS Similarity
(ii)

not similar
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 6

6.

In the given figure, △GHI 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 7

7.

In the given figure, △OPQ is isosceles right-angled at P and PR ⟂ QO. ∠Q =

(i)

∠S
(ii)

∠P
(iii)

∠R
(iv)

∠T
(v)

∠O

Question 8

8.

In the given figure, △MNO is isosceles right-angled at N and NP ⟂ OM. ∠MNP ≠

(i)

∠OMN
(ii)

∠NOP
(iii)

∠MNO
(iv)

∠PNO
(v)

∠PMN

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)

△FEH
(iii)

△ACF
(iv)

△FDA
(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.

∠HAB =

(i)

∠AFD
(ii)

∠FEH
(iii)

∠FDA
(iv)

∠FAC
(v)

∠HFE

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)

∠ABH
(ii)

∠ACF
(iii)

∠DAF
(iv)

∠EHF
(v)

∠FEH

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)

∠AFD
(ii)

∠HFE
(iii)

∠CFA
(iv)

∠DAF
(v)

∠BHA

Question 13

13.

In the given figure, KLMN is a trapezium in which

NO
=
(

x

+

4

)
cm, find the value of x

(i)

(

2

,

20

)
(ii)

(

19

,

1

)
(iii)

(

20

,

0

)
(iv)

(

18

,

-1

)
(v)

(

18

,

0

)

Question 14

14.

In the given figure, FGHI is a trapezium in which

(i)

△IFG
(ii)

△JIF
(iii)

△JFG
(iv)

△GHI
(v)

△JGH

Question 15

15.

In the given figure, the altitudes NJ and KO of △IJK meet at M. △MJK ∼

(i)

△MON
(ii)

△OJK
(iii)

△OJM
(iv)

△NKM
(v)

△NKJ

Question 16

16.

In the given figure, the altitudes MJ and KN of △IJK meet at L. ∠MLK =

(i)

∠LKM
(ii)

∠LNJ
(iii)

∠KML
(iv)

∠JLN
(v)

∠NJL

Question 17

17.

In the given figure, RS ∥ DE , and median CF bisects RS.
△CGS ∼

(i)

△CDE
(ii)

△CRG
(iii)

△DEC
(iv)

△CDF
(v)

△CFE

Question 18

18.

In the given figure, △ABC is a triangle in which AD is the internal bisector of ∠A and CE ∥ DA meeting BA produced at E . ∠CEA =

(i)

∠ADC
(ii)

∠EAC
(iii)

∠BDA
(iv)

∠DAB
(v)

∠DCA

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)

{a,e,c}
(ii)

{a,c}
(iii)

{d,f,c}
(iv)

{b,e}
(v)

{c,e}

Question 20

20.

Which of the following are true?

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

(i)

{b,a}
(ii)

{a,d,e}
(iii)

{b,a,d}
(iv)

{b,c,e}
(v)

{c,d}

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

(i)

{b,a}
(ii)

{a,c}
(iii)

{b,d,a}
(iv)

{b,c,a}
(v)

{d,c}

Question 22

22.

Which of the following are true?

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

(i)

{b,a,c}
(ii)

{b,a}
(iii)

{a,c,d}
(iv)

{b,d}
(v)

{b,c}

Question 23

23.

Which of the following are true?

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

(i)

{c,a}
(ii)

{a,b,d}
(iii)

{c,a,b}
(iv)

{c,b}
(v)

{c,d}

Question 24

24.

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
2

of area of △GHI
(ii)
1
3

of area of △GHI
(iii)
1
4

of area of △GHI
(iv)
3
4

of area of △GHI
(v)
2
3

of area of △GHI

Question 25

25.

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)
5
4

the area of the triangle
(ii)
twice

the area of the triangle
(iii)
3
2

the area of the triangle
(iv)
4
3

the area of the triangle
(v)
thrice

the area of the triangle

Question 26

26.

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

(i)

JL : KM
(ii)

LM : JK
(iii)

JK : LM
(iv)

JM : KL
(v)

KL : JM

Question 27

27.

In the given two similar triangles, if e = 16 cm, f = 15 cm, g = 15 cm, h = 9.6 cm, find i

(i)

11.00 cm
(ii)

7.00 cm
(iii)

8.00 cm
(iv)

10.00 cm
(v)

9.00 cm

Question 28

28.

In the given figure, given ∠JGH = ∠IGJ, x : y = 7.56 cm : 9.44 cm and q = 20 cm, find p =

(i)

15.00 cm
(ii)

14.00 cm
(iii)

17.00 cm
(iv)

18.00 cm
(v)

16.00 cm

Question 29

29.

In the given figure, given ∠FCD = ∠ECF, p = 9.5 cm, q = 9.5 cm and DE = 19 cm, find DF =

(i)

7.50 cm
(ii)

9.50 cm
(iii)

8.50 cm
(iv)

11.50 cm
(v)

10.50 cm

Question 30

30.

In the given figure, BCDE is a trapezium where OB = 13 cm , OD = 4 cm and OE = 4 cm . Find OC =

(i)

12 cm
(ii)

15 cm
(iii)

14 cm
(iv)

11 cm
(v)

13 cm

Question 31

31.

In the given figure, ∠DAB = 48.45°, find the value of x =

(i)

41.55°
(ii)

39.55°
(iii)

43.55°
(iv)

42.55°
(v)

40.55°

Question 32

32.

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

(i)

42.65°
(ii)

39.65°
(iii)

41.65°
(iv)

40.65°
(v)

38.65°

Question 33

33.

In the given figure, if DE ∥ FG then

(i)

△HDE ∼ △HFG
(ii)

△DEH ∼ △GFH
(iii)

△DEH ∼ △HFG
(iv)

△DEH ∼ △HGF
(v)

△HED ∼ △HGF

Question 34

34.

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

a)

CE

2
=
BE
.
ED

b)

CD

2
=
BD
.
BE

c)

BC

2
=
BD
.
BE

d)

BC

2
=
DB
.
DE

e)

CD

2
=
DB
.
DE

(i)

{a,c,e}
(ii)

{b,a,c}
(iii)

{b,a}
(iv)

{d,c}
(v)

{b,d,e}

Question 35

35.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If EF = 19 cm, EG = 13.07 cm, then find DE.

(i)

20.00 cm
(ii)

16.00 cm
(iii)

18.00 cm
(iv)

17.00 cm
(v)

19.00 cm

Question 36

36.

In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If KJ = 11.7 cm, IK = 10.92 cm, then find HK.

(i)

10.20 cm
(ii)

8.20 cm
(iii)

12.20 cm
(iv)

11.20 cm
(v)

9.20 cm

Question 37

37.

In the given figure, △ABC ∼ △OPQ and AB = 14 cm, OP = 19.6 cm.

(i)

120.28 sq.cm
(ii)

121.28 sq.cm
(iii)

124.28 sq.cm
(iv)

123.28 sq.cm
(v)

122.28 sq.cm

Question 38

38.

In the given figure, △CDE ∼ △QRS and DE = 11 cm , RS = 15.4 cm and

(i)

129.87 sq.cm
(ii)

127.87 sq.cm
(iii)

126.87 sq.cm
(iv)

128.87 sq.cm
(v)

125.87 sq.cm

Question 39

39.

In the given figure, △CDE & △NOP are similar triangles. If the ratio of the heights CF : NQ = 10 : 14, then the ratio of their areas is

(i)

101

sq.cm

:

196

sq.cm
(ii)

100

sq.cm

:

194

sq.cm
(iii)

100

sq.cm

:

196

sq.cm
(iv)

99

sq.cm

:

196

sq.cm
(v)

100

sq.cm

:

198

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)

All four small triangles have equal areas

b)

c)

Area of △HIJ = 4 times area of △KLM

d)

Area of trapezium IJLM is thrice the area of △HML

e)

(i)

{b,a}
(ii)

{e,c}
(iii)

{b,e,d}
(iv)

{a,c,d}
(v)

{b,a,c}

Question 41

41.

In the given figure, points E , F and G are the mid-points of sides CD, DB and BC of △BCD. Which of the following are true?

a)	△EGF ∼ △BCD
b)	△GCE ∼ △BCD
c)	△BGF ∼ △BCD
d)	△FED ∼ △BCD
e)	△EFG ∼ △BCD

(i)

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

{a,c}
(iii)

{a,e,b}
(iv)

{a,d}
(v)

{a,b}

Question 42

42.

The perimeters of two similar triangles are 30 cm and 15 cm respectively. If one side of the first triangle is 14 cm, find the length of the corresponding side of the second triangle.

(i)

7.00 cm
(ii)

5.00 cm
(iii)

9.00 cm
(iv)

8.00 cm
(v)

6.00 cm

Question 43

43.

In the given figure, K is a point on side IJ of △HIJ such that ∠JHI = ∠HKJ = 105° , ∠KJH = 21°. Find ∠JHK

(i)

54°
(ii)

52°
(iii)

55°
(iv)

53°
(v)

56°

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)
1
2

a sq.units
(ii)
1
2

√

3

a sq.units
(iii)
a

2

sq.units
(iv)
2a sq.units
(v)
√

3

a sq.units

Question 45

45.

HIJK is a cyclic trapezium. Diagonals IK and HJ intersect at L. If KH = 16 cm, find IJ

(i)

14 cm
(ii)

18 cm
(iii)

17 cm
(iv)

15 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)

118 m
(ii)

121 m
(iii)

120 m
(iv)

122 m
(v)

119 m

Question 47

47.

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

a)

ab
=
pc

b)

c)

1

a

2
+
1

b

2
=
1

p

2

d)

a

2
+
b

2
=
c

2

e)

(i)

{b,a,c}
(ii)

{a,c,d}
(iii)

{b,a}
(iv)

{e,c}
(v)

{b,e,d}

Question 48

48.

In the given figure, ∠HEF = ∠GEH and EH ∥ IG and EF = 16 cm, FH = 9 cm and HG = 9 cm. Find EI

(i)

18.00 cm
(ii)

16.00 cm
(iii)

14.00 cm
(iv)

15.00 cm
(v)

17.00 cm

Question 49

49.

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

(i)

22.00 cm
(ii)

20.00 cm
(iii)

19.00 cm
(iv)

21.00 cm
(v)

23.00 cm

Question 50

50.

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

:

10
.

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

(i)

10

:

5
(ii)

4

:

10
(iii)

5

:

12
(iv)

5

:

8
(v)

6

:

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)

15.44 cm
(ii)

11.44 cm
(iii)

13.44 cm
(iv)

14.44 cm
(v)

12.44 cm

Assignment Key