EduSahara™ Worksheet

Question 1

1.

In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. Which of the following are true?

a)

GI

2
=
FI
.
IH

b)

GH

2
=
FH
.
FI

c)

FG

2
=
HF
.
HI

d)

FG

2
=
FH
.
FI

e)

GH

2
=
HF
.
HI

(i)

{a,d,e}
(ii)

{b,a}
(iii)

{c,d}
(iv)

{b,c,e}
(v)

{b,a,d}

Question 2

2.

In the given figure, BCDE is a trapezium where OB = 13 cm , OD = 4 cm and OE = 4 cm . Find OC =

(i)

15 cm
(ii)

14 cm
(iii)

12 cm
(iv)

13 cm
(v)

11 cm

Question 3

3.

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)

∠DAF
(iii)

∠EHF
(iv)

∠FEH
(v)

∠FDA

Question 4

4.

In the given figure, TU ∥ CD , and median BE bisects TU.
△BTF ∼

(i)

△CDB
(ii)

△BFU
(iii)

△BED
(iv)

△BCE
(v)

△BCD

Question 5

5.

EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 6 cm, find FG

(i)

4 cm
(ii)

7 cm
(iii)

6 cm
(iv)

8 cm
(v)

5 cm

Question 6

6.

Which of the following are necessary conditions for similarity of two polygons ?

a)	The corresponding angles are equal.
b)	The corresponding sides are proportional.
c)	The corresponding angles are proportional.
d)	The corresponding sides are equal.

(i)

{c,a}
(ii)

{c,b,a}
(iii)

{a,b}
(iv)

{c,d,a}
(v)

{d,b}

Question 7

7.

In the given figure, RS ∥ FG and ER = 13.2 cm, EF = 22 cm and FG = 25 cm, find RS

(i)

16.0 cm
(ii)

15.0 cm
(iii)

14.0 cm
(iv)

17.0 cm
(v)

13.0 cm

Question 8

8.

Identify the property by which the two given triangles are similar

(i)

AAA Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 9

9.

The foot of a ladder resting on a wall from the foot of the wall is 12 m. If the height of the top of the ladder from ground is 10 m, find the length of the ladder

(i)

16.62 m
(ii)

15.62 m
(iii)

13.62 m
(iv)

14.62 m
(v)

17.62 m

Question 10

10.

In the given figure, J and K are points on the sides GH and GI respectively of △GHI.For which of the following cases, JK ∥ HI

a)	GJ = 9.82 cm, JH = 8.18 cm, GK = 8.73 cm and KI = 7.27 cm
b)	GH = 18 cm, GJ = 11.82 cm, GI = 16 cm and KI = 7.27 cm
c)	GH = 18 cm, JH = 8.18 cm, GI = 16 cm and GK = 8.73 cm
d)	GH = 18 cm, JH = 8.18 cm, GK = 10.73 cm and GI = 16 cm

(i)

{b,a}
(ii)

{a,c}
(iii)

{b,d,a}
(iv)

{d,c}
(v)

{b,c,a}

Question 11

11.

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)
2
3

of area of △GHI
(ii)
1
4

of area of △GHI
(iii)
1
2

of area of △GHI
(iv)
3
4

of area of △GHI
(v)
1
3

of area of △GHI

Question 12

12.

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

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

(i)
thrice

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
4
3

the area of the triangle
(iv)
5
4

the area of the triangle
(v)
twice

the area of the triangle

Question 13

13.

The perimeters of two similar triangles are 33 cm and 24 cm respectively. If one side of the first triangle is 11 cm, find the length of the corresponding side of the second triangle.

(i)

6.00 cm
(ii)

10.00 cm
(iii)

9.00 cm
(iv)

8.00 cm
(v)

7.00 cm

Question 14

14.

In the given figure, FGHI is a trapezium in which

(i)

△JIF
(ii)

△GHI
(iii)

△IFG
(iv)

△JGH
(v)

△JFG

Question 15

15.

In the given figure, △ABC is isosceles with AB = AC and BD ⟂ AC. Then

(i)
BD

2

+

AD

2

= 2

CD

.

AD
(ii)
BD

2

−

CD

2

= 2

CD

.

AD
(iii)
BD

2

−

AD

2

= 2

CD

.

AD
(iv)
BD

2

+

CD

2

= 2

CD

.

AD

Question 16

16.

In the given figure, △EGF is right-angled at G, GH ⟂ EF.

a)

b)

c)

a

2
+
b

2
=
c

2

d)

1

a

2
+
1

b

2
=
1

p

2

e)

ab
=
pc

(i)

{c,d,e}
(ii)

{a,b,e}
(iii)

{b,d}
(iv)

{a,c,d}
(v)

{a,c}

Question 17

17.

In the given figure, GHIJ is a trapezium in which

JK
=
(

x

+

54

)
cm, find the value of x

(i)

(

66

,

65

)
(ii)

(

67

,

67

)
(iii)

(

69

,

66

)
(iv)

(

68

,

68

)
(v)

(

66

,

66

)

Question 18

18.

In the given figure, △DEF & △PQR are similar triangles. If the ratio of the heights DG : PS = 10 : 14, then the ratio of their areas is

(i)

100

sq.cm

:

198

sq.cm
(ii)

100

sq.cm

:

196

sq.cm
(iii)

101

sq.cm

:

196

sq.cm
(iv)

99

sq.cm

:

196

sq.cm
(v)

100

sq.cm

:

193

sq.cm

Question 19

19.

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

(i)

1
2

4
√

2
(ii)

1
(iii)

1
2

√

2
(iv)

1
2

√

-1
(v)

1
2

√

4

Question 20

20.

Which of the following are true?

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

(i)

{a,b}
(ii)

{b,c,e}
(iii)

{d,c}
(iv)

{a,b,c}
(v)

{a,d,e}

Question 21

21.

In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 23 cm and AP = 9 cm. Find PB

(i)

14.00 cm
(ii)

13.00 cm
(iii)

12.00 cm
(iv)

16.00 cm
(v)

15.00 cm

Question 22

22.

In the given figure, given ∠KHI = ∠JHK, x : y = 7.74 cm : 8.26 cm and p = 15 cm, find q =

(i)

15.00 cm
(ii)

17.00 cm
(iii)

14.00 cm
(iv)

18.00 cm
(v)

16.00 cm

Question 23

23.

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)
a

2

sq.units
(ii)
1
2

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

√

3

a sq.units
(v)
√

3

a sq.units

Question 24

24.

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)

∠AFD
(ii)

∠HFE
(iii)

∠EHF
(iv)

∠CFA
(v)

∠BHA

Question 25

25.

In the given figure, O is a point in the interior of the rectangle CDEF. Then

(i)
OC

2

+

OE

2

=

OD

2

+

OF

2
(ii)
OC

2

−

OE

2

=

OD

2

−

OF

2
(iii)
OC

2

+

OD

2

+

OE

2

+

OF

2

=

CD

2

+

DE

2

+

EF

2

+

FC

2
(iv)
OC

2

+

OD

2

+

OE

2

+

OF

2

=

CE

2

+

DF

2

Assignment Key