EduSahara™ Worksheet

Question 1

1.

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)	GH = 17 cm, JH = 6.8 cm, GI = 16 cm and GK = 9.6 cm
b)	GH = 17 cm, GJ = 12.2 cm, GI = 16 cm and KI = 6.4 cm
c)	GH = 17 cm, JH = 6.8 cm, GK = 11.6 cm and GI = 16 cm
d)	GJ = 10.2 cm, JH = 6.8 cm, GK = 9.6 cm and KI = 6.4 cm

(i)

{b,c,a}
(ii)

{b,d,a}
(iii)

{c,d}
(iv)

{a,d}
(v)

{b,a}

Question 2

2.

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)

{d,b}
(ii)

{c,d,a}
(iii)

{c,b,a}
(iv)

{c,a}
(v)

{a,b}

Question 3

3.

In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠P =

(i)

∠R
(ii)

∠T
(iii)

∠U
(iv)

∠S
(v)

∠Q

Question 4

4.

In the given figure,
LM
∥
JK
.

(i)

7.65 cm
(ii)

6.65 cm
(iii)

9.65 cm
(iv)

5.65 cm
(v)

8.65 cm

Question 5

5.

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)

∠AFD
(ii)

∠CFA
(iii)

∠DAF
(iv)

∠HFE
(v)

∠BHA

Question 6

6.

In the given figure, △FGH is a triangle in which FG = FH and I is a point on GH. Then

(i)
FG

2

−

FI

2

=

FI

.

GI
(ii)
FG

2

+

FI

2

=

GH

2
(iii)
FG

2

−

FI

2

=

FI

.

HI
(iv)
FG

2

−

FI

2

=

GI

.

HI
(v)
FG

2

+

FI

2

=

GI

.

HI

Question 7

7.

If the ratio of the bases of two triangles is E : F and the ratio of the corresponding heights is G : H , the ratio of their areas in the same order is

(i)

EF : GH
(ii)

GH : EF
(iii)

EG : FH
(iv)

FG : EH
(v)

EH : FG

Question 8

8.

Which of the following are true?

a)	Any two circles are similar.
b)	Any two circles are congruent.
c)	Any two squares are congruent.
d)	Any two squares are similar.
e)	Any two triangles are similar.
f)	Any two triangles are congruent.

(i)

{b,a}
(ii)

{c,d}
(iii)

{e,f,a}
(iv)

{b,d,a}
(v)

{a,d}

Question 9

9.

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

(i)

EH . FI . GJ = EF . FG . GE
(ii)

EH . FI . GJ = OE . OF . OG
(iii)

EH . FI . GJ = HI . IJ . JH
(iv)

EH . FI . GJ = HF . IG . JE
(v)

EH . FI . GJ = OH . OI . OJ

Question 10

10.

In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. Which of the following are true?

a)

DE

2
=
FD
.
FG

b)

DE

2
=
DF
.
DG

c)

EG

2
=
DG
.
GF

d)

EF

2
=
FD
.
FG

e)

EF

2
=
DF
.
DG

(i)

{a,b,c}
(ii)

{b,c,d}
(iii)

{e,c}
(iv)

{a,b}
(v)

{a,e,d}

Question 11

11.

In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 26 cm. Find AP

(i)

11.40 cm
(ii)

8.40 cm
(iii)

10.40 cm
(iv)

12.40 cm
(v)

9.40 cm

Question 12

12.

In the given figure, DF is the angular bisector of
∠D
&
∠F

(i)

18.00 cm
(ii)

19.00 cm
(iii)

20.00 cm
(iv)

22.00 cm
(v)

21.00 cm

Question 13

13.

In the given figure, △DEF , G is the mid-point of EF and DH ⟂ EF. Which of the following are true?

a)

b)

c)

d)

e)

(i)

{b,c,e}
(ii)

{b,a,d}
(iii)

{c,d}
(iv)

{b,a}
(v)

{a,d,e}

Question 14

14.

Identify the property by which the two given triangles are similar

(i)

SSS Similarity
(ii)

AAA Similarity
(iii)

not similar
(iv)

SAS Similarity

Question 15

15.

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

(i)

∠FDE
(ii)

∠EGD
(iii)

∠DEG
(iv)

∠EFG
(v)

∠GDE

Question 16

16.

In the given figure, △EFG is a triangle with EH being the median of FG. Then

(i)
EF

2

+

EG

2

=

2

HG

2

+

2

EH

2
(ii)
EF

2

+

EG

2

=

EH

2
(iii)
EF

2

+

EG

2

=

FG

2
(iv)
EF

2

+

EG

2

=

2

FH

2

+

2

EH

2
(v)
EF

2

+

EG

2

=

2

FH

2

+

2

HG

2

Question 17

17.

In the given figure, △CDE is an acute angled triangle and CF ⟂ DE. Then

(i)
CE

2

=

CD

2

+

DE

2

−

2

CD

.

DE
(ii)
CE

2

=

CD

2

+

DE

2

+

2

DE

.

DF
(iii)
CE

2

=

CD

2

+

DE

2

−

CF

2
(iv)
CE

2

=

CD

2

+

DE

2

−

2

DE

.

DF
(v)
CE

2

=

CD

2

+

DE

2

+

2

CD

.

DE

Question 18

18.

In the given figure, given ∠EBC = ∠DBE, x : y = 10.53 cm : 9.47 cm and q = 18 cm, find p =

(i)

20.00 cm
(ii)

18.00 cm
(iii)

21.00 cm
(iv)

22.00 cm
(v)

19.00 cm

Question 19

19.

Which of the following are true?

a)	Any two triangles are similar if the corresponding angles are equal.
b)	Any two triangles are similar if the corresponding sides are proportional.
c)	Any two quadrilaterals are similar if the corresponding angles are equal.
d)	Any two quadrilaterals are similar if the corresponding sides are proportional.

(i)

{c,a,b}
(ii)

{a,b,d}
(iii)

{c,b}
(iv)

{c,a}
(v)

{c,d}

Question 20

20.

In the given figure, the altitudes QH and IR of △GHI meet at P. △QIH ∼

(i)

△RHP
(ii)

△PHI
(iii)

△RHI
(iv)

△QIP
(v)

△PRQ

Question 21

21.

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

(i)
OA

2

+

OB

2

+

OC

2

+

OD

2

=

AB

2

+

BC

2

+

CD

2

+

DA

2
(ii)
OA

2

+

OC

2

=

OB

2

+

OD

2
(iii)
OA

2

+

OB

2

+

OC

2

+

OD

2

=

AC

2

+

BD

2
(iv)
OA

2

−

OC

2

=

OB

2

−

OD

2

Question 22

22.

In the given figure, ∠JGH = 50.5°, find the value of x =

(i)

38.50°
(ii)

39.50°
(iii)

37.50°
(iv)

40.50°
(v)

41.50°

Question 23

23.

The perimeters of two similar triangles are 34 cm and 22 cm respectively. If one side of the first triangle is 11 cm, find the length of the corresponding side of the second triangle.

(i)

8.12 cm
(ii)

5.12 cm
(iii)

6.12 cm
(iv)

7.12 cm
(v)

9.12 cm

Question 24

24.

In the given figure, PQ ∥ CD , and median BE bisects PQ.
△BPF ∼

(i)

△BFQ
(ii)

△BCD
(iii)

△BCE
(iv)

△CDB
(v)

△BED

Question 25

25.

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

:

3
.

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

(i)

7

:

3
(ii)

8

:

1
(iii)

3

:

8
(iv)

9

:

3
(v)

8

:

6

Assignment Key