EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GK
=
(i)
GJ
(ii)
GH
2
(iii)
IG
2
(iv)
HI
(v)
HI
2
Question
2
2.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
CA
2
(ii)
AB
2
(iii)
BC
2
(iv)
BC
(v)
AE
Question
3
3.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GJ
=
(i)
GH
(ii)
JH
(iii)
GK
(iv)
KI
(v)
IG
Question
4
4.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
KI
=
(i)
HK
(ii)
LJ
(iii)
HI
(iv)
HL
(v)
JH
Question
5
5.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JN
=
(i)
JK
(ii)
LJ
(iii)
JM
(iv)
MK
(v)
NL
Question
6
6.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
MK
=
(i)
IM
(ii)
KI
(iii)
LJ
(iv)
IL
(v)
IJ
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
not similar
(ii)
SAS Similarity
(iii)
AAA Similarity
(iv)
SSS Similarity
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
AAA Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
AAA Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
10
10.
In the given figure, △FGH and △TUV are such that
∠G
=
∠U
and
FG
TU
=
GH
UV
.
Identify the property by which the two triangles are similar
(i)
SSS Similarity
(ii)
SAS Similarity
(iii)
AAA Similarity
(iv)
not similar
Question
11
11.
In the given figure, △EFG and △QRS are such that
∠F
=
∠R
and
∠G
=
∠S
.
Identify the property by which the two triangles are similar
(i)
SSS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SAS Similarity
Question
12
12.
In the given figure, △BCD and △TUV are such that
BC
TU
=
CD
UV
=
DB
VT
.
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,
JK
∥
HI
.
If
GJ
JH
=
3
4
and
GI
=
15.4 cm
, find
GK
(i)
5.60 cm
(ii)
8.60 cm
(iii)
6.60 cm
(iv)
4.60 cm
(v)
7.60 cm
Question
14
14.
In the given figure,
MN
∥
KL
.
If
JM
=
7.4 cm
,
JK
=
14.8 cm
and
JL
=
13.6 cm
, find
JN
(i)
8.80 cm
(ii)
4.80 cm
(iii)
5.80 cm
(iv)
6.80 cm
(v)
7.80 cm
Question
15
15.
In the given figure, PQ ∥ CD and BP = 13.2 cm, BC = 22 cm and PQ = 12 cm, find CD
(i)
18.0 cm
(ii)
20.0 cm
(iii)
19.0 cm
(iv)
21.0 cm
(v)
22.0 cm
Question
16
16.
In the given figure, △DEF is isosceles right-angled at E and EG ⟂ FD. ∠F =
(i)
∠I
(ii)
∠H
(iii)
∠D
(iv)
∠E
(v)
∠G
Question
17
17.
In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠QSP =
(i)
∠PQS
(ii)
∠SQR
(iii)
∠SPQ
(iv)
∠QRS
(v)
∠PQR
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)
△DAE
(ii)
△ABH
(iii)
△ACF
(iv)
△DCF
(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)
∠FEH
(ii)
∠FDA
(iii)
∠HFE
(iv)
∠AFD
(v)
∠HAB
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)
∠EHF
(ii)
∠ABH
(iii)
∠FEH
(iv)
∠DAF
(v)
∠ACF
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.
∠EHF =
(i)
∠AFD
(ii)
∠HFE
(iii)
∠CFA
(iv)
∠DAF
(v)
∠BHA
Question
22
22.
In the given figure, MNOP is a trapezium in which
MN ∥ OP
and the diagonals
NP
and
MO
intersect at
Q
.
If
QM
=
(
x
+
24
)
cm,
NQ
=
(
x
+
17
)
cm,
QO
=
(
x
+
11
)
cm and
PQ
=
(
x
+
5
)
cm, find the value of x
(i)
(
69
,
67
)
(ii)
(
68
,
68
)
(iii)
(
67
,
67
)
(iv)
(
69
,
69
)
(v)
(
67
,
66
)
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)
△RPQ
(ii)
△ROP
(iii)
△RQN
(iv)
△QNO
(v)
△OPQ
Question
24
24.
In the given figure, the altitudes NF and GO of △EFG meet at M. △OFG ∼
(i)
△NGF
(ii)
△MON
(iii)
△OFM
(iv)
△NGM
(v)
△MFG
Question
25
25.
In the given figure, the altitudes TB and CU of △ABC meet at S. ∠CTS =
(i)
∠BSU
(ii)
∠UBS
(iii)
∠SCT
(iv)
∠TSC
(v)
∠SUB
Question
26
26.
In the given figure, PQ ∥ CD , and median BE bisects PQ.
If BC = 18 cm, BP = 9 cm and BF = 8.95 cm, BE =
(i)
18.90 cm
(ii)
17.90 cm
(iii)
16.90 cm
(iv)
19.90 cm
(v)
15.90 cm
Question
27
27.
In the given figure, ST ∥ IJ , and median HK bisects ST.
If HK = 14.5 cm, HL = 7.91 cm and HT = 9.27 cm, HJ =
(i)
19.00 cm
(ii)
16.00 cm
(iii)
17.00 cm
(iv)
18.00 cm
(v)
15.00 cm
Question
28
28.
In the given figure, QR ∥ EF , and median DG bisects QR.
△DEG ∼
(i)
△DEF
(ii)
△EFD
(iii)
△DHR
(iv)
△DGF
(v)
△DQH
Question
29
29.
In the given figure, △CDE is a triangle in which CF is the internal bisector of ∠C and EG ∥ FC meeting DC produced at G . ∠ECF =
(i)
∠FCD
(ii)
∠DFC
(iii)
∠GCE
(iv)
∠CFE
(v)
∠FEC
Question
30
30.
In the given figure, G and H are points on the sides DE and DF respectively of △DEF.For which of the following cases, GH ∥ EF
a)
DE = 19 cm, DG = 10.64 cm, DF = 15 cm and HF = 8.18 cm
b)
DE = 19 cm, GE = 10.36 cm, DF = 15 cm and DH = 6.82 cm
c)
DE = 19 cm, GE = 10.36 cm, DH = 8.82 cm and DF = 15 cm
d)
DG = 8.64 cm, GE = 10.36 cm, DH = 6.82 cm and HF = 8.18 cm
(i)
{a,b}
(ii)
{a,c,b}
(iii)
{a,d,b}
(iv)
{c,d}
(v)
{b,d}
Question
31
31.
Which of the following are true?
a)
Any two circles are similar.
b)
Any two triangles are similar.
c)
Any two triangles are congruent.
d)
Any two squares are congruent.
e)
Any two circles are congruent.
f)
Any two squares are similar.
(i)
{c,f}
(ii)
{b,f,a}
(iii)
{a,f}
(iv)
{d,e,a}
(v)
{b,a}
Question
32
32.
Which of the following are true?
a)
A square is a polygonal region.
b)
A sector is a polygonal region.
c)
A circle is a polygonal region.
d)
A triangle is a polygonal region.
e)
A semi-circle is a polygonal region.
(i)
{c,d}
(ii)
{b,a}
(iii)
{e,b,a}
(iv)
{a,d}
(v)
{c,d,a}
Question
33
33.
Which of the following are true?
a)
Similar figures have same area.
b)
If two figures are similar, then they are congruent too.
c)
If two figures are congruent, then they are similar too.
d)
Similar and congruent are not synonymous.
e)
Congruent figures have same area.
(i)
{a,b,e}
(ii)
{b,d}
(iii)
{a,c,d}
(iv)
{c,d,e}
(v)
{a,c}
Question
34
34.
Which of the following are true?
a)
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.
b)
Area of the union of two polygonal region is not equal to the sum of the individual area.
c)
Area of the union of two polygonal region is the sum of the individual area.
d)
A polygonal region can be divided into a finite number of triangles in a unique way.
(i)
{c,a}
(ii)
{d,b}
(iii)
{c,d,a}
(iv)
{c,b,a}
(v)
{a,b}
Question
35
35.
Which of the following are necessary conditions for similarity of two polygons ?
a)
The corresponding sides are equal.
b)
The corresponding angles are equal.
c)
The corresponding sides are proportional.
d)
The corresponding angles are proportional.
(i)
{a,c,b}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{a,d,b}
(v)
{d,c}
Question
36
36.
Which of the following are true?
a)
Similarity is anti symmetric.
b)
Similarity is transitive.
c)
Similarity is symmetric.
d)
Similarity is reflexive.
(i)
{a,c}
(ii)
{a,b,c}
(iii)
{b,c,d}
(iv)
{a,d}
(v)
{a,b}
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 triangles are similar if the corresponding angles are equal.
d)
Any two quadrilaterals are similar if the corresponding sides are proportional.
(i)
{a,c,d}
(ii)
{b,c}
(iii)
{b,d}
(iv)
{b,a}
(v)
{b,a,c}
Question
38
38.
In the given figure, the area of the △MNO is x sq.cm. P,Q,R are the mid-points of the sides NO , OM and MN respectively. The area of the △PQR is
(i)
3
4
of area of △MNO
(ii)
2
3
of area of △MNO
(iii)
1
2
of area of △MNO
(iv)
1
4
of area of △MNO
(v)
1
3
of area of △MNO
Question
39
39.
In the given figure, the parallelogram HIJK and the triangle △LHI are on the same bases and between the same parallels.
The area of the
△LHI
is x sq.cm. The area of the parallelogram is
(i)
5
4
the area of the triangle
(ii)
3
2
the area of the triangle
(iii)
thrice
the area of the triangle
(iv)
4
3
the area of the triangle
(v)
twice
the area of the triangle
Question
40
40.
In the given △BCD, EF ∥ CD. If BE : EC = 9 cm : 9 cm and BD = 19 cm, BF =
(i)
10.50 cm
(ii)
11.50 cm
(iii)
9.50 cm
(iv)
8.50 cm
(v)
7.50 cm
Question
41
41.
In the given two similar triangles, if c = 16 cm, d = 17 cm, e = 19 cm, f = 9.6 cm, find g
(i)
11.20 cm
(ii)
10.20 cm
(iii)
8.20 cm
(iv)
9.20 cm
(v)
12.20 cm
Question
42
42.
In the given figure, given ∠IFG = ∠HFI, x : y = 10.56 cm : 8.44 cm and p = 20 cm, find q =
(i)
15.00 cm
(ii)
17.00 cm
(iii)
14.00 cm
(iv)
18.00 cm
(v)
16.00 cm
Question
43
43.
In the given figure, given ∠FCD = ∠ECF, p = 8.5 cm, q = 9.5 cm and DE = 18 cm, find FE =
(i)
7.50 cm
(ii)
10.50 cm
(iii)
11.50 cm
(iv)
8.50 cm
(v)
9.50 cm
Question
44
44.
In the given figure, FGHI is a trapezium where OG = 12 cm , OH = 4 cm and OI = 4 cm . Find OF =
(i)
10 cm
(ii)
13 cm
(iii)
11 cm
(iv)
14 cm
(v)
12 cm
Question
45
45.
In the given figure, ∠KHI = 40.73°, find the value of x =
(i)
49.27°
(ii)
47.27°
(iii)
48.27°
(iv)
50.27°
(v)
51.27°
Question
46
46.
In the given figure, ∠CDE = 46.87°, find the value of y =
(i)
41.13°
(ii)
44.13°
(iii)
45.13°
(iv)
42.13°
(v)
43.13°
Question
47
47.
In the given figure, if HI ∥ JK then
(i)
△HIL ∼ △LJK
(ii)
△LIH ∼ △LKJ
(iii)
△HIL ∼ △KJL
(iv)
△HIL ∼ △LKJ
(v)
△LHI ∼ △LJK
Question
48
48.
In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If BC = 17 cm, BD = 11.65 cm, then find AB.
(i)
16.00 cm
(ii)
17.00 cm
(iii)
15.00 cm
(iv)
14.00 cm
(v)
18.00 cm
Question
49
49.
In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If GJ = 11.7 cm, JI = 13.1 cm, then find HJ.
(i)
10.38 cm
(ii)
13.38 cm
(iii)
12.38 cm
(iv)
14.38 cm
(v)
11.38 cm
Question
50
50.
In the given figure, △BCD ∼ △QRS and BC = 15 cm, QR = 21 cm.
If the area of the
△QRS
=
132.72 sq.cm
, find the area of the
△BCD
(i)
65.71 sq.cm
(ii)
67.71 sq.cm
(iii)
69.71 sq.cm
(iv)
66.71 sq.cm
(v)
68.71 sq.cm
Question
51
51.
In the given figure, △ABC ∼ △NOP and BC = 12 cm , OP = 16.8 cm and
AD
=
12.05 cm
,
find the area of the
△NOP
(i)
141.72 sq.cm
(ii)
142.72 sq.cm
(iii)
143.72 sq.cm
(iv)
140.72 sq.cm
(v)
139.72 sq.cm
Question
52
52.
In the given figure, △EFG & △QRS are similar triangles. If the ratio of the heights EH : QT = 13 : 18, then the ratio of their areas is
(i)
169
sq.cm
:
322
sq.cm
(ii)
169
sq.cm
:
327
sq.cm
(iii)
170
sq.cm
:
324
sq.cm
(iv)
168
sq.cm
:
324
sq.cm
(v)
169
sq.cm
:
324
sq.cm
Question
53
53.
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
=
1
3
area of
△MNO
b)
Area of trapezium
KLNO
is
1
4
the area of
△JKL
c)
Area of △JKL = 4 times area of △MNO
d)
Area of trapezium KLNO is thrice the area of △JON
e)
All four small triangles have equal areas
(i)
{b,d}
(ii)
{a,c,d}
(iii)
{c,d,e}
(iv)
{a,b,e}
(v)
{a,c}
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)
△LHJ ∼ △GHI
b)
△KJI ∼ △GHI
c)
△JKL ∼ △GHI
d)
△GLK ∼ △GHI
e)
△JLK ∼ △GHI
(i)
{e,d,a}
(ii)
{e,a}
(iii)
{e,b}
(iv)
{e,c}
(v)
{a,b,c,d}
Question
55
55.
The perimeters of two similar triangles are 27 cm and 16 cm respectively. If one side of the first triangle is 13 cm, find the length of the corresponding side of the second triangle.
(i)
7.70 cm
(ii)
9.70 cm
(iii)
8.70 cm
(iv)
5.70 cm
(v)
6.70 cm
Question
56
56.
In the given figure, H is a point on side FG of △EFG such that ∠GEF = ∠EHG = 101° , ∠HGE = 26°. Find ∠GEH
(i)
51°
(ii)
53°
(iii)
54°
(iv)
55°
(v)
52°
Question
57
57.
JKLM is a square and △JKN is an equilateral triangle. Also, △JLO is an equilateral triangle. If area of △JKN is 'a' sq.units, then the area of △JLO is
(i)
√
3
a sq.units
(ii)
1
2
√
3
a sq.units
(iii)
2a sq.units
(iv)
1
2
a sq.units
(v)
a
2
sq.units
Question
58
58.
HIJK is a cyclic trapezium. Diagonals IK and HJ intersect at L. If KH = 16 cm, find IJ
(i)
16 cm
(ii)
15 cm
(iii)
18 cm
(iv)
14 cm
(v)
17 cm
Question
59
59.
A vertical stick
14 m
long casts a shadow of
11 m
long on the ground.
At the same time, a tower casts the shadow
88 m
long on the ground.
Find the height of the tower.
(i)
114 m
(ii)
110 m
(iii)
112 m
(iv)
113 m
(v)
111 m
Question
60
60.
In the given figure, △ABC, ST ∥ BC such that
area of
△AST
= area of
STCB
. Find
AS
AB
(i)
1
2
√
5
(ii)
1
(iii)
1
2
√
2
(iv)
1
2
4
√
2
(v)
1
2
√
1
2
Question
61
61.
In the given figure, ∠NKL = ∠MKN and KN ∥ OM and KL = 15 cm, LN = 7 cm and NM = 9 cm. Find KO
(i)
19.29 cm
(ii)
18.29 cm
(iii)
20.29 cm
(iv)
21.29 cm
(v)
17.29 cm
Question
62
62.
In the given figure, FH is the angular bisector of
∠F
&
∠H
EF
=
20 cm
,
FG
=
21 cm
and
GH
=
18 cm
.
Find
HE
(i)
19.14 cm
(ii)
16.14 cm
(iii)
18.14 cm
(iv)
15.14 cm
(v)
17.14 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 = AB . BC . CA
(ii)
AD . BE . CF = DB . EC . FA
(iii)
AD . BE . CF = OD . OE . OF
(iv)
AD . BE . CF = OA . OB . OC
(v)
AD . BE . CF = DE . EF . FD
Question
64
64.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 28 cm. Find AP
(i)
12.20 cm
(ii)
11.20 cm
(iii)
10.20 cm
(iv)
13.20 cm
(v)
9.20 cm
Question
65
65.
From the given figure and values, find x
(i)
(
19
,
-3
)
(ii)
(
19
,
-2
)
(iii)
(
21
,
-2
)
(iv)
(
20
,
-1
)
(v)
(
0
,
21
)
Question
66
66.
The ratio of the bases of two triangles ABC and DEF is
10
:
3
.
If the triangles are equal in area, then the ratio of their heights is
(i)
10
:
1
(ii)
11
:
3
(iii)
10
:
6
(iv)
9
:
3
(v)
3
:
10
Question
67
67.
If the measures are as shown in the given figure, find FG
(i)
27.0 cm
(ii)
26.0 cm
(iii)
25.0 cm
(iv)
24.0 cm
(v)
23.0 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 = 21 cm
and radius of the inner circle is
5.5 cm
.
Find the radius of the outer circle.
(i)
12.83 cm
(ii)
10.83 cm
(iii)
11.83 cm
(iv)
13.83 cm
(v)
14.83 cm
Assignment Key
1) (iii)
2) (ii)
3) (ii)
4) (i)
5) (v)
6) (i)
7) (ii)
8) (ii)
9) (i)
10) (ii)
11) (iii)
12) (ii)
13) (iii)
14) (iv)
15) (ii)
16) (iii)
17) (v)
18) (v)
19) (v)
20) (iii)
21) (iv)
22) (iii)
23) (i)
24) (i)
25) (v)
26) (ii)
27) (iii)
28) (v)
29) (i)
30) (v)
31) (iii)
32) (iv)
33) (iv)
34) (v)
35) (ii)
36) (iii)
37) (i)
38) (iv)
39) (v)
40) (iii)
41) (ii)
42) (v)
43) (v)
44) (v)
45) (i)
46) (v)
47) (iii)
48) (i)
49) (iii)
50) (ii)
51) (i)
52) (v)
53) (iii)
54) (v)
55) (i)
56) (ii)
57) (iii)
58) (i)
59) (iii)
60) (iii)
61) (i)
62) (v)
63) (ii)
64) (ii)
65) (ii)
66) (v)
67) (iii)
68) (i)
