EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CG
=
(i)
CF
(ii)
DE
(iii)
CD
2
(iv)
DE
2
(v)
EC
2
Question
2
2.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
IL
=
(i)
JK
(ii)
JK
2
(iii)
KI
2
(iv)
IJ
2
(v)
IM
Question
3
3.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FI
=
(i)
FG
(ii)
JH
(iii)
IG
(iv)
HF
(v)
FJ
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
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GK
=
(i)
JH
(ii)
IG
(iii)
GJ
(iv)
KI
(v)
GH
Question
6
6.
In the given figure
△IJK
,
L
is the mid-point of
IJ
and
LM
∥
JK
,
then
MK
=
(i)
LJ
(ii)
IM
(iii)
KI
(iv)
IJ
(v)
IL
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
not similar
(iii)
SAS Similarity
(iv)
SSS Similarity
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SAS Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
AAA Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
10
10.
In the given figure, △IJK and △STU are such that
∠J
=
∠T
and
IJ
ST
=
JK
TU
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
SSS Similarity
(iii)
AAA Similarity
(iv)
SAS Similarity
Question
11
11.
In the given figure, △CDE and △PQR are such that
∠D
=
∠Q
and
∠E
=
∠R
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
SAS Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
12
12.
In the given figure, △EFG and △STU are such that
EF
ST
=
FG
TU
=
GE
US
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
13
13.
In the given figure,
DE
∥
BC
.
If
AD
DB
=
5
3
and
AC
=
11.3 cm
, find
AE
(i)
6.06 cm
(ii)
9.06 cm
(iii)
5.06 cm
(iv)
7.06 cm
(v)
8.06 cm
Question
14
14.
In the given figure,
KL
∥
IJ
.
If
HK
=
7.38 cm
,
HI
=
12.3 cm
and
HJ
=
13.6 cm
, find
HL
(i)
10.16 cm
(ii)
6.16 cm
(iii)
7.16 cm
(iv)
8.16 cm
(v)
9.16 cm
Question
15
15.
In the given figure, PQ ∥ HI and GP = 14.4 cm, GH = 24 cm and HI = 22 cm, find PQ
(i)
15.2 cm
(ii)
11.2 cm
(iii)
12.2 cm
(iv)
13.2 cm
(v)
14.2 cm
Question
16
16.
In the given figure, △FGH is isosceles right-angled at G and GI ⟂ HF. ∠I =
(i)
∠J
(ii)
∠K
(iii)
∠F
(iv)
∠H
(v)
∠G
Question
17
17.
In the given figure, △MNO is isosceles right-angled at N and NP ⟂ OM. ∠OPN =
(i)
∠MNP
(ii)
∠NOP
(iii)
∠PNO
(iv)
∠PMN
(v)
∠MNO
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)
△ABH
(ii)
△FEH
(iii)
△DCF
(iv)
△DAE
(v)
△ACF
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.
∠HAB =
(i)
∠FEH
(ii)
∠FDA
(iii)
∠FAC
(iv)
∠AFD
(v)
∠HFE
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)
∠FEH
(ii)
∠ACF
(iii)
∠ABH
(iv)
∠DAF
(v)
∠EHF
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.
∠BHA =
(i)
∠AFD
(ii)
∠CFA
(iii)
∠HFE
(iv)
∠DAF
(v)
∠EHF
Question
22
22.
In the given figure, NOPQ is a trapezium in which
NO ∥ PQ
and the diagonals
OQ
and
NP
intersect at
R
.
If
RN
=
(
2
x
+
14
)
cm,
OR
=
(
x
+
51
)
cm,
RP
=
(
x
+
58
)
cm and
QR
=
(
x
+
37
)
cm, find the value of x
(i)
(
-38
,
61
)
(ii)
(
-40
,
60
)
(iii)
(
63
,
-38
)
(iv)
(
-40
,
61
)
(v)
(
-39
,
62
)
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)
△QNO
(ii)
△OPQ
(iii)
△RPQ
(iv)
△RQN
(v)
△ROP
Question
24
24.
In the given figure, the altitudes RE and FS of △DEF meet at Q. △RFE ∼
(i)
△QEF
(ii)
△QSR
(iii)
△SEQ
(iv)
△SEF
(v)
△RFQ
Question
25
25.
In the given figure, the altitudes OD and EP of △CDE meet at N. ∠PDN =
(i)
∠NEO
(ii)
∠EON
(iii)
∠NPD
(iv)
∠DNP
(v)
∠ONE
Question
26
26.
In the given figure, PQ ∥ FG , and median EH bisects PQ.
If EF = 17 cm, EH = 17 cm and EP = 9.27 cm, IH =
(i)
5.73 cm
(ii)
9.73 cm
(iii)
6.73 cm
(iv)
7.73 cm
(v)
8.73 cm
Question
27
27.
In the given figure, RS ∥ HI , and median GJ bisects RS.
If GJ = 14.5 cm, GK = 6.59 cm and GS = 8.18 cm, GI =
(i)
16.00 cm
(ii)
18.00 cm
(iii)
17.00 cm
(iv)
20.00 cm
(v)
19.00 cm
Question
28
28.
In the given figure, RS ∥ BC , and median AD bisects RS.
△ABD ∼
(i)
△ARE
(ii)
△ADC
(iii)
△ABC
(iv)
△BCA
(v)
△AES
Question
29
29.
In the given figure, △IJK is a triangle in which IL is the internal bisector of ∠I and KM ∥ LI meeting JI produced at M . ∠LIJ =
(i)
∠JLI
(ii)
∠IKM
(iii)
∠ILK
(iv)
∠LKI
(v)
∠MIK
Question
30
30.
In the given figure, E and F are points on the sides BC and BD respectively of △BCD.For which of the following cases, EF ∥ CD
a)
BC = 18 cm, BE = 12.8 cm, BD = 15 cm and FD = 6 cm
b)
BC = 18 cm, EC = 7.2 cm, BF = 11 cm and BD = 15 cm
c)
BE = 10.8 cm, EC = 7.2 cm, BF = 9 cm and FD = 6 cm
d)
BC = 18 cm, EC = 7.2 cm, BD = 15 cm and BF = 9 cm
(i)
{b,d}
(ii)
{a,c}
(iii)
{a,d,c}
(iv)
{a,b,c}
(v)
{c,d}
Question
31
31.
Which of the following are true?
a)
Any two squares are congruent.
b)
Any two circles are similar.
c)
Any two circles are congruent.
d)
Any two squares are similar.
e)
Any two triangles are similar.
f)
Any two triangles are congruent.
(i)
{a,d,b}
(ii)
{b,d}
(iii)
{a,b}
(iv)
{e,f,b}
(v)
{c,d}
Question
32
32.
Which of the following are true?
a)
A sector is a polygonal region.
b)
A triangle 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)
{b,e}
(ii)
{c,e}
(iii)
{d,a,b}
(iv)
{c,e,b}
(v)
{a,b}
Question
33
33.
Which of the following are true?
a)
Congruent figures have same area.
b)
Similar figures have same area.
c)
If two figures are congruent, then they are similar too.
d)
Similar and congruent are not synonymous.
e)
If two figures are similar, then they are congruent too.
(i)
{e,c}
(ii)
{a,c,d}
(iii)
{b,a}
(iv)
{b,a,c}
(v)
{b,e,d}
Question
34
34.
Which of the following are true?
a)
A polygonal region can be divided into a finite number of triangles in a unique way.
b)
Area of the union of two polygonal region is the sum of the individual area.
c)
Area of the union of two polygonal region is not equal to the sum of the individual area.
d)
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.
(i)
{a,c}
(ii)
{a,b,c}
(iii)
{a,d,c}
(iv)
{c,d}
(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 sides are proportional.
c)
The corresponding sides are equal.
d)
The corresponding angles are proportional.
(i)
{d,b}
(ii)
{c,d,a}
(iii)
{c,a}
(iv)
{c,b,a}
(v)
{a,b}
Question
36
36.
Which of the following are true?
a)
Similarity is transitive.
b)
Similarity is anti symmetric.
c)
Similarity is reflexive.
d)
Similarity is symmetric.
(i)
{b,d}
(ii)
{a,c,d}
(iii)
{b,a}
(iv)
{b,c}
(v)
{b,a,c}
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 quadrilaterals are similar if the corresponding sides are proportional.
d)
Any two triangles are similar if the corresponding sides are proportional.
(i)
{b,c}
(ii)
{b,a}
(iii)
{b,d}
(iv)
{a,c,d}
(v)
{b,a,c}
Question
38
38.
In the given figure, the area of the △KLM is x sq.cm. N,O,P are the mid-points of the sides LM , MK and KL respectively. The area of the △NOP is
(i)
1
4
of area of △KLM
(ii)
2
3
of area of △KLM
(iii)
1
2
of area of △KLM
(iv)
1
3
of area of △KLM
(v)
3
4
of area of △KLM
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)
4
3
the area of the triangle
(ii)
5
4
the area of the triangle
(iii)
thrice
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 △KLM, NO ∥ LM. If KN : NL = 9 cm : 9 cm and KM = 19 cm, OM =
(i)
7.50 cm
(ii)
11.50 cm
(iii)
9.50 cm
(iv)
8.50 cm
(v)
10.50 cm
Question
41
41.
In the given two similar triangles, if n = 19 cm, o = 18 cm, p = 15 cm, q = 11.4 cm, find r
(i)
9.80 cm
(ii)
10.80 cm
(iii)
11.80 cm
(iv)
8.80 cm
(v)
12.80 cm
Question
42
42.
In the given figure, given ∠IFG = ∠HFI, x : y = 8.64 cm : 10.36 cm and p = 15 cm, find q =
(i)
16.00 cm
(ii)
19.00 cm
(iii)
17.00 cm
(iv)
18.00 cm
(v)
20.00 cm
Question
43
43.
In the given figure, given ∠HEF = ∠GEH, p = 9.77 cm, q = 8.23 cm and FG = 18 cm, find FH =
(i)
9.77 cm
(ii)
10.77 cm
(iii)
11.77 cm
(iv)
8.77 cm
(v)
7.77 cm
Question
44
44.
In the given figure, HIJK is a trapezium where OH = 13 cm , OI = 13 cm and OK = 4 cm . Find OJ =
(i)
3 cm
(ii)
2 cm
(iii)
6 cm
(iv)
5 cm
(v)
4 cm
Question
45
45.
In the given figure, ∠KHI = 47.2°, find the value of x =
(i)
43.80°
(ii)
44.80°
(iii)
42.80°
(iv)
40.80°
(v)
41.80°
Question
46
46.
In the given figure, ∠LJK = 53.13°, find the value of y =
(i)
34.87°
(ii)
38.87°
(iii)
35.87°
(iv)
37.87°
(v)
36.87°
Question
47
47.
In the given figure, if CD ∥ EF then
(i)
△GCD ∼ △GEF
(ii)
△GDC ∼ △GFE
(iii)
△CDG ∼ △GEF
(iv)
△CDG ∼ △GFE
(v)
△CDG ∼ △FEG
Question
48
48.
In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If BC = 16 cm, CD = 15 cm, then find CE.
(i)
12.94 cm
(ii)
10.94 cm
(iii)
9.94 cm
(iv)
11.94 cm
(v)
8.94 cm
Question
49
49.
In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If KJ = 14.6 cm, IK = 12.26 cm, then find HK.
(i)
10.30 cm
(ii)
9.30 cm
(iii)
12.30 cm
(iv)
11.30 cm
(v)
8.30 cm
Question
50
50.
In the given figure, △BCD ∼ △MNO and BC = 14 cm, MN = 19.6 cm.
If the area of the
△MNO
=
107.1 sq.cm
, find the area of the
△BCD
(i)
56.64 sq.cm
(ii)
55.64 sq.cm
(iii)
52.64 sq.cm
(iv)
54.64 sq.cm
(v)
53.64 sq.cm
Question
51
51.
In the given figure, △DEF ∼ △PQR and EF = 11 cm , QR = 15.4 cm and
PS
=
18.71 cm
,
find the area of the
△DEF
(i)
71.48 sq.cm
(ii)
72.48 sq.cm
(iii)
73.48 sq.cm
(iv)
75.48 sq.cm
(v)
74.48 sq.cm
Question
52
52.
In the given figure, △CDE & △MNO are similar triangles. If the ratio of the heights CF : MP = 11 : 16, then the ratio of their areas is
(i)
121
sq.cm
:
258
sq.cm
(ii)
121
sq.cm
:
254
sq.cm
(iii)
122
sq.cm
:
256
sq.cm
(iv)
121
sq.cm
:
256
sq.cm
(v)
120
sq.cm
:
256
sq.cm
Question
53
53.
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)
Area of trapezium
HIKL
is
1
4
the area of
△GHI
b)
Area of △GHI = 4 times area of △JKL
c)
Area of trapezium HIKL is thrice the area of △GLK
d)
Area of
△GHI
=
1
3
area of
△JKL
e)
All four small triangles have equal areas
(i)
{a,b,c}
(ii)
{b,c,e}
(iii)
{a,b}
(iv)
{a,d,e}
(v)
{d,c}
Question
54
54.
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)
△MLK ∼ △IJK
b)
△NJL ∼ △IJK
c)
△LMN ∼ △IJK
d)
△LNM ∼ △IJK
e)
△INM ∼ △IJK
(i)
{d,e,a}
(ii)
{d,c}
(iii)
{d,b}
(iv)
{a,b,c,e}
(v)
{d,a}
Question
55
55.
The perimeters of two similar triangles are 29 cm and 24 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.
(i)
13.24 cm
(ii)
14.24 cm
(iii)
12.24 cm
(iv)
11.24 cm
(v)
15.24 cm
Question
56
56.
In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 105° , ∠DCA = 30°. Find ∠CAD
(i)
43°
(ii)
44°
(iii)
47°
(iv)
46°
(v)
45°
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)
2a sq.units
(ii)
a
2
sq.units
(iii)
√
3
a sq.units
(iv)
1
2
√
3
a sq.units
(v)
1
2
a sq.units
Question
58
58.
JKLM is a cyclic trapezium. Diagonals KM and JL intersect at N. If MJ = 15 cm, find KL
(i)
13 cm
(ii)
16 cm
(iii)
17 cm
(iv)
14 cm
(v)
15 cm
Question
59
59.
A vertical stick
12 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)
97 m
(ii)
95 m
(iii)
98 m
(iv)
94 m
(v)
96 m
Question
60
60.
In the given figure, △ABC, TU ∥ BC such that
area of
△ATU
= area of
TUCB
. Find
AT
AB
(i)
1
2
4
√
2
(ii)
1
2
√
2
(iii)
1
2
√
-1
(iv)
1
(v)
1
2
√
4
Question
61
61.
In the given figure, ∠LIJ = ∠KIL and IL ∥ MK and IJ = 17 cm, JL = 10 cm and LK = 10 cm. Find IM
(i)
17.00 cm
(ii)
16.00 cm
(iii)
18.00 cm
(iv)
15.00 cm
(v)
19.00 cm
Question
62
62.
In the given figure, KM is the angular bisector of
∠K
&
∠M
JK
=
20 cm
,
KL
=
20 cm
and
LM
=
23 cm
.
Find
MJ
(i)
22.00 cm
(ii)
23.00 cm
(iii)
25.00 cm
(iv)
24.00 cm
(v)
21.00 cm
Question
63
63.
In the given figure, GHI is a triangle and 'O' is a point inside △GHI. The angular bisector of ∠HOG, ∠IOH & ∠GOI meet GH, HI & IG at J, K & L respectively . Then
(i)
GJ . HK . IL = JK . KL . LJ
(ii)
GJ . HK . IL = OG . OH . OI
(iii)
GJ . HK . IL = JH . KI . LG
(iv)
GJ . HK . IL = OJ . OK . OL
(v)
GJ . HK . IL = GH . HI . IG
Question
64
64.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 26 cm and AP = 10 cm. Find PB
(i)
14.00 cm
(ii)
17.00 cm
(iii)
16.00 cm
(iv)
18.00 cm
(v)
15.00 cm
Question
65
65.
From the given figure and values, find x
(i)
(
36
,
-9
)
(ii)
(
35
,
-10
)
(iii)
(
37
,
-10
)
(iv)
(
35
,
-11
)
(v)
(
-8
,
37
)
Question
66
66.
The ratio of the bases of two triangles ABC and DEF is
5
:
8
.
If the triangles are equal in area, then the ratio of their heights is
(i)
6
:
8
(ii)
5
:
11
(iii)
4
:
8
(iv)
5
:
6
(v)
8
:
5
Question
67
67.
If the measures are as shown in the given figure, find HI
(i)
24.0 cm
(ii)
22.0 cm
(iii)
23.0 cm
(iv)
25.0 cm
(v)
26.0 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 = 24 cm
and radius of the inner circle is
6.3 cm
.
Find the radius of the outer circle.
(i)
15.12 cm
(ii)
13.12 cm
(iii)
16.12 cm
(iv)
14.12 cm
(v)
17.12 cm
Assignment Key
1) (v)
2) (iv)
3) (iii)
4) (v)
5) (iv)
6) (ii)
7) (iii)
8) (i)
9) (i)
10) (iv)
11) (i)
12) (ii)
13) (iv)
14) (iv)
15) (iv)
16) (v)
17) (v)
18) (ii)
19) (iii)
20) (i)
21) (ii)
22) (iv)
23) (iii)
24) (iv)
25) (i)
26) (iv)
27) (ii)
28) (i)
29) (ii)
30) (v)
31) (ii)
32) (i)
33) (ii)
34) (iv)
35) (v)
36) (ii)
37) (iv)
38) (i)
39) (iv)
40) (iii)
41) (ii)
42) (iv)
43) (i)
44) (v)
45) (iii)
46) (v)
47) (v)
48) (ii)
49) (i)
50) (iv)
51) (iii)
52) (iv)
53) (ii)
54) (iv)
55) (i)
56) (v)
57) (i)
58) (v)
59) (v)
60) (ii)
61) (i)
62) (ii)
63) (iii)
64) (iii)
65) (ii)
66) (v)
67) (i)
68) (i)
