EduSahara™ Worksheet

Question 1

1.

In the given figure, △LMN is isosceles right-angled at M and MO ⟂ NL. ∠N =

(i)

∠Q
(ii)

∠P
(iii)

∠M
(iv)

∠L
(v)

∠O

Question 2

2.

In the given figure, PQ ∥ CD and BP = 12 cm, BC = 20 cm and CD = 23 cm, find PQ

(i)

15.8 cm
(ii)

13.8 cm
(iii)

12.8 cm
(iv)

11.8 cm
(v)

14.8 cm

Question 3

3.

The ratio of the bases of two triangles ABC and DEF is
8

:

7
.

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

(i)

7

:

8
(ii)

8

:

5
(iii)

9

:

7
(iv)

8

:

10
(v)

7

:

7

Question 4

4.

A vehicle goes 12 km South and then 13 km West. How far is it from its starting point ?

(i)

17.69 km
(ii)

19.69 km
(iii)

16.69 km
(iv)

18.69 km
(v)

15.69 km

Question 5

5.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

AAA Similarity

Question 6

6.

In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 105° , ∠GFD = 26°. Find ∠FDG

(i)

47°
(ii)

51°
(iii)

49°
(iv)

50°
(v)

48°

Question 7

7.

In the given figure, EFGH is a rhombus. Which of the following are true?

a)

b)

FG

2
+
GH

2
=
FH

2

c)

d)

EF

2
+
FG

2
=
EG

2

e)

(i)

{b,a}
(ii)

{d,c}
(iii)

{a,c}
(iv)

{d,c,a}
(v)

{e,b,a}

Question 8

8.

The altitude and area of an equilateral triangle of side 'a' is

(i)
1
2

√

3

a,

1
4

√

3

a

2
(ii)
√

3

a,

1
2

√

3

a
(iii)
1
2

√

3

a,

1
2

√

3

a

2
(iv)
√

3

a,

1
2

√

3

a

2

Question 9

9.

In the given figure, ∠DAB = 36.87°, find the value of x =

(i)

55.13°
(ii)

53.13°
(iii)

52.13°
(iv)

51.13°
(v)

54.13°

Question 10

10.

In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If GJ = 15.6 cm, HJ = 12.49 cm, then find JI.

(i)

12.00 cm
(ii)

10.00 cm
(iii)

9.00 cm
(iv)

8.00 cm
(v)

11.00 cm

Question 11

11.

In the given figure, △DEF is isosceles with DE = DF and EG ⟂ DF. Then

(i)
EG

2

+

DG

2

= 2

FG

.

DG
(ii)
EG

2

+

FG

2

= 2

FG

.

DG
(iii)
EG

2

−

DG

2

= 2

FG

.

DG
(iv)
EG

2

−

FG

2

= 2

FG

.

DG

Question 12

12.

A vertical stick
12 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)

94 m
(ii)

97 m
(iii)

95 m
(iv)

96 m
(v)

98 m

Question 13

13.

In the given figure,
LM
∥
JK
.

(i)

7.00 cm
(ii)

6.00 cm
(iii)

9.00 cm
(iv)

5.00 cm
(v)

8.00 cm

Question 14

14.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. If FG = 16 cm, FH = 11.96 cm, then find EF.

(i)

16.00 cm
(ii)

17.00 cm
(iii)

20.00 cm
(iv)

18.00 cm
(v)

19.00 cm

Question 15

15.

In the given figure, ∠NKL = ∠MKN and KN ∥ OM and KL = 15 cm, LN = 8 cm and NM = 10 cm. Find KO

(i)

19.75 cm
(ii)

16.75 cm
(iii)

20.75 cm
(iv)

18.75 cm
(v)

17.75 cm

Question 16

16.

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

If GH = 18 cm, GJ = 18 cm and GS = 7.71 cm, KJ =

(i)

9.29 cm
(ii)

12.29 cm
(iii)

11.29 cm
(iv)

8.29 cm
(v)

10.29 cm

Question 17

17.

In the given figure, △CDE and △PQR are such that

Identify the property by which the two triangles are similar

(i)

AAA Similarity
(ii)

SSS Similarity
(iii)

not similar
(iv)

SAS Similarity

Question 18

18.

In the given figure, ABC is a triangle and 'O' is a point inside △ABC. The angular bisector of ∠BOA, ∠COB & ∠AOC meet AB, BC & CA at D, E & F respectively . Then

(i)

AD . BE . CF = DB . EC . FA
(ii)

AD . BE . CF = AB . BC . CA
(iii)

AD . BE . CF = OD . OE . OF
(iv)

AD . BE . CF = OA . OB . OC
(v)

AD . BE . CF = DE . EF . FD

Question 19

19.

ABCD is a square and △ABE is an equilateral triangle. Also, △ACF is an equilateral triangle. If area of △ABE is 'a' sq.units, then the area of △ACF is

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

2

sq.units
(iii)
1
2

√

3

a sq.units
(iv)
1
2

a sq.units
(v)
√

3

a sq.units

Question 20

20.

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

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

(i)
3
2

the area of the triangle
(ii)
5
4

the area of the triangle
(iii)
twice

the area of the triangle
(iv)
thrice

the area of the triangle
(v)
4
3

the area of the triangle

Question 21

21.

In the given figure, △ABC is a triangle in which AB = AC and D is a point on BC. Then

(i)
AB

2

+

AD

2

=

BC

2
(ii)
AB

2

−

AD

2

=

AD

.

BD
(iii)
AB

2

−

AD

2

=

AD

.

CD
(iv)
AB

2

+

AD

2

=

BD

.

CD
(v)
AB

2

−

AD

2

=

BD

.

CD

Question 22

22.

Two poles of heights 9 m and 14 m stand vertically on a plane ground. If the distance between their feet is 15 m, find the distance between their tops

(i)

17.81 m
(ii)

16.81 m
(iii)

14.81 m
(iv)

15.81 m
(v)

13.81 m

Question 23

23.

Which of the following are measures of an isosceles right angled triangle ?

(i)

KL = 12 cm , LM = 12 cm , MK = 12 cm
(ii)

KL = 10 cm , LM = 20 cm , MK = 13 cm
(iii)

KL = 11 cm , LM = 13 cm , MK = 10 cm
(iv)

KL = 14 cm , LM = 13 cm , MK = 10 cm
(v)

KL = 13 cm , LM = 13 cm , MK = 18.38 cm

Question 24

24.

In the given figure, the altitudes TE and FU of △DEF meet at S. △UES ∼

(i)

△SEF
(ii)

△SUT
(iii)

△TFS
(iv)

△TFE
(v)

△UEF

Question 25

25.

In the given figure, CDEF is a trapezium where OC = 15 cm , OD = 15 cm and OE = 5 cm . Find OF =

(i)

3 cm
(ii)

5 cm
(iii)

6 cm
(iv)

4 cm
(v)

7 cm

Assignment Key