EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

AAA Similarity
(iii)

not similar
(iv)

SSS Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 3

3.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

not similar

Question 4

4.

In the given figure, △ABC and △TUV 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, △DEF and △PQR are such that

Identify the property by which the two triangles are similar

(i)

SAS Similarity
(ii)

AAA Similarity
(iii)

not similar
(iv)

SSS Similarity

Question 6

6.

In the given figure, △GHI and △STU 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.

(i)

8.00 cm
(ii)

9.00 cm
(iii)

5.00 cm
(iv)

7.00 cm
(v)

6.00 cm

Question 8

8.

In the given figure,
EF
∥
CD
.

(i)

4.55 cm
(ii)

7.55 cm
(iii)

5.55 cm
(iv)

3.55 cm
(v)

6.55 cm

Question 9

9.

In the given figure, ST ∥ EF and DT = 12.6 cm, DF = 21 cm and EF = 22 cm, find ST

(i)

14.2 cm
(ii)

12.2 cm
(iii)

13.2 cm
(iv)

15.2 cm
(v)

11.2 cm

Question 10

10.

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

(i)

∠U
(ii)

∠R
(iii)

∠T
(iv)

∠Q
(v)

∠S

Question 11

11.

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

(i)

∠OPR
(ii)

∠PRO
(iii)

∠RPQ
(iv)

∠PQR
(v)

∠ROP

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.

△ABH ∼

(i)

△FEH
(ii)

△DCF
(iii)

△DAE
(iv)

△FDA
(v)

△ACF

Question 13

13.

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)

∠HAB
(ii)

∠FDA
(iii)

∠FAC
(iv)

∠FEH
(v)

∠HFE

Question 14

14.

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)

∠FDA
(ii)

∠EHF
(iii)

∠FEH
(iv)

∠DAF
(v)

∠ABH

Question 15

15.

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)

∠HFE
(ii)

∠CFA
(iii)

∠DAF
(iv)

∠BHA
(v)

∠AFD

Question 16

16.

In the given figure, ABCD is a trapezium in which

DE
=
(

3

x

+

6

)
cm, find the value of x

(i)

(

18

,

-1

)
(ii)

(

17

,

-3

)
(iii)

(

17

,

-2

)
(iv)

(

0

,

19

)
(v)

(

19

,

-2

)

Question 17

17.

In the given figure, DEFG is a trapezium in which

(i)

△HFG
(ii)

△HEF
(iii)

△EFG
(iv)

△HGD
(v)

△GDE

Question 18

18.

In the given figure, the altitudes SG and HT of △FGH meet at R. △TGH ∼

(i)

△RGH
(ii)

△SHG
(iii)

△TGR
(iv)

△SHR
(v)

△RTS

Question 19

19.

In the given figure, the altitudes SC and DT of △BCD meet at R. ∠DSR =

(i)

∠RDS
(ii)

∠TCR
(iii)

∠RTC
(iv)

∠CRT
(v)

∠SRD

Question 20

20.

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

If DG = 15.9 cm, DQ = 9.6 cm and DH = 9.54 cm, DE =

(i)

15.00 cm
(ii)

18.00 cm
(iii)

16.00 cm
(iv)

14.00 cm
(v)

17.00 cm

Question 21

21.

In the given figure, TU ∥ EF , and median DG bisects TU.

If DG = 14.5 cm, DF = 16 cm and DH = 4.83 cm, UF =

(i)

11.67 cm
(ii)

10.67 cm
(iii)

8.67 cm
(iv)

12.67 cm
(v)

9.67 cm

Question 22

22.

In the given figure, RS ∥ IJ , and median HK bisects RS.
△HIK ∼

(i)

△HRL
(ii)

△HIJ
(iii)

△HKJ
(iv)

△HLS
(v)

△IJH

Question 23

23.

In the given figure, △DEF is a triangle in which DG is the internal bisector of ∠D and FH ∥ GD meeting ED produced at H . ∠DFH =

(i)

∠FDG
(ii)

∠EGD
(iii)

∠GFD
(iv)

∠HDF
(v)

∠DGF

Question 24

24.

In the given figure, D and E are points on the sides AB and AC respectively of △ABC.For which of the following cases, DE ∥ BC

a)	AD = 9.14 cm, DB = 6.86 cm, AE = 8.57 cm and EC = 6.43 cm
b)	AB = 16 cm, AD = 11.14 cm, AC = 15 cm and EC = 6.43 cm
c)	AB = 16 cm, DB = 6.86 cm, AE = 10.57 cm and AC = 15 cm
d)	AB = 16 cm, DB = 6.86 cm, AC = 15 cm and AE = 8.57 cm

(i)

{a,d}
(ii)

{b,d,a}
(iii)

{b,a}
(iv)

{c,d}
(v)

{b,c,a}

Question 25

25.

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
4

of area of △GHI
(iii)
2
3

of area of △GHI
(iv)
1
3

of area of △GHI
(v)
3
4

of area of △GHI

Question 26

26.

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

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

(i)
thrice

the area of the triangle
(ii)
twice

the area of the triangle
(iii)
5
4

the area of the triangle
(iv)
4
3

the area of the triangle
(v)
3
2

the area of the triangle

Question 27

27.

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)

JM : KL
(ii)

KL : JM
(iii)

JK : LM
(iv)

JL : KM
(v)

LM : JK

Question 28

28.

In the given △FGH, IJ ∥ GH. If FI : IG = 9 cm : 9 cm and FH = 20 cm, FJ =

(i)

12.00 cm
(ii)

10.00 cm
(iii)

9.00 cm
(iv)

8.00 cm
(v)

11.00 cm

Question 29

29.

In the given two similar triangles, if j = 19 cm, k = 18 cm, l = 20 cm, m = 11.4 cm, find n

(i)

11.80 cm
(ii)

9.80 cm
(iii)

12.80 cm
(iv)

10.80 cm
(v)

8.80 cm

Question 30

30.

In the given figure, given ∠HEF = ∠GEH, x : y = 7.5 cm : 7.5 cm and p = 17 cm, find q =

(i)

16.00 cm
(ii)

19.00 cm
(iii)

18.00 cm
(iv)

15.00 cm
(v)

17.00 cm

Question 31

31.

In the given figure, given ∠KHI = ∠JHK, p = 8.26 cm, q = 7.74 cm and IJ = 16 cm, find IK =

(i)

6.26 cm
(ii)

7.26 cm
(iii)

10.26 cm
(iv)

9.26 cm
(v)

8.26 cm

Question 32

32.

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

(i)

14 cm
(ii)

10 cm
(iii)

13 cm
(iv)

12 cm
(v)

11 cm

Question 33

33.

In the given figure, ∠FGI = 46.62°, find the value of x =

(i)

45.38°
(ii)

42.38°
(iii)

43.38°
(iv)

44.38°
(v)

41.38°

Question 34

34.

In the given figure, ∠BCD = 42.93°, find the value of y =

(i)

47.07°
(ii)

49.07°
(iii)

46.07°
(iv)

45.07°
(v)

48.07°

Question 35

35.

In the given figure, if GH ∥ IJ then

(i)

△GHK ∼ △JIK
(ii)

△GHK ∼ △KIJ
(iii)

△GHK ∼ △KJI
(iv)

△KGH ∼ △KIJ
(v)

△KHG ∼ △KJI

Question 36

36.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. Which of the following are true?

a)

HI

2
=
GI
.
GJ

b)

HJ

2
=
GJ
.
JI

c)

HI

2
=
IG
.
IJ

d)

GH

2
=
IG
.
IJ

e)

GH

2
=
GI
.
GJ

(i)

{a,b,c}
(ii)

{d,c}
(iii)

{a,b}
(iv)

{a,d,e}
(v)

{b,c,e}

Question 37

37.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If EF = 20 cm, EG = 13.77 cm, then find DE.

(i)

18.00 cm
(ii)

20.00 cm
(iii)

19.00 cm
(iv)

21.00 cm
(v)

17.00 cm

Question 38

38.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AD = 14.9 cm, DC = 9.3 cm, then find BD.

(i)

13.77 cm
(ii)

11.77 cm
(iii)

12.77 cm
(iv)

9.77 cm
(v)

10.77 cm

Question 39

39.

In the given figure, △CDE ∼ △MNO and CD = 14 cm, MN = 19.6 cm.

(i)

108.10 sq.cm
(ii)

109.10 sq.cm
(iii)

105.10 sq.cm
(iv)

107.10 sq.cm
(v)

106.10 sq.cm

Question 40

40.

In the given figure, △ABC ∼ △OPQ and BC = 10 cm , PQ = 14 cm and

(i)

115.22 sq.cm
(ii)

116.22 sq.cm
(iii)

114.22 sq.cm
(iv)

117.22 sq.cm
(v)

113.22 sq.cm

Question 41

41.

In the given figure, △ABC & △QRS are similar triangles. If the ratio of the heights AD : QT = 8 : 11, then the ratio of their areas is

(i)

64

sq.cm

:

124

sq.cm
(ii)

64

sq.cm

:

119

sq.cm
(iii)

64

sq.cm

:

121

sq.cm
(iv)

63

sq.cm

:

121

sq.cm
(v)

65

sq.cm

:

121

sq.cm

Question 42

42.

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)

Area of trapezium CDFG is thrice the area of △BGF

b)

All four small triangles have equal areas

c)

d)

e)

Area of △BCD = 4 times area of △EFG

(i)

{c,d,e}
(ii)

{a,b,e}
(iii)

{d,b}
(iv)

{c,a,b}
(v)

{c,a}

Question 43

43.

In the given figure, points M , N and O are the mid-points of sides KL, LJ and JK of △JKL. Which of the following are true?

a)	△NML ∼ △JKL
b)	△JON ∼ △JKL
c)	△MON ∼ △JKL
d)	△OKM ∼ △JKL
e)	△MNO ∼ △JKL

(i)

{c,a}
(ii)

{c,b}
(iii)

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

{c,e,a}
(v)

{c,d}

Question 44

44.

The perimeters of two similar triangles are 30 cm and 16 cm respectively. If one side of the first triangle is 13 cm, find the length of the corresponding side of the second triangle.

(i)

4.93 cm
(ii)

7.93 cm
(iii)

6.93 cm
(iv)

8.93 cm
(v)

5.93 cm

Question 45

45.

In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 102° , ∠GFD = 28°. Find ∠FDG

(i)

51°
(ii)

49°
(iii)

50°
(iv)

48°
(v)

52°

Question 46

46.

KLMN is a square and △KLO is an equilateral triangle. Also, △KMP is an equilateral triangle. If area of △KLO is 'a' sq.units, then the area of △KMP is

(i)
1
2

√

3

a sq.units
(ii)
a

2

sq.units
(iii)
1
2

a sq.units
(iv)
2a sq.units
(v)
√

3

a sq.units

Question 47

47.

CDEF is a cyclic trapezium. Diagonals DF and CE intersect at G. If FC = 16 cm, find DE

(i)

18 cm
(ii)

14 cm
(iii)

17 cm
(iv)

16 cm
(v)

15 cm

Question 48

48.

A vertical stick
13 m
long casts a shadow of
16 m
long on the ground.

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

Find the height of the tower.

(i)

106 m
(ii)

104 m
(iii)

103 m
(iv)

105 m
(v)

102 m

Question 49

49.

In the given figure, △FGH, RS ∥ GH such that

(i)

1
2

√

2
(ii)

1
(iii)

1
2

4
√

2
(iv)

1
2

√

1
2
(v)

1
2

√

5

Question 50

50.

In the given figure, ∠DAB = ∠CAD and AD ∥ EC and AB = 16 cm, BD = 8 cm and DC = 7 cm. Find AE

(i)

13.00 cm
(ii)

14.00 cm
(iii)

15.00 cm
(iv)

16.00 cm
(v)

12.00 cm

Question 51

51.

In the given figure, IK is the angular bisector of
∠I
&
∠K

(i)

16.14 cm
(ii)

17.14 cm
(iii)

19.14 cm
(iv)

18.14 cm
(v)

15.14 cm

Question 52

52.

In the given figure, GHI is a triangle and 'O' is a point inside △GHI. The angular bisector of ∠HOG, ∠IOH & ∠GOI meet GH, HI & IG at J, K & L respectively . Then