EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 2

2.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

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, △FGH and △QRS 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, △DEF and △TUV are such that

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

SSS Similarity

Question 6

6.

In the given figure, △DEF and △PQR 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 7

7.

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

(i)

∠R
(ii)

∠S
(iii)

∠Q
(iv)

∠N
(v)

∠P

Question 8

8.

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

(i)

∠PQO
(ii)

∠OPQ
(iii)

∠QNO
(iv)

∠QOP
(v)

∠NOQ

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.

△ACF ∼

(i)

△FDA
(ii)

△DCF
(iii)

△ABH
(iv)

△DAE
(v)

△FEH

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)

∠HFE
(iii)

∠AFD
(iv)

∠FDA
(v)

∠FEH

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)

∠EHF
(ii)

∠ACF
(iii)

∠FEH
(iv)

∠DAF
(v)

∠ABH

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.

∠DAF =

(i)

∠BHA
(ii)

∠CFA
(iii)

∠EHF
(iv)

∠AFD
(v)

∠HFE

Question 13

13.

In the given figure, ABCD is a trapezium in which

DE
=
(

x

+

13

)
cm, find the value of x

(i)

(

22

,

19

)
(ii)

(

20

,

20

)
(iii)

(

19

,

19

)
(iv)

(

21

,

21

)
(v)

(

19

,

18

)

Question 14

14.

In the given figure, HIJK is a trapezium in which

(i)

△KHI
(ii)

△LIJ
(iii)

△LKH
(iv)

△IJK
(v)

△LJK

Question 15

15.

In the given figure, the altitudes SF and GT of △EFG meet at R. △SGF ∼

(i)

△RFG
(ii)

△SGR
(iii)

△TFG
(iv)

△TFR
(v)

△RTS

Question 16

16.

In the given figure, the altitudes NB and CO of △ABC meet at M. ∠MCN =

(i)

∠NMC
(ii)

∠CNM
(iii)

∠BMO
(iv)

∠MOB
(v)

∠OBM

Question 17

17.

In the given figure, RS ∥ JK , and median IL bisects RS.
△IRM ∼

(i)

△JKI
(ii)

△ILK
(iii)

△IJK
(iv)

△IMS
(v)

△IJL

Question 18

18.

In the given figure, △CDE is a triangle in which CF is the internal bisector of ∠C and EG ∥ FC meeting DC produced at G . ∠CEG =

(i)

∠CFE
(ii)

∠DFC
(iii)

∠FCD
(iv)

∠GCE
(v)

∠FEC

Question 19

19.

Which of the following are true?

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

(i)

{e,f}
(ii)

{a,f,e}
(iii)

{a,e}
(iv)

{c,d,e}
(v)

{b,f}

Question 20

20.

Which of the following are true?

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

(i)

{b,a}
(ii)

{a,d,e}
(iii)

{c,d}
(iv)

{b,c,e}
(v)

{b,a,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 angles are proportional.
d)	The corresponding sides are proportional.

(i)

{b,c,a}
(ii)

{c,d}
(iii)

{b,a}
(iv)

{a,d}
(v)

{b,d,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)

{a,c,d}
(iii)

{b,a,c}
(iv)

{b,c}
(v)

{b,a}

Question 23

23.

Which of the following are true?

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

(i)

{d,a,b}
(ii)

{d,b}
(iii)

{d,c}
(iv)

{d,a}
(v)

{a,b,c}

Question 24

24.

In the given figure, the area of the △DEF is x sq.cm. G,H,I are the mid-points of the sides EF , FD and DE respectively. The area of the △GHI is

(i)
2
3

of area of △DEF
(ii)
1
2

of area of △DEF
(iii)
3
4

of area of △DEF
(iv)
1
3

of area of △DEF
(v)
1
4

of area of △DEF

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)
5
4

the area of the triangle
(ii)
twice

the area of the triangle
(iii)
thrice

the area of the triangle
(iv)
4
3

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 A : B and the ratio of the corresponding heights is C : D , the ratio of their areas in the same order is

(i)

CD : AB
(ii)

AC : BD
(iii)

BC : AD
(iv)

AD : BC
(v)

AB : CD

Question 27

27.

In the given two similar triangles, if l = 20 cm, m = 16 cm, n = 16 cm, q = 9.6 cm, find o

(i)

12.00 cm
(ii)

10.00 cm
(iii)

11.00 cm
(iv)

13.00 cm
(v)

14.00 cm

Question 28

28.

In the given figure, given ∠JGH = ∠IGJ, x : y = 8.65 cm : 7.35 cm and q = 17 cm, find p =

(i)

18.00 cm
(ii)

22.00 cm
(iii)

19.00 cm
(iv)

20.00 cm
(v)

21.00 cm

Question 29

29.

In the given figure, given ∠GDE = ∠FDG, p = 7.06 cm, q = 8.94 cm and EF = 16 cm, find GF =

(i)

9.94 cm
(ii)

10.94 cm
(iii)

7.94 cm
(iv)

8.94 cm
(v)

6.94 cm

Question 30

30.

In the given figure, IJKL is a trapezium where OI = 13 cm , OJ = 13 cm and OK = 4 cm . Find OL =

(i)

5 cm
(ii)

3 cm
(iii)

2 cm
(iv)

6 cm
(v)

4 cm

Question 31

31.

In the given figure, ∠LIJ = 48.58°, find the value of x =

(i)

43.42°
(ii)

41.42°
(iii)

40.42°
(iv)

42.42°
(v)

39.42°

Question 32

32.

In the given figure, ∠EFG = 43.83°, find the value of y =

(i)

48.17°
(ii)

47.17°
(iii)

46.17°
(iv)

44.17°
(v)

45.17°

Question 33

33.

In the given figure, if IJ ∥ KL then

(i)

△IJM ∼ △MKL
(ii)

△MJI ∼ △MLK
(iii)

△IJM ∼ △LKM
(iv)

△IJM ∼ △MLK
(v)

△MIJ ∼ △MKL

Question 34

34.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. Which of the following are true?

a)

EF

2
=
EG
.
EH

b)

EF

2
=
GE
.
GH

c)

FH

2
=
EH
.
HG

d)

FG

2
=
EG
.
EH

e)

FG

2
=
GE
.
GH

(i)

{d,c}
(ii)

{b,a}
(iii)

{a,c,e}
(iv)

{b,a,c}
(v)

{b,d,e}

Question 35

35.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. If CD = 17 cm, DF = 12.95 cm, then find DE.

(i)

22.00 cm
(ii)

18.00 cm
(iii)

21.00 cm
(iv)

20.00 cm
(v)

19.00 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)

13.10 cm
(ii)

11.10 cm
(iii)

9.10 cm
(iv)

12.10 cm
(v)

10.10 cm

Question 37

37.

In the given figure, △DEF ∼ △NOP and DE = 13 cm, NO = 18.2 cm.

(i)

84.00 sq.cm
(ii)

86.00 sq.cm
(iii)

82.00 sq.cm
(iv)

85.00 sq.cm
(v)

83.00 sq.cm

Question 38

38.

In the given figure, △BCD ∼ △QRS and CD = 15 cm , RS = 21 cm and

(i)

175.78 sq.cm
(ii)

172.78 sq.cm
(iii)

173.78 sq.cm
(iv)

174.78 sq.cm
(v)

171.78 sq.cm

Question 39

39.

In the given figure, △DEF & △QRS are similar triangles. If the ratio of the heights DG : QT = 11 : 15, then the ratio of their areas is

(i)

121

sq.cm

:

227

sq.cm
(ii)

120

sq.cm

:

225

sq.cm
(iii)

122

sq.cm

:

225

sq.cm
(iv)

121

sq.cm

:

223

sq.cm
(v)

121

sq.cm

:

225

sq.cm

Question 40

40.

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)

Area of △GHI = 4 times area of △JKL

b)

c)

d)

All four small triangles have equal areas

e)

Area of trapezium HIKL is thrice the area of △GLK

(i)

{c,d}
(ii)

{b,a}
(iii)

{b,c,e}
(iv)

{a,d,e}
(v)

{b,a,d}

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)	△RNP ∼ △MNO
d)	△PRQ ∼ △MNO
e)	△QPO ∼ △MNO

(i)

{d,c}
(ii)

{d,b}
(iii)

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

{d,a}
(v)

{d,e,a}

Question 42

42.

The perimeters of two similar triangles are 30 cm and 24 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.

(i)

13.80 cm
(ii)

11.80 cm
(iii)

10.80 cm
(iv)

12.80 cm
(v)

14.80 cm

Question 43

43.

In the given figure, L is a point on side JK of △IJK such that ∠KIJ = ∠ILK = 105° , ∠LKI = 24°. Find ∠KIL

(i)

53°
(ii)

49°
(iii)

51°
(iv)

50°
(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)
a

2

sq.units
(ii)
√

3

a sq.units
(iii)
1
2

√

3

a sq.units
(iv)
1
2

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

Question 45

45.

KLMN is a cyclic trapezium. Diagonals LN and KM intersect at O. If NK = 17 cm, find LM

(i)

15 cm
(ii)

17 cm
(iii)

19 cm
(iv)

18 cm
(v)

16 cm

Question 46

46.

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

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

Find the height of the tower.

(i)

129 m
(ii)

128 m
(iii)

127 m
(iv)

126 m
(v)

130 m

Question 47

47.

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

a)

ab
=
pc

b)

c)

a

2
+
b

2
=
c

2

d)

1

a

2
+
1

b

2
=
1

p

2

e)

(i)

{b,e,d}
(ii)

{e,c}
(iii)

{b,a,c}
(iv)

{b,a}
(v)

{a,c,d}

Question 48

48.

In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 19 cm, HJ = 11 cm and JI = 9 cm. Find GK

(i)

14.55 cm
(ii)

15.55 cm
(iii)

13.55 cm
(iv)

16.55 cm
(v)

17.55 cm

Question 49

49.

In the given figure, JL is the angular bisector of
∠J
&
∠L

(i)

19.10 cm
(ii)

20.10 cm
(iii)

16.10 cm
(iv)

18.10 cm
(v)

17.10 cm

Question 50

50.

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

:

3
.

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

(i)

4

:

6
(ii)

3

:

4
(iii)

3

:

3
(iv)

5

:

3
(v)

4

:

0

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)

12.07 cm
(ii)

14.07 cm
(iii)

15.07 cm
(iv)

11.07 cm
(v)

13.07 cm

Assignment Key