EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SAS Similarity
(iii)

not similar
(iv)

SSS Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

SAS 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 △STU are such that

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

not similar
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 5

5.

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

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

not similar
(iv)

AAA Similarity

Question 6

6.

In the given figure, △GHI 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 7

7.

In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠P =

(i)

∠T
(ii)

∠Q
(iii)

∠R
(iv)

∠U
(v)

∠S

Question 8

8.

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

(i)

∠IJK
(ii)

∠KIJ
(iii)

∠HIJ
(iv)

∠HIK
(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.

△FDA ∼

(i)

△FEH
(ii)

△DAE
(iii)

△DCF
(iv)

△ACF
(v)

△ABH

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)

∠FDA
(iv)

∠AFD
(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.

∠ACF =

(i)

∠EHF
(ii)

∠FEH
(iii)

∠DAF
(iv)

∠ABH
(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)

∠AFD
(ii)

∠DAF
(iii)

∠CFA
(iv)

∠HFE
(v)

∠BHA

Question 13

13.

In the given figure, NOPQ is a trapezium in which

QR
=
(

x

+

29

)
cm, find the value of x

(i)

(

-15

,

31

)
(ii)

(

-15

,

30

)
(iii)

(

33

,

-13

)
(iv)

(

-14

,

32

)
(v)

(

-12

,

31

)

Question 14

14.

In the given figure, IJKL is a trapezium in which

(i)

△MLI
(ii)

△LIJ
(iii)

△JKL
(iv)

△MJK
(v)

△MIJ

Question 15

15.

In the given figure, the altitudes SI and JT of △HIJ meet at R. △SJI ∼

(i)

△SJR
(ii)

△RTS
(iii)

△TIR
(iv)

△TIJ
(v)

△RIJ

Question 16

16.

In the given figure, the altitudes NF and GO of △EFG meet at M. ∠GMF =

(i)

∠OMN
(ii)

∠NOM
(iii)

∠FGM
(iv)

∠MFG
(v)

∠MNO

Question 17

17.

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

(i)

△CDF
(ii)

△CDE
(iii)

△CRG
(iv)

△DEC
(v)

△CFE

Question 18

18.

In the given figure, △OPQ is a triangle in which OR is the internal bisector of ∠O and QS ∥ RO meeting PO produced at S . ∠OQS =

(i)

∠PRO
(ii)

∠SOQ
(iii)

∠ORQ
(iv)

∠ROP
(v)

∠RQO

Question 19

19.

Which of the following are true?

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

(i)

{b,d}
(ii)

{a,b}
(iii)

{c,d}
(iv)

{e,f,b}
(v)

{a,d,b}

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)	Similar figures have same area.
d)	If two figures are congruent, then they are similar too.
e)	Congruent figures have same area.

(i)

{c,d}
(ii)

{a,c,e}
(iii)

{b,d,e}
(iv)

{a,b,d}
(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)

{c,d,a}
(ii)

{a,b}
(iii)

{c,a}
(iv)

{d,b}
(v)

{c,b,a}

Question 22

22.

Which of the following are true?

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

(i)

{b,d}
(ii)

{b,a,c}
(iii)

{b,a}
(iv)

{a,c,d}
(v)

{b,c}

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

(i)

{d,b}
(ii)

{a,b,c}
(iii)

{d,a}
(iv)

{d,a,b}
(v)

{d,c}

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
3

of area of △GHI
(ii)
2
3

of area of △GHI
(iii)
3
4

of area of △GHI
(iv)
1
2

of area of △GHI
(v)
1
4

of area of △GHI

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)
thrice

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
twice

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 I : J and the ratio of the corresponding heights is K : L , the ratio of their areas in the same order is

(i)

IK : JL
(ii)

IL : JK
(iii)

KL : IJ
(iv)

JK : IL
(v)

IJ : KL

Question 27

27.

In the given two similar triangles, if d = 19 cm, e = 19 cm, f = 20 cm, h = 11.4 cm, find i

(i)

10.00 cm
(ii)

14.00 cm
(iii)

11.00 cm
(iv)

13.00 cm
(v)

12.00 cm

Question 28

28.

In the given figure, given ∠HEF = ∠GEH, x : y = 8.89 cm : 7.11 cm and p = 20 cm, find q =

(i)

15.00 cm
(ii)

18.00 cm
(iii)

16.00 cm
(iv)

17.00 cm
(v)

14.00 cm

Question 29

29.

In the given figure, given ∠JGH = ∠IGJ, p = 9.82 cm, q = 8.18 cm and HI = 18 cm, find HJ =

(i)

8.82 cm
(ii)

10.82 cm
(iii)

11.82 cm
(iv)

9.82 cm
(v)

7.82 cm

Question 30

30.

In the given figure, DEFG is a trapezium where OE = 12 cm , OF = 4 cm and OG = 4 cm . Find OD =

(i)

12 cm
(ii)

11 cm
(iii)

14 cm
(iv)

10 cm
(v)

13 cm

Question 31

31.

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

(i)

41.99°
(ii)

40.99°
(iii)

37.99°
(iv)

39.99°
(v)

38.99°

Question 32

32.

In the given figure, ∠DEF = 41.99°, find the value of y =

(i)

47.01°
(ii)

50.01°
(iii)

46.01°
(iv)

48.01°
(v)

49.01°

Question 33

33.

In the given figure, if BC ∥ DE then

(i)

△BCF ∼ △EDF
(ii)

△FBC ∼ △FDE
(iii)

△FCB ∼ △FED
(iv)

△BCF ∼ △FDE
(v)

△BCF ∼ △FED

Question 34

34.

In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. Which of the following are true?

a)

IJ

2
=
KI
.
KL

b)

JK

2
=
KI
.
KL

c)

IJ

2
=
IK
.
IL

d)

JL

2
=
IL
.
LK

e)

JK

2
=
IK
.
IL

(i)

{e,c}
(ii)

{a,b,c}
(iii)

{b,c,d}
(iv)

{a,b}
(v)

{a,e,d}

Question 35

35.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If GH = 20 cm, GI = 13.77 cm, then find FG.

(i)

18.00 cm
(ii)

17.00 cm
(iii)

21.00 cm
(iv)

19.00 cm
(v)

20.00 cm

Question 36

36.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If GJ = 11 cm, HJ = 11.63 cm, then find JI.

(i)

14.30 cm
(ii)

10.30 cm
(iii)

12.30 cm
(iv)

13.30 cm
(v)

11.30 cm

Question 37

37.

In the given figure, △EFG ∼ △OPQ and EF = 11 cm, OP = 15.4 cm.

(i)

46.93 sq.cm
(ii)

44.93 sq.cm
(iii)

45.93 sq.cm
(iv)

43.93 sq.cm
(v)

47.93 sq.cm

Question 38

38.

In the given figure, △BCD ∼ △PQR and CD = 10 cm , QR = 14 cm and

(i)

101.98 sq.cm
(ii)

99.98 sq.cm
(iii)

102.98 sq.cm
(iv)

100.98 sq.cm
(v)

98.98 sq.cm

Question 39

39.

In the given figure, △DEF & △MNO are similar triangles. If the ratio of the heights DG : MP = 13 : 19, then the ratio of their areas is

(i)

169

sq.cm

:

361

sq.cm
(ii)

169

sq.cm

:

359

sq.cm
(iii)

170

sq.cm

:

361

sq.cm
(iv)

168

sq.cm

:

361

sq.cm
(v)

169

sq.cm

:

363

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 trapezium EFHI is thrice the area of △DIH

b)

c)

All four small triangles have equal areas

d)

e)

Area of △DEF = 4 times area of △GHI

(i)

{d,c}
(ii)

{b,a}
(iii)

{a,c,e}
(iv)

{b,a,c}
(v)

{b,d,e}

Question 41

41.

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)	△HML ∼ △HIJ
b)	△MIK ∼ △HIJ
c)	△KLM ∼ △HIJ
d)	△KML ∼ △HIJ
e)	△LKJ ∼ △HIJ

(i)

{d,b}
(ii)

{d,e,a}
(iii)

{d,c}
(iv)

{a,b,c,e}
(v)

{d,a}

Question 42

42.

The perimeters of two similar triangles are 32 cm and 17 cm respectively. If one side of the first triangle is 13 cm, find the length of the corresponding side of the second triangle.

(i)

8.91 cm
(ii)

5.91 cm
(iii)

4.91 cm
(iv)

6.91 cm
(v)

7.91 cm

Question 43

43.

In the given figure, L is a point on side JK of △IJK such that ∠KIJ = ∠ILK = 108° , ∠LKI = 20°. Find ∠KIL

(i)

50°
(ii)

54°
(iii)

53°
(iv)

51°
(v)

52°

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)
√

3

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

a sq.units
(iv)
a

2

sq.units
(v)
1
2

√

3

a sq.units

Question 45

45.

EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 15 cm, find FG

(i)

15 cm
(ii)

14 cm
(iii)

17 cm
(iv)

16 cm
(v)

13 cm

Question 46

46.

A vertical stick
16 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)

127 m
(ii)

130 m
(iii)

129 m
(iv)

128 m
(v)

126 m

Question 47

47.

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

a)

a

2
+
b

2
=
c

2

b)

c)

d)

ab
=
pc

e)

1

a

2
+
1

b

2
=
1

p

2

(i)

{b,a}
(ii)

{b,a,d}
(iii)

{b,c,e}
(iv)

{a,d,e}
(v)

{c,d}

Question 48

48.

In the given figure, ∠HEF = ∠GEH and EH ∥ IG and EF = 19 cm, FH = 10 cm and HG = 10 cm. Find EI

(i)

20.00 cm
(ii)

19.00 cm
(iii)

17.00 cm
(iv)

18.00 cm
(v)

21.00 cm

Question 49

49.

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

(i)

27.00 cm
(ii)

24.00 cm
(iii)

25.00 cm
(iv)

23.00 cm
(v)

26.00 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)

10

:

10
(ii)

8

:

10
(iii)

9

:

13
(iv)

9

:

8
(v)

10

:

9

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)

16.42 cm
(ii)

15.42 cm
(iii)

13.42 cm
(iv)

14.42 cm
(v)

12.42 cm

Assignment Key