EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
BC
(ii)
BC
2
(iii)
CA
2
(iv)
AD
(v)
AB
2
Question
2
2.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BE
=
(i)
CD
2
(ii)
BC
2
(iii)
DB
2
(iv)
BF
(v)
CD
Question
3
3.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
HK
=
(i)
HL
(ii)
HI
(iii)
JH
(iv)
KI
(v)
LJ
Question
4
4.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
MK
=
(i)
JK
(ii)
NL
(iii)
JN
(iv)
LJ
(v)
JM
Question
5
5.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BF
=
(i)
FD
(ii)
DB
(iii)
BE
(iv)
EC
(v)
BC
Question
6
6.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
MK
=
(i)
KI
(ii)
LJ
(iii)
IM
(iv)
IL
(v)
IJ
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
not similar
(iii)
SAS Similarity
(iv)
AAA Similarity
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
AAA Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
not similar
(ii)
SSS Similarity
(iii)
AAA Similarity
(iv)
SAS Similarity
Question
10
10.
In the given figure, △CDE and △UVW are such that
∠D
=
∠V
and
CD
UV
=
DE
VW
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
SSS Similarity
(iii)
SAS Similarity
(iv)
AAA Similarity
Question
11
11.
In the given figure, △CDE and △QRS are such that
∠D
=
∠R
and
∠E
=
∠S
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
SAS Similarity
(iii)
SSS Similarity
(iv)
AAA Similarity
Question
12
12.
In the given figure, △ABC and △UVW are such that
AB
UV
=
BC
VW
=
CA
WU
.
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
=
1
1
and
JL
=
15.6 cm
, find
JN
(i)
9.80 cm
(ii)
5.80 cm
(iii)
7.80 cm
(iv)
8.80 cm
(v)
6.80 cm
Question
14
14.
In the given figure,
QR
∥
OP
.
If
NQ
=
4.46 cm
,
NO
=
10.4 cm
and
NP
=
10.6 cm
, find
NR
(i)
2.54 cm
(ii)
6.54 cm
(iii)
3.54 cm
(iv)
4.54 cm
(v)
5.54 cm
Question
15
15.
In the given figure, ST ∥ EF and DT = 12 cm, DF = 20 cm and ST = 13.8 cm, find EF
(i)
25.0 cm
(ii)
21.0 cm
(iii)
22.0 cm
(iv)
24.0 cm
(v)
23.0 cm
Question
16
16.
In the given figure, △BCD is isosceles right-angled at C and CE ⟂ DB. ∠B =
(i)
∠F
(ii)
∠G
(iii)
∠E
(iv)
∠C
(v)
∠D
Question
17
17.
In the given figure, △CDE is isosceles right-angled at D and DF ⟂ EC. ∠CDE =
(i)
∠DFC
(ii)
∠FCD
(iii)
∠FDE
(iv)
∠DEF
(v)
∠CDF
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.
△FDA ∼
(i)
△DAE
(ii)
△DCF
(iii)
△FEH
(iv)
△ACF
(v)
△ABH
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)
∠FEH
(ii)
∠HAB
(iii)
∠FDA
(iv)
∠AFD
(v)
∠FAC
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)
∠FDA
(ii)
∠FEH
(iii)
∠ABH
(iv)
∠EHF
(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.
∠DAF =
(i)
∠AFD
(ii)
∠CFA
(iii)
∠EHF
(iv)
∠BHA
(v)
∠HFE
Question
22
22.
In the given figure, LMNO is a trapezium in which
LM ∥ NO
and the diagonals
MO
and
LN
intersect at
P
.
If
PL
=
(
x
+
48
)
cm,
MP
=
(
3
x
+
18
)
cm,
PN
=
(
x
+
26
)
cm and
OP
=
(
2
x
+
31
)
cm, find the value of x
(i)
(
52
,
-19
)
(ii)
(
51
,
-20
)
(iii)
(
53
,
-20
)
(iv)
(
-18
,
53
)
(v)
(
51
,
-21
)
Question
23
23.
In the given figure, IJKL is a trapezium in which
IJ ∥ KL
and the diagonals
JL
and
IK
intersect at
M
.
△MKL
∼
(i)
△MIJ
(ii)
△MJK
(iii)
△JKL
(iv)
△MLI
(v)
△LIJ
Question
24
24.
In the given figure, the altitudes MC and DN of △BCD meet at L. △LCD ∼
(i)
△MDL
(ii)
△LNM
(iii)
△MDC
(iv)
△NCD
(v)
△NCL
Question
25
25.
In the given figure, the altitudes PI and JQ of △HIJ meet at O. ∠OJP =
(i)
∠OQI
(ii)
∠IOQ
(iii)
∠JPO
(iv)
∠QIO
(v)
∠POJ
Question
26
26.
In the given figure, TU ∥ DE , and median CF bisects TU.
If CD = 16 cm, CF = 15.9 cm and CT = 5.33 cm, TD =
(i)
10.67 cm
(ii)
9.67 cm
(iii)
11.67 cm
(iv)
12.67 cm
(v)
8.67 cm
Question
27
27.
In the given figure, TU ∥ IJ , and median HK bisects TU.
If HJ = 18 cm, HL = 8.8 cm and HU = 12 cm, HK =
(i)
11.20 cm
(ii)
13.20 cm
(iii)
15.20 cm
(iv)
12.20 cm
(v)
14.20 cm
Question
28
28.
In the given figure, QR ∥ DE , and median CF bisects QR.
△CGR ∼
(i)
△DEC
(ii)
△CDE
(iii)
△CFE
(iv)
△CQG
(v)
△CDF
Question
29
29.
In the given figure, △HIJ is a triangle in which HK is the internal bisector of ∠H and JL ∥ KH meeting IH produced at L . ∠HJL =
(i)
∠IKH
(ii)
∠KHI
(iii)
∠HKJ
(iv)
∠KJH
(v)
∠LHJ
Question
30
30.
In the given figure, J and K are points on the sides GH and GI respectively of △GHI.For which of the following cases, JK ∥ HI
a)
GH = 16 cm, GJ = 10 cm, GI = 18 cm and KI = 9 cm
b)
GJ = 8 cm, JH = 8 cm, GK = 9 cm and KI = 9 cm
c)
GH = 16 cm, JH = 8 cm, GI = 18 cm and GK = 9 cm
d)
GH = 16 cm, JH = 8 cm, GK = 11 cm and GI = 18 cm
(i)
{d,c}
(ii)
{a,c,b}
(iii)
{b,c}
(iv)
{a,d,b}
(v)
{a,b}
Question
31
31.
Which of the following are true?
a)
Any two circles are similar.
b)
Any two squares are congruent.
c)
Any two triangles are similar.
d)
Any two squares are similar.
e)
Any two circles are congruent.
f)
Any two triangles are congruent.
(i)
{a,d}
(ii)
{e,f,a}
(iii)
{c,d}
(iv)
{b,d,a}
(v)
{b,a}
Question
32
32.
Which of the following are true?
a)
A square is a polygonal region.
b)
A circle is a polygonal region.
c)
A sector is a polygonal region.
d)
A semi-circle is a polygonal region.
e)
A triangle is a polygonal region.
(i)
{b,a}
(ii)
{c,e}
(iii)
{a,e}
(iv)
{d,b,a}
(v)
{c,e,a}
Question
33
33.
Which of the following are true?
a)
Congruent figures have same area.
b)
If two figures are similar, then they are congruent too.
c)
Similar and congruent are not synonymous.
d)
If two figures are congruent, then they are similar too.
e)
Similar figures have same area.
(i)
{b,e,d}
(ii)
{b,a,c}
(iii)
{b,a}
(iv)
{a,c,d}
(v)
{e,c}
Question
34
34.
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)
{a,b}
(iii)
{d,b}
(iv)
{c,d,a}
(v)
{c,b,a}
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 proportional.
c)
The corresponding sides are proportional.
d)
The corresponding angles are equal.
(i)
{a,c}
(ii)
{b,d}
(iii)
{a,b,c}
(iv)
{a,d,c}
(v)
{c,d}
Question
36
36.
Which of the following are true?
a)
Similarity is symmetric.
b)
Similarity is transitive.
c)
Similarity is anti symmetric.
d)
Similarity is reflexive.
(i)
{c,d}
(ii)
{a,b,d}
(iii)
{c,a,b}
(iv)
{c,a}
(v)
{c,b}
Question
37
37.
Which of the following are true?
a)
Any two quadrilaterals are similar if the corresponding sides are proportional.
b)
Any two triangles 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 angles are equal.
(i)
{d,b}
(ii)
{d,a,b}
(iii)
{d,c}
(iv)
{a,b,c}
(v)
{d,a}
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
3
of area of △IJK
(iii)
2
3
of area of △IJK
(iv)
1
2
of area of △IJK
(v)
3
4
of area of △IJK
Question
39
39.
In the given figure, the parallelogram KLMN and the triangle △OKL are on the same bases and between the same parallels.
The area of the
△OKL
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 △BCD, EF ∥ CD. If BE : EC = 8.5 cm : 8.5 cm and BD = 20 cm, BF =
(i)
10.00 cm
(ii)
9.00 cm
(iii)
8.00 cm
(iv)
11.00 cm
(v)
12.00 cm
Question
41
41.
In the given two similar triangles, if j = 18 cm, k = 18 cm, l = 17 cm, m = 10.8 cm, find n
(i)
10.80 cm
(ii)
8.80 cm
(iii)
11.80 cm
(iv)
12.80 cm
(v)
9.80 cm
Question
42
42.
In the given figure, given ∠HEF = ∠GEH, x : y = 10 cm : 9 cm and p = 20 cm, find q =
(i)
17.00 cm
(ii)
18.00 cm
(iii)
20.00 cm
(iv)
16.00 cm
(v)
19.00 cm
Question
43
43.
In the given figure, given ∠IFG = ∠HFI, p = 7.77 cm, q = 8.23 cm and GH = 16 cm, find GI =
(i)
7.77 cm
(ii)
6.77 cm
(iii)
8.77 cm
(iv)
9.77 cm
(v)
5.77 cm
Question
44
44.
In the given figure, BCDE is a trapezium where OB = 12 cm , OC = 12 cm and OE = 4 cm . Find OD =
(i)
3 cm
(ii)
4 cm
(iii)
6 cm
(iv)
2 cm
(v)
5 cm
Question
45
45.
In the given figure, ∠CDF = 43.38°, find the value of x =
(i)
45.62°
(ii)
47.62°
(iii)
46.62°
(iv)
44.62°
(v)
48.62°
Question
46
46.
In the given figure, ∠IGH = 43.62°, find the value of y =
(i)
45.38°
(ii)
47.38°
(iii)
48.38°
(iv)
44.38°
(v)
46.38°
Question
47
47.
In the given figure, if BC ∥ DE then
(i)
△BCF ∼ △FDE
(ii)
△BCF ∼ △EDF
(iii)
△FBC ∼ △FDE
(iv)
△FCB ∼ △FED
(v)
△BCF ∼ △FED
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)
17.00 cm
(ii)
14.00 cm
(iii)
13.00 cm
(iv)
16.00 cm
(v)
15.00 cm
Question
49
49.
In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. If IL = 10.3 cm, LK = 14.6 cm, then find JL.
(i)
11.26 cm
(ii)
10.26 cm
(iii)
13.26 cm
(iv)
12.26 cm
(v)
14.26 cm
Question
50
50.
In the given figure, △CDE ∼ △OPQ and CD = 13 cm, OP = 18.2 cm.
If the area of the
△OPQ
=
125.56 sq.cm
, find the area of the
△CDE
(i)
64.06 sq.cm
(ii)
65.06 sq.cm
(iii)
63.06 sq.cm
(iv)
62.06 sq.cm
(v)
66.06 sq.cm
Question
51
51.
In the given figure, △DEF ∼ △PQR and EF = 15 cm , QR = 21 cm and
PS
=
11.96 cm
,
find the area of the
△DEF
(i)
62.06 sq.cm
(ii)
63.06 sq.cm
(iii)
65.06 sq.cm
(iv)
66.06 sq.cm
(v)
64.06 sq.cm
Question
52
52.
In the given figure, △BCD & △QRS are similar triangles. If the ratio of the heights BE : QT = 8 : 11, then the ratio of their areas is
(i)
64
sq.cm
:
124
sq.cm
(ii)
65
sq.cm
:
121
sq.cm
(iii)
64
sq.cm
:
121
sq.cm
(iv)
64
sq.cm
:
118
sq.cm
(v)
63
sq.cm
:
121
sq.cm
Question
53
53.
In the given figure, points F , G and H are the mid-points of sides DE, EC and CD of △CDE. Which of the following are true?
a)
Area of
△CDE
=
1
3
area of
△FGH
b)
Area of trapezium
DEGH
is
1
4
the area of
△CDE
c)
Area of △CDE = 4 times area of △FGH
d)
Area of trapezium DEGH is thrice the area of △CHG
e)
All four small triangles have equal areas
(i)
{b,d}
(ii)
{c,d,e}
(iii)
{a,c,d}
(iv)
{a,b,e}
(v)
{a,c}
Question
54
54.
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)
△HML ∼ △HIJ
b)
△MIK ∼ △HIJ
c)
△KML ∼ △HIJ
d)
△KLM ∼ △HIJ
e)
△LKJ ∼ △HIJ
(i)
{c,b}
(ii)
{c,a}
(iii)
{a,b,d,e}
(iv)
{c,d}
(v)
{c,e,a}
Question
55
55.
The perimeters of two similar triangles are 35 cm and 22 cm respectively. If one side of the first triangle is 10 cm, find the length of the corresponding side of the second triangle.
(i)
5.29 cm
(ii)
4.29 cm
(iii)
8.29 cm
(iv)
7.29 cm
(v)
6.29 cm
Question
56
56.
In the given figure, I is a point on side GH of △FGH such that ∠HFG = ∠FIH = 108° , ∠IHF = 30°. Find ∠HFI
(i)
40°
(ii)
41°
(iii)
44°
(iv)
43°
(v)
42°
Question
57
57.
LMNO is a square and △LMP is an equilateral triangle. Also, △LNQ is an equilateral triangle. If area of △LMP is 'a' sq.units, then the area of △LNQ is
(i)
a
2
sq.units
(ii)
1
2
√
3
a sq.units
(iii)
1
2
a sq.units
(iv)
2a sq.units
(v)
√
3
a sq.units
Question
58
58.
IJKL is a cyclic trapezium. Diagonals JL and IK intersect at M. If LI = 15 cm, find JK
(i)
14 cm
(ii)
15 cm
(iii)
13 cm
(iv)
17 cm
(v)
16 cm
Question
59
59.
A vertical stick
16 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)
129 m
(ii)
128 m
(iii)
130 m
(iv)
127 m
(v)
126 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
4
√
2
(ii)
1
(iii)
1
2
√
5
(iv)
1
2
√
1
2
(v)
1
2
√
2
Question
61
61.
In the given figure, ∠LIJ = ∠KIL and IL ∥ MK and IJ = 18 cm, JL = 9 cm and LK = 8 cm. Find IM
(i)
15.00 cm
(ii)
17.00 cm
(iii)
16.00 cm
(iv)
14.00 cm
(v)
18.00 cm
Question
62
62.
In the given figure, GI is the angular bisector of
∠G
&
∠I
FG
=
20 cm
,
GH
=
20 cm
and
HI
=
18 cm
.
Find
IF
(i)
19.00 cm
(ii)
20.00 cm
(iii)
17.00 cm
(iv)
16.00 cm
(v)
18.00 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 = OD . OE . OF
(ii)
AD . BE . CF = DE . EF . FD
(iii)
AD . BE . CF = OA . OB . OC
(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 = 28 cm and AP = 11 cm. Find PB
(i)
16.00 cm
(ii)
15.00 cm
(iii)
17.00 cm
(iv)
19.00 cm
(v)
18.00 cm
Question
65
65.
From the given figure and values, find x
(i)
(
(
-1
4
)
,
11
)
(ii)
(
(
-1
4
)
,
12
)
(iii)
(
14
,
3
4
)
(iv)
(
1
4
,
12
)
(v)
(
(
-1
6
)
,
13
)
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)
6
:
7
(iii)
5
:
10
(iv)
6
:
13
(v)
7
:
10
Question
67
67.
If the measures are as shown in the given figure, find CD
(i)
22.0 cm
(ii)
20.0 cm
(iii)
18.0 cm
(iv)
21.0 cm
(v)
19.0 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 = 10 cm
,
OY = 23 cm
and radius of the inner circle is
5.7 cm
.
Find the radius of the outer circle.
(i)
12.11 cm
(ii)
15.11 cm
(iii)
14.11 cm
(iv)
11.11 cm
(v)
13.11 cm
Assignment Key
1) (iii)
2) (ii)
3) (iv)
4) (v)
5) (i)
6) (iii)
7) (iii)
8) (ii)
9) (ii)
10) (iii)
11) (iv)
12) (iv)
13) (iii)
14) (iv)
15) (v)
16) (v)
17) (i)
18) (iii)
19) (iv)
20) (iii)
21) (iii)
22) (ii)
23) (i)
24) (ii)
25) (iv)
26) (i)
27) (ii)
28) (iii)
29) (ii)
30) (iii)
31) (i)
32) (iii)
33) (iv)
34) (ii)
35) (v)
36) (ii)
37) (iv)
38) (i)
39) (i)
40) (i)
41) (i)
42) (ii)
43) (i)
44) (ii)
45) (iii)
46) (v)
47) (ii)
48) (v)
49) (iv)
50) (i)
51) (v)
52) (iii)
53) (ii)
54) (iii)
55) (v)
56) (v)
57) (iv)
58) (ii)
59) (ii)
60) (v)
61) (iii)
62) (v)
63) (v)
64) (iii)
65) (ii)
66) (i)
67) (ii)
68) (v)
