EduSahara™ Worksheet

Question 1

1.

In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 105° , ∠GFD = 23°. Find ∠FDG

(i)

50°
(ii)

54°
(iii)

53°
(iv)

52°
(v)

51°

Question 2

2.

In the given figure, the altitudes QE and FR of △DEF meet at P. △PEF ∼

(i)

△QFP
(ii)

△REF
(iii)

△QFE
(iv)

△PRQ
(v)

△REP

Question 3

3.

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

=

BD

.

CD
(ii)
AB

2

−

AD

2

=

AD

.

CD
(iii)
AB

2

+

AD

2

=

BD

.

CD
(iv)
AB

2

−

AD

2

=

AD

.

BD
(v)
AB

2

+

AD

2

=

BC

2

Question 4

4.

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

(i)
OD

2

−

OF

2

=

OE

2

−

OG

2
(ii)
OD

2

+

OE

2

+

OF

2

+

OG

2

=

DE

2

+

EF

2

+

FG

2

+

GD

2
(iii)
OD

2

+

OF

2

=

OE

2

+

OG

2
(iv)
OD

2

+

OE

2

+

OF

2

+

OG

2

=

DF

2

+

EG

2

Question 5

5.

In the given figure, △JKL is isosceles right-angled at K and KM ⟂ LJ. ∠L =

(i)

∠N
(ii)

∠M
(iii)

∠J
(iv)

∠K
(v)

∠O

Question 6

6.

The ratio of the bases of two triangles ABC and DEF is
7

:

6
.

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

(i)

6

:

7
(ii)

6

:

6
(iii)

7

:

9
(iv)

8

:

6
(v)

7

:

4

Question 7

7.

In the given figure, △BCD , E is the mid-point of CD and BF ⟂ CD. Which of the following are true?

a)

b)

c)

d)

e)

(i)

{c,d,e}
(ii)

{a,c,d}
(iii)

{b,d}
(iv)

{a,c}
(v)

{a,b,e}

Question 8

8.

In the given figure, ∠EBC = ∠DBE and BE ∥ FD and BC = 18 cm, CE = 10 cm and ED = 10 cm. Find BF

(i)

16.00 cm
(ii)

20.00 cm
(iii)

19.00 cm
(iv)

17.00 cm
(v)

18.00 cm

Question 9

9.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

AAA Similarity
(iii)

SSS Similarity
(iv)

SAS Similarity

Question 10

10.

In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 27 cm. Find AP

(i)

11.80 cm
(ii)

12.80 cm
(iii)

10.80 cm
(iv)

8.80 cm
(v)

9.80 cm

Question 11

11.

In the given figure,
RS
∥
PQ
.

(i)

9.37 cm
(ii)

7.37 cm
(iii)

6.37 cm
(iv)

5.37 cm
(v)

8.37 cm

Question 12

12.

In the given two similar triangles, if k = 17 cm, l = 20 cm, m = 15 cm, n = 10.2 cm, find o

(i)

14.00 cm
(ii)

11.00 cm
(iii)

12.00 cm
(iv)

13.00 cm
(v)

10.00 cm

Question 13

13.

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

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 14

14.

In the given figure, the area of the △MNO is x sq.cm. P,Q,R are the mid-points of the sides NO , OM and MN respectively. The area of the △PQR is

(i)
1
3

of area of △MNO
(ii)
2
3

of area of △MNO
(iii)
1
2

of area of △MNO
(iv)
3
4

of area of △MNO
(v)
1
4

of area of △MNO

Question 15

15.

In the given figure, if EF ∥ GH then

(i)

△IEF ∼ △IGH
(ii)

△IFE ∼ △IHG
(iii)

△EFI ∼ △HGI
(iv)

△EFI ∼ △IGH
(v)

△EFI ∼ △IHG

Question 16

16.

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)
1
2

√

3

a sq.units
(ii)
√

3

a sq.units
(iii)
1
2

a sq.units
(iv)
2a sq.units
(v)
a

2

sq.units

Question 17

17.

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

a)

a

2
+
b

2
=
c

2

b)

ab
=
pc

c)

d)

1

a

2
+
1

b

2
=
1

p

2

e)

(i)

{c,e,d}
(ii)

{e,b}
(iii)

{c,a}
(iv)

{c,a,b}
(v)

{a,b,d}

Question 18

18.

In the given figure, △IJK and △RST are such that

Identify the property by which the two triangles are similar

(i)

SSS Similarity
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

not similar

Question 19

19.

Which of the following are true?

a)	Similarity is reflexive.
b)	Similarity is anti symmetric.
c)	Similarity is transitive.
d)	Similarity is symmetric.

(i)

{b,d}
(ii)

{b,c}
(iii)

{b,a,c}
(iv)

{a,c,d}
(v)

{b,a}

Question 20

20.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

not similar
(iii)

SAS Similarity
(iv)

AAA Similarity

Question 21

21.

In the given figure, in △FGH, 'O' is a point inside the triangle. OI ⟂ GH, OJ ⟂ FH and OK ⟂ FG. Then

(i)
FK

2

+

GI

2

+

HJ

2

=

OF

2

+

OG

2

+

OH

2

+

OI

2

+

OJ

2

+

OK

2
(ii)
FK

2

+

GI

2

+

HJ

2

=

OF

2

+

OG

2

+

OH

2

−

OI

2

−

OJ

2

−

OK

2
(iii)
FK

2

+

GI

2

+

HJ

2

=

FG

2

+

IH

2

+

HF

2

−

GK

2

−

HI

2

−

JF

2
(iv)
FK

2

+

GI

2

+

HJ

2

=

OK

2

+

OJ

2

+

OI

2

Question 22

22.

In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If BC = 16 cm, CD = 20 cm, then find CE.

(i)

14.49 cm
(ii)

13.49 cm
(iii)

12.49 cm
(iv)

11.49 cm
(v)

10.49 cm

Question 23

23.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 24

24.

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

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

(i)

{a,c}
(ii)

{b,d}
(iii)

{a,b,c}
(iv)

{a,d,c}
(v)

{c,d}

Question 25

25.

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)

b)

All four small triangles have equal areas

c)

Area of △EFG = 4 times area of △HIJ

d)

Area of trapezium FGIJ is thrice the area of △EJI

e)

(i)

{b,c,d}
(ii)

{a,e,d}
(iii)

{e,c}
(iv)

{a,b}
(v)

{a,b,c}

Assignment Key