EduSahara™ Worksheet

Question 1

1.

In the given figure, △DFE is right-angled at F, FG ⟂ DE.

a)

b)

ab
=
pc

c)

1

a

2
+
1

b

2
=
1

p

2

d)

e)

a

2
+
b

2
=
c

2

(i)

{a,b}
(ii)

{a,b,c}
(iii)

{a,d,e}
(iv)

{b,c,e}
(v)

{d,c}

Question 2

2.

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

=

OK

.

OI

+

OI

.

OJ

+

OJ

.

OK
(ii)
FK

2

+

GI

2

+

HJ

2

=

FJ

2

+

HI

2

+

GK

2
(iii)
FK

2

+

GI

2

+

HJ

2

=

OF

.

OG

+

OG

.

OH

+

OH

.

OF
(iv)
FK

2

+

GI

2

+

HJ

2

=

OI

2

+

OJ

2

+

OK

2

Question 3

3.

The ratio of the bases of two triangles ABC and DEF is
9

:

4
.

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

(i)

8

:

4
(ii)

10

:

4
(iii)

9

:

6
(iv)

9

:

2
(v)

4

:

9

Question 4

4.

In the given figure, in △EFG, 'O' is a point inside the triangle. OH ⟂ FG, OI ⟂ EG and OJ ⟂ EF. Then

(i)
EJ

2

+

FH

2

+

GI

2

=

OJ

2

+

OI

2

+

OH

2
(ii)
EJ

2

+

FH

2

+

GI

2

=

OE

2

+

OF

2

+

OG

2

−

OH

2

−

OI

2

−

OJ

2
(iii)
EJ

2

+

FH

2

+

GI

2

=

OE

2

+

OF

2

+

OG

2

+

OH

2

+

OI

2

+

OJ

2
(iv)
EJ

2

+

FH

2

+

GI

2

=

EF

2

+

HG

2

+

GE

2

−

FJ

2

−

GH

2

−

IE

2

Question 5

5.

In the given figure, RS ∥ CD and BR = 14.4 cm, RS = 12.6 cm and CD = 21 cm, find BC

(i)

25.0 cm
(ii)

22.0 cm
(iii)

26.0 cm
(iv)

23.0 cm
(v)

24.0 cm

Question 6

6.

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)

13.32 cm
(ii)

14.32 cm
(iii)

12.32 cm
(iv)

10.32 cm
(v)

11.32 cm

Question 7

7.

GHIJ is a cyclic trapezium. Diagonals HJ and GI intersect at K. If JG = 17 cm, find HI

(i)

18 cm
(ii)

16 cm
(iii)

19 cm
(iv)

17 cm
(v)

15 cm

Question 8

8.

Identify the property by which the two given triangles are similar

(i)

SAS Similarity
(ii)

AAA Similarity
(iii)

SSS Similarity
(iv)

not similar

Question 9

9.

The foot of a ladder resting on a wall from the foot of the wall is 14 m. If the height of the top of the ladder from ground is 15 m, find the length of the ladder

(i)

20.52 m
(ii)

18.52 m
(iii)

22.52 m
(iv)

19.52 m
(v)

21.52 m

Question 10

10.

In the given figure, △GHI is a triangle in which GH = GI and J is a point on HI. Then

(i)
GH

2

+

GJ

2

=

HJ

.

IJ
(ii)
GH

2

+

GJ

2

=

HI

2
(iii)
GH

2

−

GJ

2

=

GJ

.

IJ
(iv)
GH

2

−

GJ

2

=

HJ

.

IJ
(v)
GH

2

−

GJ

2

=

GJ

.

HJ

Question 11

11.

Which of the following are true?

a)	Area of the union of two polygonal region is not equal to the sum of the individual area.
b)	Area of a convex polygonal region is equal to the sum of the areas of all triangles formed by joining the vertices of the polygon with an interior point.
c)	A polygonal region can be divided into a finite number of triangles in a unique way.
d)	Area of the union of two polygonal region is the sum of the individual area.

(i)

{c,a}
(ii)

{d,b}
(iii)

{a,b}
(iv)

{c,b,a}
(v)

{c,d,a}

Question 12

12.

In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 22 cm. Find AP

(i)

7.80 cm
(ii)

8.80 cm
(iii)

10.80 cm
(iv)

9.80 cm
(v)

6.80 cm

Question 13

13.

In the given figure, △CDE ∼ △MNO and CD = 13 cm, MN = 18.2 cm.

(i)

125.98 sq.cm
(ii)

126.98 sq.cm
(iii)

124.98 sq.cm
(iv)

128.98 sq.cm
(v)

127.98 sq.cm

Question 14

14.

Which of the following are measures of a right angled triangle ?

(i)

OP = 12 cm , PQ = 13 cm , QO = 11 cm
(ii)

OP = 12 cm , PQ = 10 cm , QO = 15.62 cm
(iii)

OP = 12 cm , PQ = 19 cm , QO = 10 cm
(iv)

OP = 12 cm , PQ = 11 cm , QO = 13 cm
(v)

OP = 14 cm , PQ = 14 cm , QO = 14 cm

Question 15

15.

In the given figure, the altitudes TD and EU of △CDE meet at S. ∠ETS =

(i)

∠SET
(ii)

∠TSE
(iii)

∠SUD
(iv)

∠DSU
(v)

∠UDS

Question 16

16.

Which of the following are true?

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

(i)

{a,e,b}
(ii)

{d,f,b}
(iii)

{a,b}
(iv)

{c,e}
(v)

{b,e}

Question 17

17.

In the given figure, ST ∥ CD , and median BE bisects ST.

If BD = 19 cm, BF = 11.27 cm and BT = 12.67 cm, BE =

(i)

14.90 cm
(ii)

17.90 cm
(iii)

16.90 cm
(iv)

18.90 cm
(v)

15.90 cm

Question 18

18.

In the given figure
△KLM
,

(i)

KL

2
(ii)

LM

2
(iii)

LM
(iv)

KN
(v)

MK

2

Question 19

19.

In the given figure, △ABC is a triangle with AD being the median of BC. Then

(i)
AB

2

+

AC

2

=

2

BD

2

+

2

DC

2
(ii)
AB

2

+

AC

2

=

BC

2
(iii)
AB

2

+

AC

2

=

2

DC

2

+

2

AD

2
(iv)
AB

2

+

AC

2

=

AD

2
(v)
AB

2

+

AC

2

=

2

BD

2

+

2

AD

2

Question 20

20.

In the given figure, points K , L and M are the mid-points of sides IJ, JH and HI of △HIJ. Which of the following are true?

a)	△KLM ∼ △HIJ
b)	△LKJ ∼ △HIJ
c)	△KML ∼ △HIJ
d)	△MIK ∼ △HIJ
e)	△HML ∼ △HIJ

(i)

{c,d}
(ii)

{c,e,a}
(iii)

{a,b,d,e}
(iv)

{c,b}
(v)

{c,a}

Question 21

21.

In the given figure, M and N are points on the sides JK and JL respectively of △JKL.For which of the following cases, MN ∥ KL

a)	JK = 16 cm, MK = 8 cm, JL = 19 cm and JN = 9.5 cm
b)	JK = 16 cm, MK = 8 cm, JN = 11.5 cm and JL = 19 cm
c)	JM = 8 cm, MK = 8 cm, JN = 9.5 cm and NL = 9.5 cm
d)	JK = 16 cm, JM = 10 cm, JL = 19 cm and NL = 9.5 cm

(i)

{b,a}
(ii)

{a,c}
(iii)

{b,d,a}
(iv)

{d,c}
(v)

{b,c,a}

Question 22

22.

The perimeters of two similar triangles are 27 cm and 22 cm respectively. If one side of the first triangle is 13 cm, find the length of the corresponding side of the second triangle.

(i)

11.59 cm
(ii)

9.59 cm
(iii)

12.59 cm
(iv)

8.59 cm
(v)

10.59 cm

Question 23

23.

In the given figure, DEFG is a trapezium where OE = 13 cm , OF = 4 cm and OG = 4 cm . Find OD =

(i)

11 cm
(ii)

12 cm
(iii)

13 cm
(iv)

15 cm
(v)

14 cm

Question 24

24.

MNOP is a square and △MNQ is an equilateral triangle. Also, △MOR is an equilateral triangle. If area of △MNQ is 'a' sq.units, then the area of △MOR is

(i)
2a sq.units
(ii)
1
2

√

3

a sq.units
(iii)
√

3

a sq.units
(iv)
1
2

a sq.units
(v)
a

2

sq.units

Question 25

25.

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

(i)

∠LMN
(ii)

∠OLM
(iii)

∠OMN
(iv)

∠LMO
(v)

∠MNO

Assignment Key