EduSahara™ Worksheet

Question 1

1.

ABCD is a cyclic trapezium. Diagonals BD and AC intersect at E. If DA = 16 cm, find BC

(i)

14 cm
(ii)

15 cm
(iii)

16 cm
(iv)

18 cm
(v)

17 cm

Question 2

2.

In the given figure, PQ ∥ GH , and median FI bisects PQ.

If FG = 15 cm, FI = 15 cm and FP = 6.67 cm, JI =

(i)

9.33 cm
(ii)

8.33 cm
(iii)

10.33 cm
(iv)

7.33 cm
(v)

6.33 cm

Question 3

3.

a)

b)

c)

d)

e)

(i)

{c,d}
(ii)

{a,c,e}
(iii)

{a,b,d}
(iv)

{b,d,e}
(v)

{a,b}

Question 4

4.

In the given figure, △DEF is a triangle with DG being the median of EF. Then

(i)
DE

2

+

DF

2

=

2

EG

2

+

2

DG

2
(ii)
DE

2

+

DF

2

=

2

EG

2

+

2

GF

2
(iii)
DE

2

+

DF

2

=

DG

2
(iv)
DE

2

+

DF

2

=

EF

2
(v)
DE

2

+

DF

2

=

2

GF

2

+

2

DG

2

Question 5

5.

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

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

(i)

{d,b}
(ii)

{a,b}
(iii)

{c,b,a}
(iv)

{c,a}
(v)

{c,d,a}

Question 6

6.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

not similar
(iii)

SSS Similarity
(iv)

AAA Similarity

Question 7

7.

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

Identify the property by which the two triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

SAS Similarity
(iv)

AAA Similarity

Question 8

8.

Which of the following are true?

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

(i)

{d,a,b}
(ii)

{d,e,c}
(iii)

{d,a}
(iv)

{e,b}
(v)

{a,b,c}

Question 9

9.

Two poles of heights 7 m and 14 m stand vertically on a plane ground. If the distance between their feet is 10 m, find the distance between their tops

(i)

10.21 m
(ii)

13.21 m
(iii)

14.21 m
(iv)

11.21 m
(v)

12.21 m

Question 10

10.

(i)

7.95 cm
(ii)

6.95 cm
(iii)

4.95 cm
(iv)

3.95 cm
(v)

5.95 cm

Question 11

11.

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

(i)

∠LJK
(ii)

∠MJK
(iii)

∠MKL
(iv)

∠KLM
(v)

∠JKL

Question 12

12.

In the given figure, points M , N and O are the mid-points of sides KL, LJ and JK of △JKL. Which of the following are true?

a)

Area of △JKL = 4 times area of △MNO

b)

c)

d)

Area of trapezium KLNO is thrice the area of △JON

e)

All four small triangles have equal areas

(i)

{b,a}
(ii)

{c,d}
(iii)

{b,a,d}
(iv)

{b,c,e}
(v)

{a,d,e}

Question 13

13.

In the given figure, △BCD is isosceles with BC = BD and CE ⟂ BD. Then

(i)
CE

2

+

BE

2

= 2

DE

.

BE
(ii)
CE

2

−

DE

2

= 2

DE

.

BE
(iii)
CE

2

−

BE

2

= 2

DE

.

BE
(iv)
CE

2

+

DE

2

= 2

DE

.

BE

Question 14

14.

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

(i)

∠P
(ii)

∠T
(iii)

∠Q
(iv)

∠U
(v)

∠R

Question 15

15.

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

a)

b)

c)

CD

2
+
DE

2
=
CE

2

d)

DE

2
+
EF

2
=
DF

2

e)

(i)

{c,e,b}
(ii)

{b,e}
(iii)

{d,a,b}
(iv)

{a,b}
(v)

{c,e}

Question 16

16.

In the given figure, △CDE is an obtuse 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

−

2

DE

.

DF
(iv)
CE

2

=

CD

2

+

DE

2

+

2

DF

.

EF
(v)
CE

2

=

CD

2

+

DE

2

+

DF

2

Question 17

17.

In the given figure, △CDE, CF ⟂ DE. Which of the following are true?

a)

b)

c)

d)

e)

(i)

{c,d,b}
(ii)

{e,a,b}
(iii)

{c,d}
(iv)

{b,d}
(v)

{a,b}

Question 18

18.

The foot of a ladder resting on a wall from the foot of the wall is 10 m. If the height of the top of the ladder from ground is 13 m, find the length of the ladder

(i)

18.40 m
(ii)

15.40 m
(iii)

16.40 m
(iv)

17.40 m
(v)

14.40 m

Question 19

19.

In the given figure, △HIJ is a triangle in which HI = HJ and K is a point on IJ. Then

(i)
HI

2

+

HK

2

=

IJ

2
(ii)
HI

2

−

HK

2

=

HK

.

JK
(iii)
HI

2

+

HK

2

=

IK

.

JK
(iv)
HI

2

−

HK

2

=

HK

.

IK
(v)
HI

2

−

HK

2

=

IK

.

JK

Question 20

20.

The ratio of the bases of two triangles ABC and DEF is
10

:

4
.

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

(i)

4

:

10
(ii)

11

:

4
(iii)

10

:

7
(iv)

10

:

1
(v)

9

:

4

Question 21

21.

In the given figure, given ∠EBC = ∠DBE, x : y = 8.44 cm : 9.56 cm and q = 17 cm, find p =

(i)

14.00 cm
(ii)

13.00 cm
(iii)

17.00 cm
(iv)

15.00 cm
(v)

16.00 cm

Question 22

22.

In the given figure, TU ∥ BC and AT = 15 cm, TU = 13.8 cm and BC = 23 cm, find AB

(i)

25.0 cm
(ii)

23.0 cm
(iii)

24.0 cm
(iv)

26.0 cm
(v)

27.0 cm

Question 23

23.

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

a)

b)

ab
=
pc

c)

d)

1

a

2
+
1

b

2
=
1

p

2

e)

a

2
+
b

2
=
c

2

(i)

{c,d}
(ii)

{b,d,e}
(iii)

{a,b}
(iv)

{a,c,e}
(v)

{a,b,d}

Question 24

24.

If the measures are as shown in the given figure, find EF

(i)

24.0 cm
(ii)

27.0 cm
(iii)

25.0 cm
(iv)

26.0 cm
(v)

23.0 cm

Question 25

25.

In the given figure, the two circles touch each other internally.

Diameter
OB
passes through the centre of the smaller circle.

Find the radius of the outer circle.

(i)

13.03 cm
(ii)

15.03 cm
(iii)

16.03 cm
(iv)

14.03 cm
(v)

12.03 cm

Assignment Key