EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
EI
=
(i)
FG
(ii)
FG
2
(iii)
EH
(iv)
GE
2
(v)
EF
2
Question
2
2.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BE
=
(i)
CD
(ii)
BC
2
(iii)
CD
2
(iv)
DB
2
(v)
BF
Question
3
3.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
IL
=
(i)
IM
(ii)
KI
(iii)
IJ
(iv)
MK
(v)
LJ
Question
4
4.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
EC
=
(i)
DB
(ii)
FD
(iii)
BE
(iv)
BF
(v)
BC
Question
5
5.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
DH
=
(i)
DG
(ii)
FD
(iii)
DE
(iv)
HF
(v)
GE
Question
6
6.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
IG
=
(i)
EH
(ii)
EF
(iii)
HF
(iv)
GE
(v)
EI
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
SSS Similarity
(iii)
AAA Similarity
(iv)
not similar
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
AAA Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SAS Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
10
10.
In the given figure, △IJK and △RST are such that
∠J
=
∠S
and
IJ
RS
=
JK
ST
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
AAA Similarity
(iii)
SSS Similarity
(iv)
SAS Similarity
Question
11
11.
In the given figure, △GHI and △QRS are such that
∠H
=
∠R
and
∠I
=
∠S
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
12
12.
In the given figure, △IJK and △UVW are such that
IJ
UV
=
JK
VW
=
KI
WU
.
Identify the property by which the two triangles are similar
(i)
SAS Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
AAA Similarity
Question
13
13.
In the given figure,
HI
∥
FG
.
If
EH
HF
=
5
4
and
EG
=
13.7 cm
, find
EI
(i)
5.61 cm
(ii)
9.61 cm
(iii)
7.61 cm
(iv)
6.61 cm
(v)
8.61 cm
Question
14
14.
In the given figure,
PQ
∥
NO
.
If
MP
=
4.93 cm
,
MN
=
11.5 cm
and
MO
=
15.9 cm
, find
MQ
(i)
5.81 cm
(ii)
4.81 cm
(iii)
6.81 cm
(iv)
7.81 cm
(v)
8.81 cm
Question
15
15.
In the given figure, PQ ∥ HI and GP = 15 cm, GH = 25 cm and PQ = 12.6 cm, find HI
(i)
22.0 cm
(ii)
19.0 cm
(iii)
21.0 cm
(iv)
23.0 cm
(v)
20.0 cm
Question
16
16.
In the given figure, △EFG is isosceles right-angled at F and FH ⟂ GE. ∠H =
(i)
∠E
(ii)
∠I
(iii)
∠J
(iv)
∠F
(v)
∠G
Question
17
17.
In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠GHI =
(i)
∠GHJ
(ii)
∠IJH
(iii)
∠HIJ
(iv)
∠JHI
(v)
∠JGH
Question
18
18.
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.
△FEH ∼
(i)
△DCF
(ii)
△DAE
(iii)
△ABH
(iv)
△ACF
(v)
△FDA
Question
19
19.
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.
∠HFE =
(i)
∠FAC
(ii)
∠AFD
(iii)
∠HAB
(iv)
∠FEH
(v)
∠FDA
Question
20
20.
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.
∠ACF =
(i)
∠ABH
(ii)
∠EHF
(iii)
∠DAF
(iv)
∠FEH
(v)
∠FDA
Question
21
21.
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.
∠CFA =
(i)
∠HFE
(ii)
∠EHF
(iii)
∠AFD
(iv)
∠BHA
(v)
∠DAF
Question
22
22.
In the given figure, BCDE is a trapezium in which
BC ∥ DE
and the diagonals
CE
and
BD
intersect at
F
.
If
FB
=
(
8
x
+
4
)
cm,
CF
=
(
6
x
+
3
)
cm,
FD
=
(
x
+
18
)
cm and
EF
=
(
x
+
8
)
cm, find the value of x
(i)
(
25
,
(
-1
2
)
)
(ii)
(
1
2
,
24
)
(iii)
(
22
,
(
-1
2
)
)
(iv)
(
22
,
-1
)
(v)
(
23
,
(
-1
4
)
)
Question
23
23.
In the given figure, KLMN is a trapezium in which
KL ∥ MN
and the diagonals
LN
and
KM
intersect at
O
.
△OKL
∼
(i)
△OLM
(ii)
△OMN
(iii)
△LMN
(iv)
△ONK
(v)
△NKL
Question
24
24.
In the given figure, the altitudes TF and GU of △EFG meet at S. △SFG ∼
(i)
△UFG
(ii)
△SUT
(iii)
△UFS
(iv)
△TGF
(v)
△TGS
Question
25
25.
In the given figure, the altitudes TE and FU of △DEF meet at S. ∠FSE =
(i)
∠SEF
(ii)
∠UST
(iii)
∠TUS
(iv)
∠EFS
(v)
∠STU
Question
26
26.
In the given figure, RS ∥ IJ , and median HK bisects RS.
If HI = 19 cm, HK = 19.1 cm and HR = 10.86 cm, LK =
(i)
6.19 cm
(ii)
8.19 cm
(iii)
10.19 cm
(iv)
9.19 cm
(v)
7.19 cm
Question
27
27.
In the given figure, QR ∥ DE , and median CF bisects QR.
If CF = 15 cm, CE = 17 cm and CR = 6.8 cm, CG =
(i)
6.00 cm
(ii)
4.00 cm
(iii)
8.00 cm
(iv)
5.00 cm
(v)
7.00 cm
Question
28
28.
In the given figure, QR ∥ IJ , and median HK bisects QR.
△HQL ∼
(i)
△HIK
(ii)
△HLR
(iii)
△HKJ
(iv)
△HIJ
(v)
△IJH
Question
29
29.
In the given figure, △KLM is a triangle in which KN is the internal bisector of ∠K and MO ∥ NK meeting LK produced at O . ∠MKN =
(i)
∠OKM
(ii)
∠KNM
(iii)
∠KMO
(iv)
∠NMK
(v)
∠LNK
Question
30
30.
In the given figure, P and Q are points on the sides MN and MO respectively of △MNO.For which of the following cases, PQ ∥ NO
a)
MN = 17 cm, PN = 9.44 cm, MO = 15 cm and MQ = 6.67 cm
b)
MN = 17 cm, PN = 9.44 cm, MQ = 8.67 cm and MO = 15 cm
c)
MN = 17 cm, MP = 9.56 cm, MO = 15 cm and QO = 8.33 cm
d)
MP = 7.56 cm, PN = 9.44 cm, MQ = 6.67 cm and QO = 8.33 cm
(i)
{c,d}
(ii)
{b,a}
(iii)
{a,d}
(iv)
{b,c,a}
(v)
{b,d,a}
Question
31
31.
Which of the following are true?
a)
Any two squares are congruent.
b)
Any two squares are similar.
c)
Any two circles are congruent.
d)
Any two triangles are similar.
e)
Any two circles are similar.
f)
Any two triangles are congruent.
(i)
{a,e,b}
(ii)
{d,f,b}
(iii)
{a,b}
(iv)
{c,e}
(v)
{b,e}
Question
32
32.
Which of the following are true?
a)
A triangle is a polygonal region.
b)
A sector is a polygonal region.
c)
A semi-circle is a polygonal region.
d)
A circle is a polygonal region.
e)
A square is a polygonal region.
(i)
{c,e,a}
(ii)
{c,e}
(iii)
{a,e}
(iv)
{b,a}
(v)
{d,b,a}
Question
33
33.
Which of the following are true?
a)
Similar and congruent are not synonymous.
b)
Similar figures have same area.
c)
If two figures are congruent, then they are similar too.
d)
If two figures are similar, then they are congruent too.
e)
Congruent figures have same area.
(i)
{a,c,e}
(ii)
{b,d,e}
(iii)
{d,c}
(iv)
{b,a,c}
(v)
{b,a}
Question
34
34.
Which of the following are true?
a)
Area of the union of two polygonal region is the sum of the individual area.
b)
A polygonal region can be divided into a finite number of triangles in a unique way.
c)
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.
d)
Area of the union of two polygonal region is not equal to the sum of the individual area.
(i)
{c,d}
(ii)
{a,c}
(iii)
{a,d,c}
(iv)
{a,b,c}
(v)
{b,d}
Question
35
35.
Which of the following are necessary conditions for similarity of two polygons ?
a)
The corresponding angles are equal.
b)
The corresponding angles are proportional.
c)
The corresponding sides are equal.
d)
The corresponding sides are proportional.
(i)
{b,c,a}
(ii)
{b,d,a}
(iii)
{c,d}
(iv)
{b,a}
(v)
{a,d}
Question
36
36.
Which of the following are true?
a)
Similarity is reflexive.
b)
Similarity is symmetric.
c)
Similarity is anti symmetric.
d)
Similarity is transitive.
(i)
{a,b,d}
(ii)
{c,d}
(iii)
{c,b}
(iv)
{c,a,b}
(v)
{c,a}
Question
37
37.
Which of the following are true?
a)
Any two triangles are similar if the corresponding angles are equal.
b)
Any two quadrilaterals are similar if the corresponding angles are equal.
c)
Any two triangles are similar if the corresponding sides are proportional.
d)
Any two quadrilaterals are similar if the corresponding sides are proportional.
(i)
{b,a,c}
(ii)
{b,d}
(iii)
{b,c}
(iv)
{b,a}
(v)
{a,c,d}
Question
38
38.
In the given figure, the area of the △IJK is x sq.cm. L,M,N are the mid-points of the sides JK , KI and IJ respectively. The area of the △LMN is
(i)
1
4
of area of △IJK
(ii)
1
2
of area of △IJK
(iii)
1
3
of area of △IJK
(iv)
2
3
of area of △IJK
(v)
3
4
of area of △IJK
Question
39
39.
In the given figure, the parallelogram IJKL and the triangle △MIJ are on the same bases and between the same parallels.
The area of the
△MIJ
is x sq.cm. The area of the parallelogram is
(i)
twice
the area of the triangle
(ii)
5
4
the area of the triangle
(iii)
thrice
the area of the triangle
(iv)
4
3
the area of the triangle
(v)
3
2
the area of the triangle
Question
40
40.
In the given △HIJ, KL ∥ IJ. If HK : KI = 7.71 cm : 10.29 cm and HJ = 20 cm, HL =
(i)
6.57 cm
(ii)
8.57 cm
(iii)
10.57 cm
(iv)
9.57 cm
(v)
7.57 cm
Question
41
41.
In the given two similar triangles, if e = 17 cm, f = 17 cm, g = 20 cm, h = 10.2 cm, find i
(i)
9.20 cm
(ii)
11.20 cm
(iii)
8.20 cm
(iv)
12.20 cm
(v)
10.20 cm
Question
42
42.
In the given figure, given ∠KHI = ∠JHK, x : y = 8 cm : 8 cm and q = 15 cm, find p =
(i)
16.00 cm
(ii)
14.00 cm
(iii)
15.00 cm
(iv)
17.00 cm
(v)
13.00 cm
Question
43
43.
In the given figure, given ∠FCD = ∠ECF, p = 9.5 cm, q = 9.5 cm and DE = 19 cm, find DF =
(i)
11.50 cm
(ii)
9.50 cm
(iii)
10.50 cm
(iv)
8.50 cm
(v)
7.50 cm
Question
44
44.
In the given figure, FGHI is a trapezium where OF = 15 cm , OG = 15 cm and OH = 5 cm . Find OI =
(i)
3 cm
(ii)
7 cm
(iii)
6 cm
(iv)
4 cm
(v)
5 cm
Question
45
45.
In the given figure, ∠HEF = 46.59°, find the value of x =
(i)
41.41°
(ii)
43.41°
(iii)
45.41°
(iv)
44.41°
(v)
42.41°
Question
46
46.
In the given figure, ∠LJK = 42.27°, find the value of y =
(i)
45.73°
(ii)
47.73°
(iii)
49.73°
(iv)
46.73°
(v)
48.73°
Question
47
47.
In the given figure, if CD ∥ EF then
(i)
△CDG ∼ △GEF
(ii)
△GCD ∼ △GEF
(iii)
△CDG ∼ △FEG
(iv)
△GDC ∼ △GFE
(v)
△CDG ∼ △GFE
Question
48
48.
In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FG = 18 cm, GI = 11.52 cm, then find GH.
(i)
14.00 cm
(ii)
15.00 cm
(iii)
16.00 cm
(iv)
13.00 cm
(v)
17.00 cm
Question
49
49.
In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If ED = 12.1 cm, CE = 13.38 cm, then find BE.
(i)
13.80 cm
(ii)
15.80 cm
(iii)
14.80 cm
(iv)
12.80 cm
(v)
16.80 cm
Question
50
50.
In the given figure, △DEF ∼ △MNO and DE = 10 cm, MN = 14 cm.
If the area of the
△MNO
=
96.82 sq.cm
, find the area of the
△DEF
(i)
51.40 sq.cm
(ii)
49.40 sq.cm
(iii)
50.40 sq.cm
(iv)
48.40 sq.cm
(v)
47.40 sq.cm
Question
51
51.
In the given figure, △CDE ∼ △NOP and DE = 13 cm , OP = 18.2 cm and
NQ
=
13.24 cm
,
find the area of the
△CDE
(i)
59.48 sq.cm
(ii)
62.48 sq.cm
(iii)
63.48 sq.cm
(iv)
60.48 sq.cm
(v)
61.48 sq.cm
Question
52
52.
In the given figure, △BCD & △NOP are similar triangles. If the ratio of the heights BE : NQ = 11 : 15, then the ratio of their areas is
(i)
121
sq.cm
:
225
sq.cm
(ii)
121
sq.cm
:
227
sq.cm
(iii)
121
sq.cm
:
222
sq.cm
(iv)
122
sq.cm
:
225
sq.cm
(v)
120
sq.cm
:
225
sq.cm
Question
53
53.
In the given figure, points L , M and N are the mid-points of sides JK, KI and IJ of △IJK. Which of the following are true?
a)
Area of △IJK = 4 times area of △LMN
b)
All four small triangles have equal areas
c)
Area of
△IJK
=
1
3
area of
△LMN
d)
Area of trapezium JKMN is thrice the area of △INM
e)
Area of trapezium
JKMN
is
1
4
the area of
△IJK
(i)
{c,a}
(ii)
{e,b}
(iii)
{a,b,d}
(iv)
{c,a,b}
(v)
{c,e,d}
Question
54
54.
In the given figure, points J , K and L are the mid-points of sides HI, IG and GH of △GHI. Which of the following are true?
a)
△GLK ∼ △GHI
b)
△JLK ∼ △GHI
c)
△LHJ ∼ △GHI
d)
△JKL ∼ △GHI
e)
△KJI ∼ △GHI
(i)
{a,c,d,e}
(ii)
{b,a}
(iii)
{b,c}
(iv)
{b,e,a}
(v)
{b,d}
Question
55
55.
The perimeters of two similar triangles are 34 cm and 23 cm respectively. If one side of the first triangle is 14 cm, find the length of the corresponding side of the second triangle.
(i)
7.47 cm
(ii)
11.47 cm
(iii)
10.47 cm
(iv)
8.47 cm
(v)
9.47 cm
Question
56
56.
In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 107° , ∠DCA = 20°. Find ∠CAD
(i)
53°
(ii)
52°
(iii)
55°
(iv)
54°
(v)
51°
Question
57
57.
EFGH is a square and △EFI is an equilateral triangle. Also, △EGJ is an equilateral triangle. If area of △EFI is 'a' sq.units, then the area of △EGJ is
(i)
1
2
√
3
a sq.units
(ii)
2a sq.units
(iii)
1
2
a sq.units
(iv)
a
2
sq.units
(v)
√
3
a sq.units
Question
58
58.
KLMN is a cyclic trapezium. Diagonals LN and KM intersect at O. If NK = 17 cm, find LM
(i)
18 cm
(ii)
19 cm
(iii)
15 cm
(iv)
17 cm
(v)
16 cm
Question
59
59.
A vertical stick
12 m
long casts a shadow of
14 m
long on the ground.
At the same time, a tower casts the shadow
112 m
long on the ground.
Find the height of the tower.
(i)
96 m
(ii)
98 m
(iii)
97 m
(iv)
94 m
(v)
95 m
Question
60
60.
In the given figure, △DEF, QR ∥ EF such that
area of
△DQR
= area of
QRFE
. Find
DQ
DE
(i)
1
2
√
2
(ii)
1
(iii)
1
2
√
1
2
(iv)
1
2
√
5
(v)
1
2
4
√
2
Question
61
61.
In the given figure, ∠FCD = ∠ECF and CF ∥ GE and CD = 18 cm, DF = 9 cm and FE = 10 cm. Find CG
(i)
19.00 cm
(ii)
21.00 cm
(iii)
18.00 cm
(iv)
20.00 cm
(v)
22.00 cm
Question
62
62.
In the given figure, JL is the angular bisector of
∠J
&
∠L
IJ
=
20 cm
,
JK
=
20 cm
and
KL
=
20 cm
.
Find
LI
(i)
20.00 cm
(ii)
22.00 cm
(iii)
19.00 cm
(iv)
18.00 cm
(v)
21.00 cm
Question
63
63.
In the given figure, ABC is a triangle and 'O' is a point inside △ABC. The angular bisector of ∠BOA, ∠COB & ∠AOC meet AB, BC & CA at D, E & F respectively . Then
(i)
AD . BE . CF = OA . OB . OC
(ii)
AD . BE . CF = OD . OE . OF
(iii)
AD . BE . CF = DE . EF . FD
(iv)
AD . BE . CF = AB . BC . CA
(v)
AD . BE . CF = DB . EC . FA
Question
64
64.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 27 cm. Find AP
(i)
10.80 cm
(ii)
9.80 cm
(iii)
11.80 cm
(iv)
12.80 cm
(v)
8.80 cm
Question
65
65.
From the given figure and values, find x
(i)
(
21
,
1
)
(ii)
(
20
,
0
)
(iii)
(
2
,
22
)
(iv)
(
23
,
0
)
(v)
(
20
,
-1
)
Question
66
66.
The ratio of the bases of two triangles ABC and DEF is
9
:
7
.
If the triangles are equal in area, then the ratio of their heights is
(i)
7
:
9
(ii)
10
:
7
(iii)
8
:
7
(iv)
9
:
4
(v)
9
:
10
Question
67
67.
If the measures are as shown in the given figure, find HI
(i)
23.0 cm
(ii)
19.0 cm
(iii)
20.0 cm
(iv)
22.0 cm
(v)
21.0 cm
Question
68
68.
In the given figure, the two circles touch each other internally.
Diameter
OB
passes through the centre of the smaller circle.
OX = 8 cm
,
OY = 20 cm
and radius of the inner circle is
5.3 cm
.
Find the radius of the outer circle.
(i)
14.25 cm
(ii)
11.25 cm
(iii)
12.25 cm
(iv)
13.25 cm
(v)
15.25 cm
Assignment Key
1) (iv)
2) (ii)
3) (v)
4) (iii)
5) (iv)
6) (v)
7) (i)
8) (ii)
9) (iv)
10) (iv)
11) (i)
12) (ii)
13) (iii)
14) (iii)
15) (iii)
16) (iv)
17) (ii)
18) (v)
19) (ii)
20) (i)
21) (iv)
22) (iii)
23) (ii)
24) (ii)
25) (ii)
26) (ii)
27) (i)
28) (i)
29) (iii)
30) (iii)
31) (v)
32) (iii)
33) (i)
34) (i)
35) (v)
36) (i)
37) (v)
38) (i)
39) (i)
40) (ii)
41) (v)
42) (iii)
43) (ii)
44) (v)
45) (ii)
46) (ii)
47) (iii)
48) (ii)
49) (iii)
50) (ii)
51) (v)
52) (i)
53) (iii)
54) (i)
55) (v)
56) (i)
57) (ii)
58) (iv)
59) (i)
60) (i)
61) (iv)
62) (i)
63) (v)
64) (i)
65) (ii)
66) (i)
67) (v)
68) (iv)
