EduSahara™ Worksheet

Question 1

1.

(i)

6.93 cm
(ii)

7.93 cm
(iii)

5.93 cm
(iv)

4.93 cm
(v)

3.93 cm

Question 2

2.

In the given figure,
HI
∥
FG
.

(i)

7.98 cm
(ii)

6.98 cm
(iii)

8.98 cm
(iv)

5.98 cm
(v)

9.98 cm

Question 3

3.

In the given figure, RS ∥ GH and FS = 12.6 cm, FH = 21 cm and RS = 15 cm, find GH

(i)

23.0 cm
(ii)

24.0 cm
(iii)

26.0 cm
(iv)

25.0 cm
(v)

27.0 cm

Question 4

4.

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

(i)

∠T
(ii)

∠S
(iii)

∠P
(iv)

∠R
(v)

∠O

Question 5

5.

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

(i)

∠MNL
(ii)

∠MKL
(iii)

∠LMN
(iv)

∠KLN
(v)

∠NLM

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.

△FEH ∼

(i)

△ACF
(ii)

△ABH
(iii)

△FDA
(iv)

△DAE
(v)

△DCF

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.

∠HFE =

(i)

∠HAB
(ii)

∠AFD
(iii)

∠FEH
(iv)

∠FAC
(v)

∠FDA

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.

∠ABH =

(i)

∠EHF
(ii)

∠ACF
(iii)

∠FEH
(iv)

∠FDA
(v)

∠DAF

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.

∠EHF =

(i)

∠DAF
(ii)

∠CFA
(iii)

∠BHA
(iv)

∠AFD
(v)

∠HFE

Question 10

10.

In the given figure, CDEF is a trapezium in which

FG
=
(

x

+

33

)
cm, find the value of x

(i)

(

43

,

42

)
(ii)

(

43

,

43

)
(iii)

(

46

,

43

)
(iv)

(

44

,

44

)
(v)

(

45

,

45

)

Question 11

11.

In the given figure, the altitudes UE and FV of △DEF meet at T. ∠FUT =

(i)

∠TFU
(ii)

∠UTF
(iii)

∠VET
(iv)

∠TVE
(v)

∠ETV

Question 12

12.

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

If DG = 18 cm, DS = 11.25 cm and DH = 11.25 cm, DE =

(i)

18.00 cm
(ii)

16.00 cm
(iii)

17.00 cm
(iv)

20.00 cm
(v)

19.00 cm

Question 13

13.

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

If GJ = 14.9 cm, GI = 17 cm and GT = 8.5 cm, GK =

(i)

9.45 cm
(ii)

5.45 cm
(iii)

6.45 cm
(iv)

8.45 cm
(v)

7.45 cm

Question 14

14.

In the given figure, △NOP is a triangle in which NQ is the internal bisector of ∠N and PR ∥ QN meeting ON produced at R . ∠NPR =

(i)

∠OQN
(ii)

∠NQP
(iii)

∠PRN
(iv)

∠QPN
(v)

∠RNP

Question 15

15.

In the given figure, R and S are points on the sides OP and OQ respectively of △OPQ.For which of the following cases, RS ∥ PQ

a)	OR = 7.6 cm, RP = 11.4 cm, OS = 7.2 cm and SQ = 10.8 cm
b)	OP = 19 cm, RP = 11.4 cm, OS = 9.2 cm and OQ = 18 cm
c)	OP = 19 cm, OR = 9.6 cm, OQ = 18 cm and SQ = 10.8 cm
d)	OP = 19 cm, RP = 11.4 cm, OQ = 18 cm and OS = 7.2 cm

(i)

{a,d}
(ii)

{b,d,a}
(iii)

{b,c,a}
(iv)

{c,d}
(v)

{b,a}

Question 16

16.

In the given figure, the area of the △KLM is x sq.cm. N,O,P are the mid-points of the sides LM , MK and KL respectively. The area of the △NOP is

(i)
2
3

of area of △KLM
(ii)
1
4

of area of △KLM
(iii)
3
4

of area of △KLM
(iv)
1
2

of area of △KLM
(v)
1
3

of area of △KLM

Question 17

17.

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)
5
4

the area of the triangle
(ii)
4
3

the area of the triangle
(iii)
twice

the area of the triangle
(iv)
3
2

the area of the triangle
(v)
thrice

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)

KM : LN
(ii)

KL : MN
(iii)

LM : KN
(iv)

MN : KL
(v)

KN : LM

Question 19

19.

In the given △IJK, LM ∥ JK. If IL : LJ = 7.71 cm : 10.29 cm and IK = 17 cm, MK =

(i)

10.71 cm
(ii)

11.71 cm
(iii)

9.71 cm
(iv)

8.71 cm
(v)

7.71 cm

Question 20

20.

In the given figure, given ∠JGH = ∠IGJ, x : y = 8.72 cm : 8.28 cm and p = 20 cm, find q =

(i)

18.00 cm
(ii)

17.00 cm
(iii)

19.00 cm
(iv)

21.00 cm
(v)

20.00 cm

Question 21

21.

In the given figure, given ∠DAB = ∠CAD, p = 7.53 cm, q = 8.47 cm and BC = 16 cm, find BD =

(i)

6.53 cm
(ii)

9.53 cm
(iii)

8.53 cm
(iv)

5.53 cm
(v)

7.53 cm

Question 22

22.

In the given figure, HIJK is a trapezium where OI = 15 cm , OJ = 5 cm and OK = 5 cm . Find OH =

(i)

14 cm
(ii)

16 cm
(iii)

17 cm
(iv)

13 cm
(v)

15 cm

Question 23

23.

In the given figure, ∠KHI = 42.14°, find the value of x =

(i)

46.86°
(ii)

48.86°
(iii)

49.86°
(iv)

47.86°
(v)

45.86°

Question 24

24.

In the given figure, ∠KIJ = 43.62°, find the value of y =

(i)

48.38°
(ii)

47.38°
(iii)

44.38°
(iv)

46.38°
(v)

45.38°

Question 25

25.

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

a)

GH

2
=
GI
.
GJ

b)

GH

2
=
IG
.
IJ

c)

HI

2
=
GI
.
GJ

d)

HJ

2
=
GJ
.
JI

e)

HI

2
=
IG
.
IJ

(i)

{b,a}
(ii)

{b,a,d}
(iii)

{b,c,e}
(iv)

{a,d,e}
(v)

{c,d}

Question 26

26.

In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If BC = 16 cm, CD = 17 cm, then find CE.

(i)

13.65 cm
(ii)

11.65 cm
(iii)

10.65 cm
(iv)

12.65 cm
(v)

9.65 cm

Question 27

27.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. If CF = 10.6 cm, DF = 11.96 cm, then find FE.

(i)

13.50 cm
(ii)

11.50 cm
(iii)

12.50 cm
(iv)

15.50 cm
(v)

14.50 cm

Question 28

28.

In the given figure, △EFG ∼ △PQR and EF = 12 cm, PQ = 16.8 cm.

(i)

141.72 sq.cm
(ii)

139.72 sq.cm
(iii)

142.72 sq.cm
(iv)

143.72 sq.cm
(v)

140.72 sq.cm

Question 29

29.

In the given figure, △EFG ∼ △MNO and FG = 15 cm , NO = 21 cm and

(i)

107.78 sq.cm
(ii)

106.78 sq.cm
(iii)

108.78 sq.cm
(iv)

109.78 sq.cm
(v)

105.78 sq.cm

Question 30

30.

In the given figure, △BCD & △OPQ are similar triangles. If the ratio of the heights BE : OR = 8 : 12, then the ratio of their areas is

(i)

64

sq.cm

:

141

sq.cm
(ii)

64

sq.cm

:

146

sq.cm
(iii)

64

sq.cm

:

144

sq.cm
(iv)

65

sq.cm

:

144

sq.cm
(v)

63

sq.cm

:

144

sq.cm

Question 31

31.

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 trapezium HIKL is thrice the area of △GLK

b)

c)

All four small triangles have equal areas

d)

e)

Area of △GHI = 4 times area of △JKL

(i)

{d,c}
(ii)

{a,c,e}
(iii)

{b,d,e}
(iv)

{b,a,c}
(v)

{b,a}

Question 32

32.

The perimeters of two similar triangles are 35 cm and 17 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.

(i)

5.77 cm
(ii)

7.77 cm
(iii)

8.77 cm
(iv)

9.77 cm
(v)

6.77 cm

Question 33

33.

In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 102° , ∠DCA = 21°. Find ∠CAD

(i)

55°
(ii)

57°
(iii)

59°
(iv)

58°
(v)

56°

Question 34

34.

EFGH is a square and △EFI is an equilateral triangle. Also, △EGJ is an equilateral triangle. If area of △EFI is 'a' sq.units, then the area of △EGJ is

(i)
1
2

√

3

a sq.units
(ii)
2a sq.units
(iii)
√

3

a sq.units
(iv)
a

2

sq.units
(v)
1
2

a sq.units

Question 35

35.

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

(i)

14 cm
(ii)

13 cm
(iii)

16 cm
(iv)

17 cm
(v)

15 cm

Question 36

36.

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

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

Find the height of the tower.

(i)

104 m
(ii)

102 m
(iii)

105 m
(iv)

106 m
(v)

103 m

Question 37

37.

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

(i)

1
2

4
√

2
(ii)

1
(iii)

1
2

√

2
(iv)

1
2

√

5
(v)

1
2

√

1
2

Question 38

38.

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

a)

b)

c)

a

2
+
b

2
=
c

2

d)

ab
=
pc

e)

1

a

2
+
1

b

2
=
1

p

2

(i)

{a,c}
(ii)

{c,d,e}
(iii)

{b,d}
(iv)

{a,b,e}
(v)

{a,c,d}

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)
9 AD

2

=

7 AB

2
(iv)
7 AD

2

=

9 AB

2

Question 40

40.

In the given figure, ∠MJK = ∠LJM and JM ∥ NL and JK = 17 cm, KM = 8 cm and ML = 9 cm. Find JN

(i)

20.12 cm
(ii)

19.12 cm
(iii)

17.12 cm
(iv)

21.12 cm
(v)

18.12 cm

Question 41

41.

In the given figure, MO is the angular bisector of
∠M
&
∠O

(i)

17.00 cm
(ii)

18.00 cm
(iii)

19.00 cm
(iv)

16.00 cm
(v)

15.00 cm

Question 42

42.

In the given figure, CDE is a triangle and 'O' is a point inside △CDE. The angular bisector of ∠DOC, ∠EOD & ∠COE meet CD, DE & EC at F, G & H respectively . Then