EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

AAA Similarity

Question 4

4.

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

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

SAS Similarity
(iii)

not similar
(iv)

SSS Similarity

Question 5

5.

In the given figure, △IJK and △RST 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, △CDE and △PQR 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 7

7.

In the given figure, △BCD is isosceles right-angled at C and CE ⟂ DB. ∠D =

(i)

∠B
(ii)

∠E
(iii)

∠G
(iv)

∠C
(v)

∠F

Question 8

8.

In the given figure, △DEF is isosceles right-angled at E and EG ⟂ FD. ∠EGD =

(i)

∠GDE
(ii)

∠DEG
(iii)

∠GEF
(iv)

∠DEF
(v)

∠EFG

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)

△DCF
(ii)

△FEH
(iii)

△ACF
(iv)

△DAE
(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.

∠HAB =

(i)

∠FEH
(ii)

∠AFD
(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.

∠FEH =

(i)

∠ABH
(ii)

∠FDA
(iii)

∠ACF
(iv)

∠DAF
(v)

∠EHF

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)

∠BHA
(ii)

∠CFA
(iii)

∠DAF
(iv)

∠AFD
(v)

∠HFE

Question 13

13.

In the given figure, ABCD is a trapezium in which

DE
=
(

2

x

+

2

)
cm, find the value of x

(i)

(

-1

,

28

)
(ii)

(

29

,

-3

)
(iii)

(

26

,

-3

)
(iv)

(

26

,

-4

)
(v)

(

27

,

-2

)

Question 14

14.

In the given figure, HIJK is a trapezium in which

(i)

△IJK
(ii)

△LKH
(iii)

△LJK
(iv)

△KHI
(v)

△LIJ

Question 15

15.

In the given figure, the altitudes PD and EQ of △CDE meet at O. △OQP ∼

(i)

△QDO
(ii)

△PED
(iii)

△ODE
(iv)

△PEO
(v)

△QDE

Question 16

16.

In the given figure, the altitudes NC and DO of △BCD meet at M. ∠DMC =

(i)

∠CDM
(ii)

∠NOM
(iii)

∠MNO
(iv)

∠MCD
(v)

∠OMN

Question 17

17.

In the given figure, QR ∥ EF , and median DG bisects QR.
△DQH ∼

(i)

△DGF
(ii)

△EFD
(iii)

△DHR
(iv)

△DEF
(v)

△DEG

Question 18

18.

In the given figure, △FGH is a triangle in which FI is the internal bisector of ∠F and HJ ∥ IF meeting GF produced at J . ∠HFI =

(i)

∠JFH
(ii)

∠IFG
(iii)

∠IHF
(iv)

∠FIH
(v)

∠GIF

Question 19

19.

Which of the following are true?

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

(i)

{a,c}
(ii)

{e,f,a}
(iii)

{b,c,a}
(iv)

{d,c}
(v)

{b,a}

Question 20

20.

Which of the following are true?

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

(i)

{d,e,c}
(ii)

{e,b}
(iii)

{d,a}
(iv)

{d,a,b}
(v)

{a,b,c}

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

(i)

{d,b}
(ii)

{c,b,a}
(iii)

{a,b}
(iv)

{c,d,a}
(v)

{c,a}

Question 22

22.

Which of the following are true?

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

(i)

{a,b}
(ii)

{b,c,d}
(iii)

{a,d}
(iv)

{a,c}
(v)

{a,b,c}

Question 23

23.

Which of the following are true?

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

{b,d}
(ii)

{b,a}
(iii)

{b,c}
(iv)

{a,c,d}
(v)

{b,a,c}

Question 24

24.

In the given figure, the area of the △HIJ is x sq.cm. K,L,M are the mid-points of the sides IJ , JH and HI respectively. The area of the △KLM is

(i)
2
3

of area of △HIJ
(ii)
1
3

of area of △HIJ
(iii)
1
2

of area of △HIJ
(iv)
1
4

of area of △HIJ
(v)
3
4

of area of △HIJ

Question 25

25.

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

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

(i)
4
3

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
thrice

the area of the triangle
(v)
twice

the area of the triangle

Question 26

26.

If the ratio of the bases of two triangles is C : D and the ratio of the corresponding heights is E : F , the ratio of their areas in the same order is

(i)

CF : DE
(ii)

EF : CD
(iii)

CE : DF
(iv)

DE : CF
(v)

CD : EF

Question 27

27.

In the given two similar triangles, if b = 19 cm, c = 15 cm, d = 15 cm, g = 9 cm, find e

(i)

13.40 cm
(ii)

11.40 cm
(iii)

12.40 cm
(iv)

10.40 cm
(v)

9.40 cm

Question 28

28.

In the given figure, given ∠GDE = ∠FDG, x : y = 10 cm : 10 cm and q = 18 cm, find p =

(i)

19.00 cm
(ii)

20.00 cm
(iii)

18.00 cm
(iv)

17.00 cm
(v)

16.00 cm

Question 29

29.

In the given figure, given ∠FCD = ∠ECF, p = 9 cm, q = 10 cm and DE = 19 cm, find DF =

(i)

7.00 cm
(ii)

11.00 cm
(iii)

10.00 cm
(iv)

8.00 cm
(v)

9.00 cm

Question 30

30.

In the given figure, HIJK is a trapezium where OH = 14 cm , OI = 14 cm and OK = 5 cm . Find OJ =

(i)

5 cm
(ii)

7 cm
(iii)

4 cm
(iv)

3 cm
(v)

6 cm

Question 31

31.

In the given figure, ∠FCD = 53.13°, find the value of x =

(i)

34.87°
(ii)

38.87°
(iii)

36.87°
(iv)

37.87°
(v)

35.87°

Question 32

32.

In the given figure, ∠JKL = 53.13°, find the value of y =

(i)

35.87°
(ii)

34.87°
(iii)

37.87°
(iv)

36.87°
(v)

38.87°

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, △HIJ is right-angled at I. Also, IK ⟂ HJ. Which of the following are true?

a)

HI

2
=
HJ
.
HK

b)

HI

2
=
JH
.
JK

c)

IJ

2
=
JH
.
JK

d)

IK

2
=
HK
.
KJ

e)

IJ

2
=
HJ
.
HK

(i)

{e,c}
(ii)

{b,a,c}
(iii)

{a,c,d}
(iv)

{b,a}
(v)

{b,e,d}

Question 35

35.

In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. If JK = 19 cm, JL = 12.67 cm, then find IJ.

(i)

17.00 cm
(ii)

15.00 cm
(iii)

19.00 cm
(iv)

18.00 cm
(v)

16.00 cm

Question 36

36.

In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. If IL = 15.2 cm, JL = 12.99 cm, then find LK.

(i)

10.10 cm
(ii)

9.10 cm
(iii)

13.10 cm
(iv)

12.10 cm
(v)

11.10 cm

Question 37

37.

In the given figure, △CDE ∼ △QRS and CD = 10 cm, QR = 14 cm.

(i)

43.30 sq.cm
(ii)

45.30 sq.cm
(iii)

42.30 sq.cm
(iv)

44.30 sq.cm
(v)

41.30 sq.cm

Question 38

38.

In the given figure, △DEF ∼ △PQR and EF = 13 cm , QR = 18.2 cm and

(i)

58.00 sq.cm
(ii)

59.00 sq.cm
(iii)

57.00 sq.cm
(iv)

56.00 sq.cm
(v)

55.00 sq.cm

Question 39

39.

In the given figure, △CDE & △NOP are similar triangles. If the ratio of the heights CF : NQ = 9 : 12, then the ratio of their areas is

(i)

81

sq.cm

:

144

sq.cm
(ii)

81

sq.cm

:

146

sq.cm
(iii)

81

sq.cm

:

142

sq.cm
(iv)

82

sq.cm

:

144

sq.cm
(v)

80

sq.cm

:

144

sq.cm

Question 40

40.

In the given figure, points I , J and K are the mid-points of sides GH, HF and FG of △FGH. Which of the following are true?

a)

All four small triangles have equal areas

b)

c)

d)

Area of △FGH = 4 times area of △IJK

e)

Area of trapezium GHJK is thrice the area of △FKJ

(i)

{b,a,d}
(ii)

{c,d}
(iii)

{a,d,e}
(iv)

{b,a}
(v)

{b,c,e}

Question 41

41.

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)	△PQR ∼ △MNO
b)	△MRQ ∼ △MNO
c)	△PRQ ∼ △MNO
d)	△RNP ∼ △MNO
e)	△QPO ∼ △MNO

(i)

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

{c,d}
(iii)

{c,a}
(iv)

{c,e,a}
(v)

{c,b}

Question 42

42.

The perimeters of two similar triangles are 35 cm and 19 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.

(i)

7.69 cm
(ii)

6.69 cm
(iii)

10.69 cm
(iv)

8.69 cm
(v)

9.69 cm

Question 43

43.

In the given figure, H is a point on side FG of △EFG such that ∠GEF = ∠EHG = 105° , ∠HGE = 23°. Find ∠GEH

(i)

53°
(ii)

54°
(iii)

50°
(iv)

51°
(v)

52°

Question 44

44.

LMNO is a square and △LMP is an equilateral triangle. Also, △LNQ is an equilateral triangle. If area of △LMP is 'a' sq.units, then the area of △LNQ is

(i)
√

3

a sq.units
(ii)
1
2

√

3

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

a sq.units
(v)
a

2

sq.units

Question 45

45.

BCDE is a cyclic trapezium. Diagonals CE and BD intersect at F. If EB = 15 cm, find CD

(i)

16 cm
(ii)

15 cm
(iii)

17 cm
(iv)

14 cm
(v)

13 cm

Question 46

46.

A vertical stick
14 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)

113 m
(ii)

114 m
(iii)

111 m
(iv)

112 m
(v)

110 m

Question 47

47.

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

a)

1

a

2
+
1

b

2
=
1

p

2

b)

a

2
+
b

2
=
c

2

c)

d)

ab
=
pc

e)

(i)

{e,b}
(ii)

{a,b,d}
(iii)

{c,a}
(iv)

{c,a,b}
(v)

{c,e,d}

Question 48

48.

In the given figure, ∠LIJ = ∠KIL and IL ∥ MK and IJ = 15 cm, JL = 9 cm and LK = 11 cm. Find IM

(i)

18.33 cm
(ii)

20.33 cm
(iii)

19.33 cm
(iv)

16.33 cm
(v)

17.33 cm

Question 49

49.

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

(i)

19.00 cm
(ii)

22.00 cm
(iii)

21.00 cm
(iv)

20.00 cm
(v)

23.00 cm

Question 50

50.

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

:

7
.

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

(i)

4

:

7
(ii)

5

:

4
(iii)

5

:

10
(iv)

7

:

5
(v)

6

:

7

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)

12.86 cm
(ii)

11.86 cm
(iii)

13.86 cm
(iv)

14.86 cm
(v)

15.86 cm

Assignment Key