EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

AAA Similarity
(iii)

SAS Similarity
(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)

SSS Similarity
(ii)

SAS Similarity
(iii)

not similar
(iv)

AAA Similarity

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

SAS Similarity
(ii)

SSS Similarity
(iii)

not similar
(iv)

AAA Similarity

Question 5

5.

In the given figure, △FGH and △STU 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 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)

not similar
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 7

7.

In the given figure, △CDE is isosceles right-angled at D and DF ⟂ EC. ∠C =

(i)

∠G
(ii)

∠F
(iii)

∠H
(iv)

∠D
(v)

∠E

Question 8

8.

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

(i)

∠NOQ
(ii)

∠QOP
(iii)

∠OPQ
(iv)

∠QNO
(v)

∠PQO

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)

△DAE
(ii)

△ACF
(iii)

△ABH
(iv)

△FEH
(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.

∠AFD =

(i)

∠FDA
(ii)

∠FEH
(iii)

∠HAB
(iv)

∠HFE
(v)

∠FAC

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)

∠ACF
(ii)

∠EHF
(iii)

∠FDA
(iv)

∠FEH
(v)

∠DAF

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)

∠AFD
(ii)

∠DAF
(iii)

∠EHF
(iv)

∠BHA
(v)

∠HFE

Question 13

13.

In the given figure, NOPQ is a trapezium in which

QR
=
(

3

x

+

6

)
cm, find the value of x

(i)

(

18

,

-2

)
(ii)

(

0

,

20

)
(iii)

(

21

,

-2

)
(iv)

(

18

,

-3

)
(v)

(

19

,

-1

)

Question 14

14.

In the given figure, IJKL is a trapezium in which

(i)

△JKL
(ii)

△MJK
(iii)

△MLI
(iv)

△MKL
(v)

△LIJ

Question 15

15.

In the given figure, the altitudes UC and DV of △BCD meet at T. △TVU ∼

(i)

△TCD
(ii)

△VCD
(iii)

△UDT
(iv)

△UDC
(v)

△VCT

Question 16

16.

In the given figure, the altitudes MD and EN of △CDE meet at L. ∠MLE =

(i)

∠NDL
(ii)

∠EML
(iii)

∠DLN
(iv)

∠LEM
(v)

∠LND

Question 17

17.

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

(i)

△DEC
(ii)

△CGS
(iii)

△CDE
(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 . ∠CAD =

(i)

∠ADC
(ii)

∠EAC
(iii)

∠BDA
(iv)

∠DCA
(v)

∠DAB

Question 19

19.

Which of the following are true?

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

(i)

{c,a}
(ii)

{d,b}
(iii)

{a,b}
(iv)

{c,b,a}
(v)

{e,f,a}

Question 20

20.

Which of the following are true?

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

(i)

{c,a,b}
(ii)

{c,a}
(iii)

{d,b}
(iv)

{c,d,e}
(v)

{a,b,e}

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

(i)

{c,a}
(ii)

{d,b}
(iii)

{c,d,a}
(iv)

{a,b}
(v)

{c,b,a}

Question 22

22.

Which of the following are true?

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

(i)

{d,c}
(ii)

{d,a}
(iii)

{a,b,c}
(iv)

{d,b}
(v)

{d,a,b}

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,a}
(ii)

{c,b}
(iii)

{c,a,b}
(iv)

{a,b,d}
(v)

{c,d}

Question 24

24.

In the given figure, the area of the △ABC is x sq.cm. D,E,F are the mid-points of the sides BC , CA and AB respectively. The area of the △DEF is

(i)
2
3

of area of △ABC
(ii)
3
4

of area of △ABC
(iii)
1
2

of area of △ABC
(iv)
1
3

of area of △ABC
(v)
1
4

of area of △ABC

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)
thrice

the area of the triangle
(ii)
4
3

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
twice

the area of the triangle
(v)
3
2

the area of the triangle

Question 26

26.

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

(i)

GI : HJ
(ii)

IJ : GH
(iii)

HI : GJ
(iv)

GJ : HI
(v)

GH : IJ

Question 27

27.

In the given two similar triangles, if n = 15 cm, o = 19 cm, p = 20 cm, s = 12 cm, find q

(i)

8.00 cm
(ii)

7.00 cm
(iii)

9.00 cm
(iv)

11.00 cm
(v)

10.00 cm

Question 28

28.

In the given figure, given ∠IFG = ∠HFI, x : y = 7.5 cm : 7.5 cm and q = 15 cm, find p =

(i)

17.00 cm
(ii)

13.00 cm
(iii)

14.00 cm
(iv)

16.00 cm
(v)

15.00 cm

Question 29

29.

In the given figure, given ∠IFG = ∠HFI, p = 8.5 cm, q = 8.5 cm and GH = 17 cm, find IH =

(i)

9.50 cm
(ii)

6.50 cm
(iii)

10.50 cm
(iv)

7.50 cm
(v)

8.50 cm

Question 30

30.

In the given figure, FGHI is a trapezium where OF = 13 cm , OH = 4 cm and OI = 4 cm . Find OG =

(i)

15 cm
(ii)

13 cm
(iii)

14 cm
(iv)

11 cm
(v)

12 cm

Question 31

31.

In the given figure, ∠IJL = 48.62°, find the value of x =

(i)

39.38°
(ii)

42.38°
(iii)

43.38°
(iv)

40.38°
(v)

41.38°

Question 32

32.

In the given figure, ∠FGH = 41.7°, find the value of y =

(i)

46.30°
(ii)

50.30°
(iii)

48.30°
(iv)

49.30°
(v)

47.30°

Question 33

33.

In the given figure, if AB ∥ CD then

(i)

△EAB ∼ △ECD
(ii)

△EBA ∼ △EDC
(iii)

△ABE ∼ △ECD
(iv)

△ABE ∼ △EDC
(v)

△ABE ∼ △DCE

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)

CD

2
=
BD
.
BE

c)

CE

2
=
BE
.
ED

d)

CD

2
=
DB
.
DE

e)

BC

2
=
DB
.
DE

(i)

{b,a}
(ii)

{a,c,d}
(iii)

{e,c}
(iv)

{b,e,d}
(v)

{b,a,c}

Question 35

35.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. If FG = 15 cm, FH = 11.52 cm, then find EF.

(i)

17.00 cm
(ii)

19.00 cm
(iii)

20.00 cm
(iv)

16.00 cm
(v)

18.00 cm

Question 36

36.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If DG = 12.3 cm, EG = 13.08 cm, then find GF.

(i)

14.90 cm
(ii)

11.90 cm
(iii)

15.90 cm
(iv)

12.90 cm
(v)

13.90 cm

Question 37

37.

In the given figure, △BCD ∼ △PQR and BC = 14 cm, PQ = 19.6 cm.

(i)

150.30 sq.cm
(ii)

149.30 sq.cm
(iii)

148.30 sq.cm
(iv)

152.30 sq.cm
(v)

151.30 sq.cm

Question 38

38.

In the given figure, △EFG ∼ △QRS and FG = 14 cm , RS = 19.6 cm and

(i)

165.35 sq.cm
(ii)

167.35 sq.cm
(iii)

164.35 sq.cm
(iv)

166.35 sq.cm
(v)

168.35 sq.cm

Question 39

39.

In the given figure, △ABC & △PQR are similar triangles. If the ratio of the heights AD : PS = 9 : 13, then the ratio of their areas is

(i)

80

sq.cm

:

169

sq.cm
(ii)

81

sq.cm

:

171

sq.cm
(iii)

82

sq.cm

:

169

sq.cm
(iv)

81

sq.cm

:

166

sq.cm
(v)

81

sq.cm

:

169

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 trapezium NOQR is thrice the area of △MRQ

b)

c)

d)

All four small triangles have equal areas

e)

Area of △MNO = 4 times area of △PQR

(i)

{c,d}
(ii)

{a,d,e}
(iii)

{b,a,d}
(iv)

{b,c,e}
(v)

{b,a}

Question 41

41.

In the given figure, points J , K and L are the mid-points of sides HI, IG and GH of △GHI. Which of the following are true?

a)	△GLK ∼ △GHI
b)	△JLK ∼ △GHI
c)	△JKL ∼ △GHI
d)	△KJI ∼ △GHI
e)	△LHJ ∼ △GHI

(i)

{b,a}
(ii)

{b,c}
(iii)

{b,d}
(iv)

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

{b,e,a}

Question 42

42.

The perimeters of two similar triangles are 34 cm and 25 cm respectively. If one side of the first triangle is 14 cm, find the length of the corresponding side of the second triangle.

(i)

10.29 cm
(ii)

9.29 cm
(iii)

12.29 cm
(iv)

11.29 cm
(v)

8.29 cm

Question 43

43.

In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 105° , ∠DCA = 20°. Find ∠CAD

(i)

53°
(ii)

55°
(iii)

54°
(iv)

56°
(v)

57°

Question 44

44.

HIJK is a square and △HIL is an equilateral triangle. Also, △HJM is an equilateral triangle. If area of △HIL is 'a' sq.units, then the area of △HJM is

(i)
1
2

a sq.units
(ii)
√

3

a sq.units
(iii)
1
2

√

3

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

2

sq.units

Question 45

45.

EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 16 cm, find FG

(i)

17 cm
(ii)

15 cm
(iii)

14 cm
(iv)

18 cm
(v)

16 cm

Question 46

46.

A vertical stick
15 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)

122 m
(ii)

121 m
(iii)

119 m
(iv)

120 m
(v)

118 m

Question 47

47.

In the given figure, △BDC is right-angled at D, DE ⟂ BC.

a)

b)

ab
=
pc

c)

1

a

2
+
1

b

2
=
1

p

2

d)

e)

a

2
+
b

2
=
c

2

(i)

{a,b,c}
(ii)

{a,b}
(iii)

{b,c,e}
(iv)

{d,c}
(v)

{a,d,e}

Question 48

48.

In the given figure, ∠HEF = ∠GEH and EH ∥ IG and EF = 17 cm, FH = 9 cm and HG = 11 cm. Find EI

(i)

21.78 cm
(ii)

18.78 cm
(iii)

20.78 cm
(iv)

19.78 cm
(v)

22.78 cm

Question 49

49.

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

(i)

25.00 cm
(ii)

21.00 cm
(iii)

23.00 cm
(iv)

22.00 cm
(v)

24.00 cm

Question 50

50.

The ratio of the bases of two triangles ABC and DEF is
4

:

9
.

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

(i)

4

:

12
(ii)

4

:

6
(iii)

3

:

9
(iv)

5

:

9
(v)

9

:

4

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)

14.41 cm
(ii)

13.41 cm
(iii)

15.41 cm
(iv)

11.41 cm
(v)

12.41 cm

Assignment Key