EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HL
=
(i)
IJ
(ii)
HK
(iii)
JH
2
(iv)
HI
2
(v)
IJ
2
Question
2
2.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JM
=
(i)
KL
(ii)
JK
2
(iii)
LJ
2
(iv)
KL
2
(v)
JN
Question
3
3.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BE
=
(i)
BC
(ii)
DB
(iii)
EC
(iv)
FD
(v)
BF
Question
4
4.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
NL
=
(i)
KN
(ii)
KO
(iii)
OM
(iv)
MK
(v)
KL
Question
5
5.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CG
=
(i)
FD
(ii)
GE
(iii)
EC
(iv)
CF
(v)
CD
Question
6
6.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
HF
=
(i)
DE
(ii)
GE
(iii)
FD
(iv)
DG
(v)
DH
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
SAS Similarity
(iii)
AAA Similarity
(iv)
not similar
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SAS Similarity
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
10
10.
In the given figure, △HIJ and △STU are such that
∠I
=
∠T
and
HI
ST
=
IJ
TU
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
11
11.
In the given figure, △EFG and △STU are such that
∠F
=
∠T
and
∠G
=
∠U
.
Identify the property by which the two triangles are similar
(i)
SAS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SSS Similarity
Question
12
12.
In the given figure, △IJK and △QRS are such that
IJ
QR
=
JK
RS
=
KI
SQ
.
Identify the property by which the two triangles are similar
(i)
SAS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SSS Similarity
Question
13
13.
In the given figure,
MN
∥
KL
.
If
JM
MK
=
5
2
and
JL
=
13.7 cm
, find
JN
(i)
11.79 cm
(ii)
9.79 cm
(iii)
7.79 cm
(iv)
10.79 cm
(v)
8.79 cm
Question
14
14.
In the given figure,
OP
∥
MN
.
If
LO
=
3.91 cm
,
LM
=
13.7 cm
and
LN
=
14.4 cm
, find
LP
(i)
5.11 cm
(ii)
3.11 cm
(iii)
4.11 cm
(iv)
2.11 cm
(v)
6.11 cm
Question
15
15.
In the given figure, PQ ∥ DE and CQ = 12 cm, CE = 20 cm and PQ = 15 cm, find DE
(i)
24.0 cm
(ii)
25.0 cm
(iii)
26.0 cm
(iv)
27.0 cm
(v)
23.0 cm
Question
16
16.
In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠J =
(i)
∠K
(ii)
∠G
(iii)
∠L
(iv)
∠H
(v)
∠I
Question
17
17.
In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠QSP =
(i)
∠SPQ
(ii)
∠PQS
(iii)
∠QRS
(iv)
∠RSQ
(v)
∠SQR
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.
△ACF ∼
(i)
△FEH
(ii)
△DCF
(iii)
△ABH
(iv)
△DAE
(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.
∠FAC =
(i)
∠HAB
(ii)
∠FEH
(iii)
∠HFE
(iv)
∠FDA
(v)
∠AFD
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.
∠FDA =
(i)
∠ABH
(ii)
∠EHF
(iii)
∠ACF
(iv)
∠FEH
(v)
∠DAF
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)
∠EHF
(ii)
∠AFD
(iii)
∠BHA
(iv)
∠DAF
(v)
∠HFE
Question
22
22.
In the given figure, CDEF is a trapezium in which
CD ∥ EF
and the diagonals
DF
and
CE
intersect at
G
.
If
GC
=
(
23
x
+
4
)
cm,
DG
=
(
26
x
+
3
)
cm,
GE
=
(
20
x
+
2
)
cm and
FG
=
(
22
x
+
4
)
cm, find the value of x
(i)
(
7
,
(
-1
7
)
)
(ii)
(
5
,
(
-1
7
)
)
(iii)
(
20
7
,
7
)
(iv)
(
6
,
(
-1
9
)
)
(v)
(
5
,
(
-1
5
)
)
Question
23
23.
In the given figure, NOPQ is a trapezium in which
NO ∥ PQ
and the diagonals
OQ
and
NP
intersect at
R
.
△RNO
∼
(i)
△ROP
(ii)
△OPQ
(iii)
△QNO
(iv)
△RQN
(v)
△RPQ
Question
24
24.
In the given figure, the altitudes TC and DU of △BCD meet at S. △SCD ∼
(i)
△TDS
(ii)
△UCD
(iii)
△UCS
(iv)
△SUT
(v)
△TDC
Question
25
25.
In the given figure, the altitudes SH and IT of △GHI meet at R. ∠SRI =
(i)
∠RTH
(ii)
∠THR
(iii)
∠ISR
(iv)
∠RIS
(v)
∠HRT
Question
26
26.
In the given figure, RS ∥ HI , and median GJ bisects RS.
If GH = 18 cm, GJ = 17.9 cm and GK = 10.23 cm, GR =
(i)
10.29 cm
(ii)
9.29 cm
(iii)
8.29 cm
(iv)
12.29 cm
(v)
11.29 cm
Question
27
27.
In the given figure, PQ ∥ FG , and median EH bisects PQ.
If EH = 15.7 cm, EG = 17 cm and EI = 8.72 cm, QG =
(i)
9.56 cm
(ii)
7.56 cm
(iii)
6.56 cm
(iv)
8.56 cm
(v)
5.56 cm
Question
28
28.
In the given figure, RS ∥ IJ , and median HK bisects RS.
△HRL ∼
(i)
△IJH
(ii)
△HIJ
(iii)
△HLS
(iv)
△HIK
(v)
△HKJ
Question
29
29.
In the given figure, △LMN is a triangle in which LO is the internal bisector of ∠L and NP ∥ OL meeting ML produced at P . ∠LNP =
(i)
∠ONL
(ii)
∠LON
(iii)
∠OLM
(iv)
∠PLN
(v)
∠MOL
Question
30
30.
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)
JM = 9 cm, MK = 6 cm, JN = 10.2 cm and NL = 6.8 cm
b)
JK = 15 cm, MK = 6 cm, JN = 12.2 cm and JL = 17 cm
c)
JK = 15 cm, JM = 11 cm, JL = 17 cm and NL = 6.8 cm
d)
JK = 15 cm, MK = 6 cm, JL = 17 cm and JN = 10.2 cm
(i)
{a,d}
(ii)
{b,a}
(iii)
{c,d}
(iv)
{b,d,a}
(v)
{b,c,a}
Question
31
31.
Which of the following are true?
a)
Any two triangles are congruent.
b)
Any two squares are similar.
c)
Any two circles are similar.
d)
Any two squares are congruent.
e)
Any two circles are congruent.
f)
Any two triangles are similar.
(i)
{d,c}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{a,c,b}
(v)
{e,f,b}
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 square is a polygonal region.
d)
A circle is a polygonal region.
e)
A semi-circle is a polygonal region.
(i)
{d,c,a}
(ii)
{a,c}
(iii)
{b,a}
(iv)
{e,b,a}
(v)
{d,c}
Question
33
33.
Which of the following are true?
a)
If two figures are similar, then they are congruent too.
b)
Congruent figures have same area.
c)
If two figures are congruent, then they are similar too.
d)
Similar figures have same area.
e)
Similar and congruent are not synonymous.
(i)
{a,b}
(ii)
{a,d,e}
(iii)
{a,b,c}
(iv)
{d,c}
(v)
{b,c,e}
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)
{b,d}
(ii)
{c,d}
(iii)
{a,c}
(iv)
{a,d,c}
(v)
{a,b,c}
Question
35
35.
Which of the following are necessary conditions for similarity of two polygons ?
a)
The corresponding angles are proportional.
b)
The corresponding sides are equal.
c)
The corresponding angles are equal.
d)
The corresponding sides are proportional.
(i)
{b,d}
(ii)
{a,d,c}
(iii)
{a,c}
(iv)
{a,b,c}
(v)
{c,d}
Question
36
36.
Which of the following are true?
a)
Similarity is symmetric.
b)
Similarity is anti symmetric.
c)
Similarity is reflexive.
d)
Similarity is transitive.
(i)
{a,c,d}
(ii)
{b,a}
(iii)
{b,a,c}
(iv)
{b,c}
(v)
{b,d}
Question
37
37.
Which of the following are true?
a)
Any two triangles are similar if the corresponding sides are proportional.
b)
Any two quadrilaterals are similar if the corresponding angles are equal.
c)
Any two quadrilaterals are similar if the corresponding sides are proportional.
d)
Any two triangles are similar if the corresponding angles are equal.
(i)
{b,a}
(ii)
{a,c,d}
(iii)
{b,c}
(iv)
{b,a,c}
(v)
{b,d}
Question
38
38.
In the given figure, the area of the △EFG is x sq.cm. H,I,J are the mid-points of the sides FG , GE and EF respectively. The area of the △HIJ is
(i)
1
3
of area of △EFG
(ii)
1
2
of area of △EFG
(iii)
1
4
of area of △EFG
(iv)
3
4
of area of △EFG
(v)
2
3
of area of △EFG
Question
39
39.
In the given figure, the parallelogram DEFG and the triangle △HDE are on the same bases and between the same parallels.
The area of the
△HDE
is x sq.cm. The area of the parallelogram is
(i)
5
4
the area of the triangle
(ii)
thrice
the area of the triangle
(iii)
4
3
the area of the triangle
(iv)
twice
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 = 10.29 cm : 7.71 cm and HJ = 17 cm, LJ =
(i)
7.29 cm
(ii)
8.29 cm
(iii)
6.29 cm
(iv)
9.29 cm
(v)
5.29 cm
Question
41
41.
In the given two similar triangles, if g = 19 cm, h = 19 cm, i = 19 cm, j = 11.4 cm, find k
(i)
11.40 cm
(ii)
13.40 cm
(iii)
12.40 cm
(iv)
9.40 cm
(v)
10.40 cm
Question
42
42.
In the given figure, given ∠DAB = ∠CAD, x : y = 9.24 cm : 9.76 cm and q = 19 cm, find p =
(i)
17.00 cm
(ii)
18.00 cm
(iii)
16.00 cm
(iv)
19.00 cm
(v)
20.00 cm
Question
43
43.
In the given figure, given ∠GDE = ∠FDG, p = 7.03 cm, q = 7.97 cm and EF = 15 cm, find EG =
(i)
6.03 cm
(ii)
8.03 cm
(iii)
7.03 cm
(iv)
5.03 cm
(v)
9.03 cm
Question
44
44.
In the given figure, DEFG is a trapezium where OD = 13 cm , OE = 13 cm and OF = 4 cm . Find OG =
(i)
5 cm
(ii)
4 cm
(iii)
3 cm
(iv)
6 cm
(v)
2 cm
Question
45
45.
In the given figure, ∠JGH = 44.07°, find the value of x =
(i)
47.93°
(ii)
43.93°
(iii)
46.93°
(iv)
44.93°
(v)
45.93°
Question
46
46.
In the given figure, ∠IGH = 49.35°, find the value of y =
(i)
39.65°
(ii)
41.65°
(iii)
38.65°
(iv)
42.65°
(v)
40.65°
Question
47
47.
In the given figure, if EF ∥ GH then
(i)
△IEF ∼ △IGH
(ii)
△EFI ∼ △IGH
(iii)
△IFE ∼ △IHG
(iv)
△EFI ∼ △HGI
(v)
△EFI ∼ △IHG
Question
48
48.
In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If DE = 16 cm, EG = 10.94 cm, then find EF.
(i)
16.00 cm
(ii)
17.00 cm
(iii)
13.00 cm
(iv)
14.00 cm
(v)
15.00 cm
Question
49
49.
In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If HK = 14.6 cm, KJ = 13 cm, then find IK.
(i)
14.78 cm
(ii)
11.78 cm
(iii)
15.78 cm
(iv)
12.78 cm
(v)
13.78 cm
Question
50
50.
In the given figure, △CDE ∼ △OPQ and CD = 12 cm, OP = 16.8 cm.
If the area of the
△CDE
=
63.71 sq.cm
, find the area of the
△OPQ
(i)
123.86 sq.cm
(ii)
126.86 sq.cm
(iii)
122.86 sq.cm
(iv)
124.86 sq.cm
(v)
125.86 sq.cm
Question
51
51.
In the given figure, △BCD ∼ △MNO and CD = 10 cm , NO = 14 cm and
MP
=
17.94 cm
,
find the area of the
△BCD
(i)
63.06 sq.cm
(ii)
65.06 sq.cm
(iii)
66.06 sq.cm
(iv)
62.06 sq.cm
(v)
64.06 sq.cm
Question
52
52.
In the given figure, △EFG & △QRS are similar triangles. If the ratio of the heights EH : QT = 12 : 16, then the ratio of their areas is
(i)
144
sq.cm
:
258
sq.cm
(ii)
144
sq.cm
:
256
sq.cm
(iii)
145
sq.cm
:
256
sq.cm
(iv)
144
sq.cm
:
254
sq.cm
(v)
143
sq.cm
:
256
sq.cm
Question
53
53.
In the given figure, points H , I and J are the mid-points of sides FG, GE and EF of △EFG. Which of the following are true?
a)
Area of
△EFG
=
1
3
area of
△HIJ
b)
Area of trapezium FGIJ is thrice the area of △EJI
c)
Area of △EFG = 4 times area of △HIJ
d)
All four small triangles have equal areas
e)
Area of trapezium
FGIJ
is
1
4
the area of
△EFG
(i)
{a,b}
(ii)
{a,b,c}
(iii)
{e,c}
(iv)
{a,e,d}
(v)
{b,c,d}
Question
54
54.
In the given figure, points I , J and K are the mid-points of sides GH, HF and FG of △FGH. Which of the following are true?
a)
△FKJ ∼ △FGH
b)
△IKJ ∼ △FGH
c)
△IJK ∼ △FGH
d)
△JIH ∼ △FGH
e)
△KGI ∼ △FGH
(i)
{b,e,a}
(ii)
{b,d}
(iii)
{b,a}
(iv)
{a,c,d,e}
(v)
{b,c}
Question
55
55.
The perimeters of two similar triangles are 27 cm and 18 cm respectively. If one side of the first triangle is 9 cm, find the length of the corresponding side of the second triangle.
(i)
7.00 cm
(ii)
5.00 cm
(iii)
6.00 cm
(iv)
8.00 cm
(v)
4.00 cm
Question
56
56.
In the given figure, I is a point on side GH of △FGH such that ∠HFG = ∠FIH = 109° , ∠IHF = 20°. Find ∠HFI
(i)
52°
(ii)
51°
(iii)
49°
(iv)
50°
(v)
53°
Question
57
57.
GHIJ is a square and △GHK is an equilateral triangle. Also, △GIL is an equilateral triangle. If area of △GHK is 'a' sq.units, then the area of △GIL is
(i)
a
2
sq.units
(ii)
√
3
a sq.units
(iii)
2a sq.units
(iv)
1
2
√
3
a sq.units
(v)
1
2
a sq.units
Question
58
58.
KLMN is a cyclic trapezium. Diagonals LN and KM intersect at O. If NK = 15 cm, find LM
(i)
17 cm
(ii)
16 cm
(iii)
14 cm
(iv)
15 cm
(v)
13 cm
Question
59
59.
A vertical stick
11 m
long casts a shadow of
15 m
long on the ground.
At the same time, a tower casts the shadow
120 m
long on the ground.
Find the height of the tower.
(i)
89 m
(ii)
87 m
(iii)
88 m
(iv)
90 m
(v)
86 m
Question
60
60.
In the given figure, △BCD, QR ∥ CD such that
area of
△BQR
= area of
QRDC
. Find
BQ
BC
(i)
1
2
4
√
2
(ii)
1
2
√
-1
(iii)
1
2
√
2
(iv)
1
(v)
1
2
√
5
Question
61
61.
In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 17 cm, HJ = 7 cm and JI = 9 cm. Find GK
(i)
19.86 cm
(ii)
22.86 cm
(iii)
21.86 cm
(iv)
23.86 cm
(v)
20.86 cm
Question
62
62.
In the given figure, LN is the angular bisector of
∠L
&
∠N
KL
=
20 cm
,
LM
=
20 cm
and
MN
=
21 cm
.
Find
NK
(i)
19.00 cm
(ii)
22.00 cm
(iii)
21.00 cm
(iv)
20.00 cm
(v)
23.00 cm
Question
63
63.
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 = HF . IG . JE
(ii)
EH . FI . GJ = EF . FG . GE
(iii)
EH . FI . GJ = OE . OF . OG
(iv)
EH . FI . GJ = HI . IJ . JH
(v)
EH . FI . GJ = OH . OI . OJ
Question
64
64.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 22 cm. Find AP
(i)
9.80 cm
(ii)
6.80 cm
(iii)
8.80 cm
(iv)
7.80 cm
(v)
10.80 cm
Question
65
65.
From the given figure and values, find x
(i)
(
6
,
0
)
(ii)
(
2
,
8
)
(iii)
(
6
,
-1
)
(iv)
(
9
,
0
)
(v)
(
7
,
1
)
Question
66
66.
The ratio of the bases of two triangles ABC and DEF is
6
:
10
.
If the triangles are equal in area, then the ratio of their heights is
(i)
10
:
6
(ii)
5
:
10
(iii)
6
:
8
(iv)
6
:
12
(v)
7
:
10
Question
67
67.
If the measures are as shown in the given figure, find HI
(i)
23.0 cm
(ii)
24.0 cm
(iii)
27.0 cm
(iv)
26.0 cm
(v)
25.0 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 = 9 cm
,
OY = 22 cm
and radius of the inner circle is
5.3 cm
.
Find the radius of the outer circle.
(i)
11.96 cm
(ii)
10.96 cm
(iii)
13.96 cm
(iv)
12.96 cm
(v)
14.96 cm
Assignment Key
1) (iii)
2) (ii)
3) (iii)
4) (i)
5) (ii)
6) (v)
7) (ii)
8) (iii)
9) (ii)
10) (iv)
11) (iii)
12) (iv)
13) (ii)
14) (iii)
15) (ii)
16) (iv)
17) (iv)
18) (iii)
19) (i)
20) (iv)
21) (iii)
22) (ii)
23) (v)
24) (iv)
25) (v)
26) (i)
27) (ii)
28) (iv)
29) (iii)
30) (i)
31) (ii)
32) (ii)
33) (v)
34) (ii)
35) (v)
36) (i)
37) (ii)
38) (iii)
39) (iv)
40) (i)
41) (i)
42) (ii)
43) (iii)
44) (ii)
45) (v)
46) (v)
47) (iv)
48) (v)
49) (v)
50) (iv)
51) (v)
52) (ii)
53) (v)
54) (iv)
55) (iii)
56) (ii)
57) (iii)
58) (iv)
59) (iii)
60) (iii)
61) (iii)
62) (iii)
63) (i)
64) (iii)
65) (i)
66) (i)
67) (v)
68) (iv)
