EduSahara™ Worksheet

Question 1

1.

(i)

7.85 cm
(ii)

6.85 cm
(iii)

4.85 cm
(iv)

5.85 cm
(v)

8.85 cm

Question 2

2.

In the given figure,
GH
∥
EF
.

(i)

6.55 cm
(ii)

3.55 cm
(iii)

5.55 cm
(iv)

4.55 cm
(v)

7.55 cm

Question 3

3.

In the given figure, PQ ∥ BC and AC = 21 cm, PQ = 15 cm and BC = 25 cm, find AQ

(i)

10.6 cm
(ii)

12.6 cm
(iii)

11.6 cm
(iv)

14.6 cm
(v)

13.6 cm

Question 4

4.

In the given figure, △KLM is isosceles right-angled at L and LN ⟂ MK. ∠N =

(i)

∠L
(ii)

∠P
(iii)

∠O
(iv)

∠M
(v)

∠K

Question 5

5.

In the given figure, △EFG is isosceles right-angled at F and FH ⟂ GE. ∠GHF =

(i)

∠HFG
(ii)

∠EFG
(iii)

∠FGH
(iv)

∠EFH
(v)

∠HEF

Question 6

6.

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)

△ABH
(iii)

△FEH
(iv)

△DCF
(v)

△ACF

Question 7

7.

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)

∠AFD
(ii)

∠FAC
(iii)

∠FEH
(iv)

∠FDA
(v)

∠HFE

Question 8

8.

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)

∠DAF
(ii)

∠FEH
(iii)

∠ACF
(iv)

∠ABH
(v)

∠EHF

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.

∠BHA =

(i)

∠AFD
(ii)

∠EHF
(iii)

∠HFE
(iv)

∠CFA
(v)

∠DAF

Question 10

10.

In the given figure, ABCD is a trapezium in which

DE
=
(

x

+

2

)
cm, find the value of x

(i)

(

18

,

-6

)
(ii)

(

21

,

-5

)
(iii)

(

18

,

-5

)
(iv)

(

19

,

-4

)
(v)

(

-3

,

20

)

Question 11

11.

In the given figure, the altitudes RJ and KS of △IJK meet at Q. ∠SJQ =

(i)

∠QKR
(ii)

∠QSJ
(iii)

∠KRQ
(iv)

∠RQK
(v)

∠JQS

Question 12

12.

In the given figure, RS ∥ FG , and median EH bisects RS.

If EF = 18 cm, EH = 17.9 cm and EI = 8.95 cm, ER =

(i)

8.00 cm
(ii)

10.00 cm
(iii)

7.00 cm
(iv)

11.00 cm
(v)

9.00 cm

Question 13

13.

In the given figure, RS ∥ HI , and median GJ bisects RS.

If GJ = 17.8 cm, GI = 20 cm and GK = 9.89 cm, SI =

(i)

9.89 cm
(ii)

8.89 cm
(iii)

6.89 cm
(iv)

10.89 cm
(v)

7.89 cm

Question 14

14.

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)

∠EAC
(ii)

∠BDA
(iii)

∠CEA
(iv)

∠ADC
(v)

∠DCA

Question 15

15.

In the given figure, E and F are points on the sides BC and BD respectively of △BCD.For which of the following cases, EF ∥ CD

a)	BC = 18 cm, EC = 7.2 cm, BD = 18 cm and BF = 10.8 cm
b)	BC = 18 cm, BE = 12.8 cm, BD = 18 cm and FD = 7.2 cm
c)	BC = 18 cm, EC = 7.2 cm, BF = 12.8 cm and BD = 18 cm
d)	BE = 10.8 cm, EC = 7.2 cm, BF = 10.8 cm and FD = 7.2 cm

(i)

{b,a}
(ii)

{a,d}
(iii)

{c,d}
(iv)

{b,c,a}
(v)

{b,d,a}

Question 16

16.

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)
3
4

of area of △DEF
(iii)
1
4

of area of △DEF
(iv)
1
3

of area of △DEF
(v)
1
2

of area of △DEF

Question 17

17.

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)
twice

the area of the triangle
(ii)
4
3

the area of the triangle
(iii)
thrice

the area of the triangle
(iv)
3
2

the area of the triangle
(v)
5
4

the area of the triangle

Question 18

18.

If the ratio of the bases of two triangles is K : L and the ratio of the corresponding heights is M : N , the ratio of their areas in the same order is

(i)

LM : KN
(ii)

MN : KL
(iii)

KM : LN
(iv)

KN : LM
(v)

KL : MN

Question 19

19.

In the given △NOP, QR ∥ OP. If NQ : QO = 8.44 cm : 10.56 cm and NP = 20 cm, NR =

(i)

6.89 cm
(ii)

7.89 cm
(iii)

9.89 cm
(iv)

10.89 cm
(v)

8.89 cm

Question 20

20.

In the given figure, given ∠GDE = ∠FDG, x : y = 8.89 cm : 7.11 cm and q = 16 cm, find p =

(i)

19.00 cm
(ii)

20.00 cm
(iii)

22.00 cm
(iv)

18.00 cm
(v)

21.00 cm

Question 21

21.

In the given figure, given ∠IFG = ∠HFI, p = 9.5 cm, q = 9.5 cm and GH = 19 cm, find GI =

(i)

7.50 cm
(ii)

10.50 cm
(iii)

8.50 cm
(iv)

9.50 cm
(v)

11.50 cm

Question 22

22.

In the given figure, FGHI is a trapezium where OG = 15 cm , OH = 5 cm and OI = 5 cm . Find OF =

(i)

17 cm
(ii)

16 cm
(iii)

13 cm
(iv)

15 cm
(v)

14 cm

Question 23

23.

In the given figure, ∠IJL = 41.28°, find the value of x =

(i)

49.72°
(ii)

47.72°
(iii)

46.72°
(iv)

50.72°
(v)

48.72°

Question 24

24.

In the given figure, ∠KIJ = 50.26°, find the value of y =

(i)

39.74°
(ii)

41.74°
(iii)

37.74°
(iv)

38.74°
(v)

40.74°

Question 25

25.

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)

FH

2
=
EH
.
HG

c)

FG

2
=
GE
.
GH

d)

EF

2
=
GE
.
GH

e)

FG

2
=
EG
.
EH

(i)

{d,a}
(ii)

{d,a,b}
(iii)

{d,e,c}
(iv)

{a,b,c}
(v)

{e,b}

Question 26

26.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If HI = 18 cm, HJ = 13.38 cm, then find GH.

(i)

19.00 cm
(ii)

21.00 cm
(iii)

20.00 cm
(iv)

22.00 cm
(v)

18.00 cm

Question 27

27.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AD = 14.9 cm, BD = 11.77 cm, then find DC.

(i)

9.30 cm
(ii)

10.30 cm
(iii)

11.30 cm
(iv)

8.30 cm
(v)

7.30 cm

Question 28

28.

In the given figure, △EFG ∼ △PQR and EF = 14 cm, PQ = 19.6 cm.

(i)

76.89 sq.cm
(ii)

77.89 sq.cm
(iii)

73.89 sq.cm
(iv)

74.89 sq.cm
(v)

75.89 sq.cm

Question 29

29.

In the given figure, △ABC ∼ △QRS and BC = 13 cm , RS = 18.2 cm and

(i)

149.30 sq.cm
(ii)

152.30 sq.cm
(iii)

150.30 sq.cm
(iv)

151.30 sq.cm
(v)

148.30 sq.cm

Question 30

30.

In the given figure, △EFG & △QRS are similar triangles. If the ratio of the heights EH : QT = 9 : 12, then the ratio of their areas is

(i)

82

sq.cm

:

144

sq.cm
(ii)

81

sq.cm

:

141

sq.cm
(iii)

81

sq.cm

:

144

sq.cm
(iv)

80

sq.cm

:

144

sq.cm
(v)

81

sq.cm

:

147

sq.cm

Question 31

31.

In the given figure, points F , G and H are the mid-points of sides DE, EC and CD of △CDE. Which of the following are true?

a)

Area of trapezium DEGH is thrice the area of △CHG

b)

Area of △CDE = 4 times area of △FGH

c)

d)

All four small triangles have equal areas

e)

(i)

{c,a,b}
(ii)

{a,b,d}
(iii)

{c,e,d}
(iv)

{e,b}
(v)

{c,a}

Question 32

32.

The perimeters of two similar triangles are 32 cm and 19 cm respectively. If one side of the first triangle is 15 cm, find the length of the corresponding side of the second triangle.

(i)

9.91 cm
(ii)

10.91 cm
(iii)

7.91 cm
(iv)

6.91 cm
(v)

8.91 cm

Question 33

33.

In the given figure, H is a point on side FG of △EFG such that ∠GEF = ∠EHG = 109° , ∠HGE = 22°. Find ∠GEH

(i)

48°
(ii)

51°
(iii)

47°
(iv)

49°
(v)

50°

Question 34

34.

FGHI is a square and △FGJ is an equilateral triangle. Also, △FHK is an equilateral triangle. If area of △FGJ is 'a' sq.units, then the area of △FHK is

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

a sq.units
(iii)
a

2

sq.units
(iv)
√

3

a sq.units
(v)
1
2

√

3

a sq.units

Question 35

35.

ABCD is a cyclic trapezium. Diagonals BD and AC intersect at E. If DA = 16 cm, find BC

(i)

15 cm
(ii)

14 cm
(iii)

18 cm
(iv)

17 cm
(v)

16 cm

Question 36

36.

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

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

Find the height of the tower.

(i)

127 m
(ii)

126 m
(iii)

129 m
(iv)

128 m
(v)

130 m

Question 37

37.

In the given figure, △EFG, PQ ∥ FG such that

(i)

1
2

√

5
(ii)

1
2

√

-1
(iii)

1
2

√

2
(iv)

1
(v)

1
2

4
√

2

Question 38

38.

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

a)

b)

1

a

2
+
1

b

2
=
1

p

2

c)

d)

ab
=
pc

e)

a

2
+
b

2
=
c

2

(i)

{a,b}
(ii)

{b,d,e}
(iii)

{a,b,d}
(iv)

{c,d}
(v)

{a,c,e}

Question 39

39.

In an equilateral triangle ABC, the side BC is trisected at D. Then

(i)
7 AD

2

=

3 AB

2
(ii)
3 AD

2

=

7 AB

2
(iii)
7 AD

2

=

9 AB

2
(iv)
9 AD

2

=

7 AB

2

Question 40

40.

In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 15 cm, HJ = 7 cm and JI = 9 cm. Find GK

(i)

18.29 cm
(ii)

19.29 cm
(iii)

17.29 cm
(iv)

20.29 cm
(v)

21.29 cm

Question 41

41.

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

(i)

25.00 cm
(ii)

22.00 cm
(iii)

21.00 cm
(iv)

23.00 cm
(v)

24.00 cm

Question 42

42.

In the given figure, BCD is a triangle and 'O' is a point inside △BCD. The angular bisector of ∠COB, ∠DOC & ∠BOD meet BC, CD & DB at E, F & G respectively . Then