EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Similar Triangles
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The perimeters of two similar triangles are 25 cm and 17 cm respectively. If one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.
(i)
10.16 cm
(ii)
9.16 cm
(iii)
7.16 cm
(iv)
6.16 cm
(v)
8.16 cm
Question
2
2.
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 sides are proportional.
d)
Any two quadrilaterals are similar if the corresponding angles are equal.
(i)
{d,b}
(ii)
{d,c}
(iii)
{d,a,b}
(iv)
{a,b,c}
(v)
{d,a}
Question
3
3.
In the given figure, DEFG is a rhombus. Which of the following are true?
a)
2
DE
2
=
DF
2
+
EG
2
b)
DE
2
+
EF
2
+
FG
2
+
DG
2
=
DF
2
+
EG
2
c)
4
DE
2
=
DF
2
+
EG
2
d)
EF
2
+
FG
2
=
EG
2
e)
DE
2
+
EF
2
=
DF
2
(i)
{d,c}
(ii)
{e,a,b}
(iii)
{a,b}
(iv)
{d,c,b}
(v)
{b,c}
Question
4
4.
In the given figure, D and E are points on the sides AB and AC respectively of △ABC.For which of the following cases, DE ∥ BC
a)
AD = 10.91 cm, DB = 9.09 cm, AE = 10.36 cm and EC = 8.64 cm
b)
AB = 20 cm, DB = 9.09 cm, AC = 19 cm and AE = 10.36 cm
c)
AB = 20 cm, AD = 12.91 cm, AC = 19 cm and EC = 8.64 cm
d)
AB = 20 cm, DB = 9.09 cm, AE = 12.36 cm and AC = 19 cm
(i)
{c,b,a}
(ii)
{a,b}
(iii)
{d,b}
(iv)
{c,a}
(v)
{c,d,a}
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, △FGH is isosceles right-angled at G and GI ⟂ HF. ∠FGH =
(i)
∠IGH
(ii)
∠IFG
(iii)
∠HIG
(iv)
∠FGI
(v)
∠GHI
Question
7
7.
In the given figure, PQ ∥ DE , and median CF bisects PQ.
If CF = 15.2 cm, CE = 15 cm and CG = 8.44 cm, GF =
(i)
8.76 cm
(ii)
4.76 cm
(iii)
5.76 cm
(iv)
6.76 cm
(v)
7.76 cm
Question
8
8.
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 circles are congruent.
f)
Any two squares are similar.
(i)
{d,e,b}
(ii)
{a,f,b}
(iii)
{b,f}
(iv)
{c,f}
(v)
{a,b}
Question
9
9.
In the given figure, △ABC is an obtuse angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(ii)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(iii)
AC
2
=
AB
2
+
BC
2
+
BD
2
(iv)
AC
2
=
AB
2
+
BC
2
+
2
BD
.
CD
(v)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
Question
10
10.
EFGH is a cyclic trapezium. Diagonals FH and EG intersect at I. If HE = 17 cm, find FG
(i)
18 cm
(ii)
16 cm
(iii)
19 cm
(iv)
17 cm
(v)
15 cm
Question
11
11.
In the given two similar triangles, if c = 20 cm, d = 18 cm, e = 19 cm, f = 12 cm, find g
(i)
8.80 cm
(ii)
9.80 cm
(iii)
11.80 cm
(iv)
12.80 cm
(v)
10.80 cm
Question
12
12.
In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. Which of the following are true?
a)
FH
2
=
EH
.
HG
b)
FG
2
=
GE
.
GH
c)
EF
2
=
GE
.
GH
d)
FG
2
=
EG
.
EH
e)
EF
2
=
EG
.
EH
(i)
{a,b,e}
(ii)
{c,a,b}
(iii)
{d,b}
(iv)
{c,d,e}
(v)
{c,a}
Question
13
13.
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
=
BD
.
CD
(iii)
AB
2
−
AD
2
=
AD
.
CD
(iv)
AB
2
+
AD
2
=
BC
2
(v)
AB
2
−
AD
2
=
AD
.
BD
Question
14
14.
A ladder reaches a window which is 10 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 15 m high. Find the width of the street if the length of the ladder is 19 m
(i)
28.82 m
(ii)
29.82 m
(iii)
25.82 m
(iv)
26.82 m
(v)
27.82 m
Question
15
15.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 21 cm and AP = 8 cm. Find PB
(i)
13.00 cm
(ii)
15.00 cm
(iii)
14.00 cm
(iv)
11.00 cm
(v)
12.00 cm
Question
16
16.
If the ratio of the bases of two triangles is I : J and the ratio of the corresponding heights is K : L , the ratio of their areas in the same order is
(i)
KL : IJ
(ii)
IJ : KL
(iii)
IL : JK
(iv)
JK : IL
(v)
IK : JL
Question
17
17.
In the given figure, △GHI, PQ ∥ HI such that
area of
△GPQ
= area of
PQIH
. Find
GP
GH
(i)
1
2
√
-1
(ii)
1
2
√
4
(iii)
1
2
√
2
(iv)
1
(v)
1
2
4
√
2
Question
18
18.
In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 102° , ∠GFD = 25°. Find ∠FDG
(i)
53°
(ii)
51°
(iii)
55°
(iv)
54°
(v)
52°
Question
19
19.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
3 AD
2
=
7 AB
2
(ii)
7 AD
2
=
9 AB
2
(iii)
9 AD
2
=
7 AB
2
(iv)
7 AD
2
=
3 AB
2
Question
20
20.
In the given figure, △JKL is a triangle in which JM is the internal bisector of ∠J and LN ∥ MJ meeting KJ produced at N . ∠JLN =
(i)
∠LNJ
(ii)
∠NJL
(iii)
∠KMJ
(iv)
∠MLJ
(v)
∠JML
Question
21
21.
In the given figure, MO is the angular bisector of
∠M
&
∠O
LM
=
20 cm
,
MN
=
20 cm
and
NO
=
17 cm
.
Find
OL
(i)
17.00 cm
(ii)
18.00 cm
(iii)
19.00 cm
(iv)
15.00 cm
(v)
16.00 cm
Question
22
22.
In the given figure, FGHI is a trapezium in which
FG ∥ HI
and the diagonals
GI
and
FH
intersect at
J
.
If
JF
=
(
22
x
+
2
)
cm,
GJ
=
(
23
x
+
4
)
cm,
JH
=
(
9
x
+
3
)
cm and
IJ
=
(
10
x
+
1
)
cm, find the value of x
(i)
(
24
13
,
7
)
(ii)
(
6
,
(
-2
15
)
)
(iii)
(
5
,
(
-2
11
)
)
(iv)
(
8
,
(
-2
13
)
)
(v)
(
5
,
(
-2
13
)
)
Question
23
23.
In the given figure, points G , H and I are the mid-points of sides EF, FD and DE of △DEF. Which of the following are true?
a)
Area of trapezium EFHI is thrice the area of △DIH
b)
Area of
△DEF
=
1
3
area of
△GHI
c)
Area of trapezium
EFHI
is
1
4
the area of
△DEF
d)
Area of △DEF = 4 times area of △GHI
e)
All four small triangles have equal areas
(i)
{b,a}
(ii)
{b,a,d}
(iii)
{b,c,e}
(iv)
{a,d,e}
(v)
{c,d}
Question
24
24.
In the given figure, the altitudes MB and CN of △ABC meet at L. ∠CLB =
(i)
∠MNL
(ii)
∠NLM
(iii)
∠LMN
(iv)
∠BCL
(v)
∠LBC
Question
25
25.
In the given figure, △BCD & △MNO are similar triangles. If the ratio of the heights BE : MP = 12 : 17, then the ratio of their areas is
(i)
143
sq.cm
:
289
sq.cm
(ii)
144
sq.cm
:
286
sq.cm
(iii)
144
sq.cm
:
291
sq.cm
(iv)
145
sq.cm
:
289
sq.cm
(v)
144
sq.cm
:
289
sq.cm
Assignment Key
1) (v)
2) (iv)
3) (v)
4) (ii)
5) (iii)
6) (iii)
7) (iv)
8) (iii)
9) (ii)
10) (iv)
11) (v)
12) (i)
13) (ii)
14) (v)
15) (i)
16) (v)
17) (iii)
18) (i)
19) (iii)
20) (i)
21) (i)
22) (v)
23) (iv)
24) (ii)
25) (v)
