EduSahara™ Worksheet

Question 1

1.

(i)

8.54 cm
(ii)

7.54 cm
(iii)

9.54 cm
(iv)

6.54 cm
(v)

5.54 cm

Question 2

2.

In the given figure,
IJ
∥
GH
.

(i)

7.40 cm
(ii)

4.40 cm
(iii)

3.40 cm
(iv)

5.40 cm
(v)

6.40 cm

Question 3

3.

In the given figure, QR ∥ FG and ER = 14.4 cm, EG = 24 cm and FG = 21 cm, find QR

(i)

12.6 cm
(ii)

11.6 cm
(iii)

10.6 cm
(iv)

13.6 cm
(v)

14.6 cm

Question 4

4.

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

(i)

∠I
(ii)

∠E
(iii)

∠H
(iv)

∠F
(v)

∠G

Question 5

5.

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

(i)

∠HFG
(ii)

∠EFH
(iii)

∠HEF
(iv)

∠GHF
(v)

∠GEF

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.

△ACF ∼

(i)

△ABH
(ii)

△FEH
(iii)

△DCF
(iv)

△FDA
(v)

△DAE

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)

∠HFE
(ii)

∠FEH
(iii)

∠FAC
(iv)

∠FDA
(v)

∠AFD

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.

∠FEH =

(i)

∠DAF
(ii)

∠ACF
(iii)

∠EHF
(iv)

∠ABH
(v)

∠FDA

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)

∠CFA
(ii)

∠EHF
(iii)

∠DAF
(iv)

∠HFE
(v)

∠AFD

Question 10

10.

In the given figure, MNOP is a trapezium in which

PQ
=
(

x

+

18

)
cm, find the value of x

(i)

(

-19

,

39

)
(ii)

(

-16

,

39

)
(iii)

(

41

,

-17

)
(iv)

(

-19

,

38

)
(v)

(

-18

,

40

)

Question 11

11.

In the given figure, the altitudes UC and DV of △BCD meet at T. ∠VCT =

(i)

∠UTD
(ii)

∠CTV
(iii)

∠DUT
(iv)

∠TDU
(v)

∠TVC

Question 12

12.

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

If EF = 15 cm, ET = 7.5 cm and EI = 7.5 cm, EH =

(i)

13.00 cm
(ii)

14.00 cm
(iii)

15.00 cm
(iv)

16.00 cm
(v)

17.00 cm

Question 13

13.

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

If GJ = 15.7 cm, GI = 20 cm and GS = 11.43 cm, GK =

(i)

6.97 cm
(ii)

8.97 cm
(iii)

10.97 cm
(iv)

9.97 cm
(v)

7.97 cm

Question 14

14.

In the given figure, △KLM is a triangle in which KN is the internal bisector of ∠K and MO ∥ NK meeting LK produced at O . ∠MKN =

(i)

∠KMO
(ii)

∠NMK
(iii)

∠OKM
(iv)

∠KNM
(v)

∠LNK

Question 15

15.

In the given figure, L and M are points on the sides IJ and IK respectively of △IJK.For which of the following cases, LM ∥ JK

a)	IJ = 19 cm, IL = 13.4 cm, IK = 16 cm and MK = 6.4 cm
b)	IJ = 19 cm, LJ = 7.6 cm, IM = 11.6 cm and IK = 16 cm
c)	IL = 11.4 cm, LJ = 7.6 cm, IM = 9.6 cm and MK = 6.4 cm
d)	IJ = 19 cm, LJ = 7.6 cm, IK = 16 cm and IM = 9.6 cm

(i)

{c,d}
(ii)

{a,c}
(iii)

{b,d}
(iv)

{a,d,c}
(v)

{a,b,c}

Question 16

16.

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)
1
4

of area of △HIJ
(ii)
3
4

of area of △HIJ
(iii)
1
2

of area of △HIJ
(iv)
2
3

of area of △HIJ
(v)
1
3

of area of △HIJ

Question 17

17.

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

The area of the
△NJK
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)
4
3

the area of the triangle
(iv)
thrice

the area of the triangle
(v)
3
2

the area of the triangle

Question 18

18.

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

(i)

CD : BE
(ii)

BE : CD
(iii)

BC : DE
(iv)

DE : BC
(v)

BD : CE

Question 19

19.

In the given △DEF, GH ∥ EF. If DG : GE = 10.36 cm : 8.64 cm and DF = 18 cm, HF =

(i)

8.18 cm
(ii)

10.18 cm
(iii)

6.18 cm
(iv)

9.18 cm
(v)

7.18 cm

Question 20

20.

In the given figure, given ∠HEF = ∠GEH, x : y = 8.5 cm : 8.5 cm and q = 20 cm, find p =

(i)

18.00 cm
(ii)

21.00 cm
(iii)

22.00 cm
(iv)

19.00 cm
(v)

20.00 cm

Question 21

21.

In the given figure, given ∠HEF = ∠GEH, p = 7.5 cm, q = 7.5 cm and FG = 15 cm, find HG =

(i)

9.50 cm
(ii)

7.50 cm
(iii)

6.50 cm
(iv)

5.50 cm
(v)

8.50 cm

Question 22

22.

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

(i)

7 cm
(ii)

3 cm
(iii)

5 cm
(iv)

6 cm
(v)

4 cm

Question 23

23.

In the given figure, ∠LIJ = 41.98°, find the value of x =

(i)

50.02°
(ii)

49.02°
(iii)

46.02°
(iv)

48.02°
(v)

47.02°

Question 24

24.

In the given figure, ∠EFG = 46.59°, find the value of y =

(i)

44.41°
(ii)

42.41°
(iii)

43.41°
(iv)

45.41°
(v)

41.41°

Question 25

25.

In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. Which of the following are true?

a)

CD

2
=
EC
.
EF

b)

DE

2
=
EC
.
EF

c)

CD

2
=
CE
.
CF

d)

DE

2
=
CE
.
CF

e)

DF

2
=
CF
.
FE

(i)

{a,b}
(ii)

{a,b,c}
(iii)

{d,c}
(iv)

{b,c,e}
(v)

{a,d,e}

Question 26

26.

In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AB = 20 cm, BC = 18 cm, then find BD.

(i)

11.38 cm
(ii)

13.38 cm
(iii)

14.38 cm
(iv)

15.38 cm
(v)

12.38 cm

Question 27

27.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If JI = 10 cm, HJ = 12.49 cm, then find GJ.

(i)

17.60 cm
(ii)

16.60 cm
(iii)

13.60 cm
(iv)

15.60 cm
(v)

14.60 cm

Question 28

28.

In the given figure, △EFG ∼ △PQR and EF = 10 cm, PQ = 14 cm.

(i)

50.00 sq.cm
(ii)

46.00 sq.cm
(iii)

49.00 sq.cm
(iv)

48.00 sq.cm
(v)

47.00 sq.cm

Question 29

29.

In the given figure, △CDE ∼ △NOP and DE = 10 cm , OP = 14 cm and

(i)

139.59 sq.cm
(ii)

138.59 sq.cm
(iii)

140.59 sq.cm
(iv)

137.59 sq.cm
(v)

136.59 sq.cm

Question 30

30.

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

(i)

121

sq.cm

:

223

sq.cm
(ii)

121

sq.cm

:

227

sq.cm
(iii)

120

sq.cm

:

225

sq.cm
(iv)

122

sq.cm

:

225

sq.cm
(v)

121

sq.cm

:

225

sq.cm

Question 31

31.

In the given figure, points H , I and J are the mid-points of sides FG, GE and EF of △EFG. Which of the following are true?

a)

Area of trapezium FGIJ is thrice the area of △EJI

b)

c)

All four small triangles have equal areas

d)

e)

Area of △EFG = 4 times area of △HIJ

(i)

{b,a,c}
(ii)

{d,c}
(iii)

{a,c,e}
(iv)

{b,d,e}
(v)

{b,a}

Question 32

32.

The perimeters of two similar triangles are 26 cm and 17 cm respectively. If one side of the first triangle is 13 cm, find the length of the corresponding side of the second triangle.

(i)

8.50 cm
(ii)

10.50 cm
(iii)

6.50 cm
(iv)

9.50 cm
(v)

7.50 cm

Question 33

33.

In the given figure, K is a point on side IJ of △HIJ such that ∠JHI = ∠HKJ = 100° , ∠KJH = 30°. Find ∠JHK

(i)

52°
(ii)

50°
(iii)

49°
(iv)

51°
(v)

48°

Question 34

34.

DEFG is a square and △DEH is an equilateral triangle. Also, △DFI is an equilateral triangle. If area of △DEH is 'a' sq.units, then the area of △DFI is

(i)
1
2

a sq.units
(ii)
a

2

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

√

3

a sq.units
(v)
√

3

a sq.units

Question 35

35.

DEFG is a cyclic trapezium. Diagonals EG and DF intersect at H. If GD = 6 cm, find EF

(i)

4 cm
(ii)

6 cm
(iii)

5 cm
(iv)

7 cm
(v)

8 cm

Question 36

36.

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)

110 m
(ii)

111 m
(iii)

112 m
(iv)

114 m
(v)

113 m

Question 37

37.

In the given figure, △ABC, TU ∥ BC such that

(i)

1
(ii)

1
2

√

5
(iii)

1
2

√

2
(iv)

1
2

4
√

2
(v)

1
2

√

1
2

Question 38

38.

In the given figure, △ACB is right-angled at C, CD ⟂ AB.

a)

b)

a

2
+
b

2
=
c

2

c)

1

a

2
+
1

b

2
=
1

p

2

d)

e)

ab
=
pc

(i)

{a,d,e}
(ii)

{d,c}
(iii)

{a,b}
(iv)

{b,c,e}
(v)

{a,b,c}

Question 39

39.

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

(i)
7 AD

2

=

9 AB

2
(ii)
9 AD

2

=

7 AB

2
(iii)
7 AD

2

=

3 AB

2
(iv)
3 AD

2

=

7 AB

2

Question 40

40.

In the given figure, ∠KHI = ∠JHK and HK ∥ LJ and HI = 19 cm, IK = 11 cm and KJ = 9 cm. Find HL

(i)

13.55 cm
(ii)

16.55 cm
(iii)

14.55 cm
(iv)

15.55 cm
(v)

17.55 cm

Question 41

41.

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

(i)

18.00 cm
(ii)

22.00 cm
(iii)

19.00 cm
(iv)

20.00 cm
(v)

21.00 cm

Question 42

42.

In the given figure, EFG is a triangle and 'O' is a point inside △EFG. The angular bisector of ∠FOE, ∠GOF & ∠EOG meet EF, FG & GE at H, I & J respectively . Then