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)
AD
(ii)
BC
2
(iii)
AB
2
(iv)
CA
2
(v)
BC
Question
2
2.
In the given figure
△BCD
,
E
is the mid-point of
BC
and
EF
∥
CD
,
then
BE
=
(i)
BF
(ii)
BC
2
(iii)
CD
2
(iv)
DB
2
(v)
CD
Question
3
3.
In the given figure
△JKL
,
M
is the mid-point of
JK
and
MN
∥
KL
,
then
JM
=
(i)
NL
(ii)
LJ
(iii)
MK
(iv)
JN
(v)
JK
Question
4
4.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
HF
=
(i)
EF
(ii)
EH
(iii)
IG
(iv)
EI
(v)
GE
Question
5
5.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
GK
=
(i)
JH
(ii)
GH
(iii)
KI
(iv)
GJ
(v)
IG
Question
6
6.
In the given figure
△DEF
,
G
is the mid-point of
DE
and
GH
∥
EF
,
then
HF
=
(i)
FD
(ii)
DE
(iii)
DG
(iv)
GE
(v)
DH
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
AAA Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SSS Similarity
Question
10
10.
In the given figure, △GHI and △QRS are such that
∠H
=
∠R
and
GH
QR
=
HI
RS
.
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, △HIJ and △RST are such that
∠I
=
∠S
and
∠J
=
∠T
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
AAA Similarity
(iii)
SAS Similarity
(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)
SSS Similarity
(ii)
AAA Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
13
13.
In the given figure,
DE
∥
BC
.
If
AD
DB
=
3
4
and
AC
=
10.4 cm
, find
AE
(i)
2.46 cm
(ii)
4.46 cm
(iii)
3.46 cm
(iv)
5.46 cm
(v)
6.46 cm
Question
14
14.
In the given figure,
LM
∥
JK
.
If
IL
=
6.15 cm
,
IJ
=
12.3 cm
and
IK
=
14.6 cm
, find
IM
(i)
9.30 cm
(ii)
8.30 cm
(iii)
5.30 cm
(iv)
6.30 cm
(v)
7.30 cm
Question
15
15.
In the given figure, TU ∥ FG and EU = 12.6 cm, EG = 21 cm and FG = 25 cm, find TU
(i)
13.0 cm
(ii)
15.0 cm
(iii)
16.0 cm
(iv)
17.0 cm
(v)
14.0 cm
Question
16
16.
In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠G =
(i)
∠I
(ii)
∠J
(iii)
∠K
(iv)
∠L
(v)
∠H
Question
17
17.
In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠IJH =
(i)
∠HIJ
(ii)
∠HJG
(iii)
∠JHI
(iv)
∠JGH
(v)
∠GHJ
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)
△FDA
(ii)
△ABH
(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.
∠HFE =
(i)
∠HAB
(ii)
∠FDA
(iii)
∠AFD
(iv)
∠FAC
(v)
∠FEH
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.
∠ABH =
(i)
∠ACF
(ii)
∠FEH
(iii)
∠FDA
(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.
∠EHF =
(i)
∠AFD
(ii)
∠HFE
(iii)
∠DAF
(iv)
∠CFA
(v)
∠BHA
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
=
(
4
x
+
10
)
cm,
OR
=
(
4
x
+
15
)
cm,
RP
=
(
3
x
+
12
)
cm and
QR
=
(
3
x
+
16
)
cm, find the value of x
(i)
(
20
,
20
)
(ii)
(
20
,
19
)
(iii)
(
22
,
22
)
(iv)
(
22
,
20
)
(v)
(
21
,
21
)
Question
23
23.
In the given figure, CDEF is a trapezium in which
CD ∥ EF
and the diagonals
DF
and
CE
intersect at
G
.
△GEF
∼
(i)
△GFC
(ii)
△GDE
(iii)
△FCD
(iv)
△DEF
(v)
△GCD
Question
24
24.
In the given figure, the altitudes QB and CR of △ABC meet at P. △QCP ∼
(i)
△RBC
(ii)
△QCB
(iii)
△PRQ
(iv)
△PBC
(v)
△RBP
Question
25
25.
In the given figure, the altitudes RG and HS of △FGH meet at Q. ∠SGQ =
(i)
∠HRQ
(ii)
∠RQH
(iii)
∠GQS
(iv)
∠QHR
(v)
∠QSG
Question
26
26.
In the given figure, PQ ∥ JK , and median IL bisects PQ.
If IJ = 20 cm, IL = 20 cm and IP = 8 cm, IM =
(i)
6.00 cm
(ii)
9.00 cm
(iii)
7.00 cm
(iv)
10.00 cm
(v)
8.00 cm
Question
27
27.
In the given figure, PQ ∥ CD , and median BE bisects PQ.
If BE = 16.7 cm, BF = 9.54 cm and BQ = 10.29 cm, BD =
(i)
19.00 cm
(ii)
20.00 cm
(iii)
16.00 cm
(iv)
17.00 cm
(v)
18.00 cm
Question
28
28.
In the given figure, TU ∥ DE , and median CF bisects TU.
△CTG ∼
(i)
△DEC
(ii)
△CDE
(iii)
△CGU
(iv)
△CFE
(v)
△CDF
Question
29
29.
In the given figure, △NOP is a triangle in which NQ is the internal bisector of ∠N and PR ∥ QN meeting ON produced at R . ∠QNO =
(i)
∠PRN
(ii)
∠RNP
(iii)
∠QPN
(iv)
∠OQN
(v)
∠NQP
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 = 10.56 cm, MK = 8.44 cm, JN = 10 cm and NL = 8 cm
b)
JK = 19 cm, JM = 12.56 cm, JL = 18 cm and NL = 8 cm
c)
JK = 19 cm, MK = 8.44 cm, JN = 12 cm and JL = 18 cm
d)
JK = 19 cm, MK = 8.44 cm, JL = 18 cm and JN = 10 cm
(i)
{b,c,a}
(ii)
{a,d}
(iii)
{b,d,a}
(iv)
{b,a}
(v)
{c,d}
Question
31
31.
Which of the following are true?
a)
Any two triangles are congruent.
b)
Any two triangles are similar.
c)
Any two squares are similar.
d)
Any two circles are congruent.
e)
Any two circles are similar.
f)
Any two squares are congruent.
(i)
{c,e}
(ii)
{b,e}
(iii)
{d,f,c}
(iv)
{a,c}
(v)
{a,e,c}
Question
32
32.
Which of the following are true?
a)
A semi-circle is a polygonal region.
b)
A circle is a polygonal region.
c)
A square is a polygonal region.
d)
A triangle is a polygonal region.
e)
A sector is a polygonal region.
(i)
{c,d}
(ii)
{e,a,c}
(iii)
{a,c}
(iv)
{b,d,c}
(v)
{b,d}
Question
33
33.
Which of the following are true?
a)
If two figures are congruent, then they are similar too.
b)
If two figures are similar, then they are congruent too.
c)
Similar figures have same area.
d)
Congruent figures have same area.
e)
Similar and congruent are not synonymous.
(i)
{a,d,e}
(ii)
{b,a}
(iii)
{b,a,d}
(iv)
{b,c,e}
(v)
{c,d}
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)
Area of the union of two polygonal region is not equal to the sum of the individual area.
c)
A polygonal region can be divided into a finite number of triangles in a unique way.
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)
{c,d}
(ii)
{a,d,b}
(iii)
{b,d}
(iv)
{a,b}
(v)
{a,c,b}
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 proportional.
d)
The corresponding sides are equal.
(i)
{b,c,a}
(ii)
{b,a}
(iii)
{d,c}
(iv)
{b,d,a}
(v)
{a,c}
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)
{b,c}
(ii)
{b,a,c}
(iii)
{b,a}
(iv)
{b,d}
(v)
{a,c,d}
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)
{a,c,d}
(ii)
{b,a,c}
(iii)
{b,c}
(iv)
{b,d}
(v)
{b,a}
Question
38
38.
In the given figure, the area of the △CDE is x sq.cm. F,G,H are the mid-points of the sides DE , EC and CD respectively. The area of the △FGH is
(i)
1
3
of area of △CDE
(ii)
1
2
of area of △CDE
(iii)
3
4
of area of △CDE
(iv)
1
4
of area of △CDE
(v)
2
3
of area of △CDE
Question
39
39.
In the given figure, the parallelogram CDEF and the triangle △GCD are on the same bases and between the same parallels.
The area of the
△GCD
is x sq.cm. The area of the parallelogram is
(i)
4
3
the area of the triangle
(ii)
thrice
the area of the triangle
(iii)
3
2
the area of the triangle
(iv)
5
4
the area of the triangle
(v)
twice
the area of the triangle
Question
40
40.
In the given △EFG, HI ∥ FG. If EH : HF = 6.8 cm : 10.2 cm and EG = 17 cm, EI =
(i)
6.80 cm
(ii)
8.80 cm
(iii)
7.80 cm
(iv)
5.80 cm
(v)
4.80 cm
Question
41
41.
In the given two similar triangles, if e = 18 cm, f = 19 cm, g = 15 cm, j = 9 cm, find h
(i)
8.80 cm
(ii)
10.80 cm
(iii)
9.80 cm
(iv)
12.80 cm
(v)
11.80 cm
Question
42
42.
In the given figure, given ∠EBC = ∠DBE, x : y = 7.26 cm : 7.74 cm and q = 16 cm, find p =
(i)
14.00 cm
(ii)
16.00 cm
(iii)
17.00 cm
(iv)
13.00 cm
(v)
15.00 cm
Question
43
43.
In the given figure, given ∠KHI = ∠JHK, p = 7.06 cm, q = 8.94 cm and IJ = 16 cm, find IK =
(i)
9.06 cm
(ii)
7.06 cm
(iii)
5.06 cm
(iv)
6.06 cm
(v)
8.06 cm
Question
44
44.
In the given figure, DEFG is a trapezium where OD = 12 cm , OF = 4 cm and OG = 4 cm . Find OE =
(i)
11 cm
(ii)
13 cm
(iii)
14 cm
(iv)
12 cm
(v)
10 cm
Question
45
45.
In the given figure, ∠IJL = 43.62°, find the value of x =
(i)
45.38°
(ii)
48.38°
(iii)
46.38°
(iv)
47.38°
(v)
44.38°
Question
46
46.
In the given figure, ∠CDE = 48.27°, find the value of y =
(i)
41.73°
(ii)
39.73°
(iii)
40.73°
(iv)
43.73°
(v)
42.73°
Question
47
47.
In the given figure, if DE ∥ FG then
(i)
△HED ∼ △HGF
(ii)
△DEH ∼ △HFG
(iii)
△HDE ∼ △HFG
(iv)
△DEH ∼ △HGF
(v)
△DEH ∼ △GFH
Question
48
48.
In the given figure, △IJK is right-angled at J. Also, JL ⟂ IK. If JK = 20 cm, JL = 13.38 cm, then find IJ.
(i)
18.00 cm
(ii)
20.00 cm
(iii)
16.00 cm
(iv)
19.00 cm
(v)
17.00 cm
Question
49
49.
In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AD = 12.8 cm, BD = 11.26 cm, then find DC.
(i)
8.90 cm
(ii)
9.90 cm
(iii)
11.90 cm
(iv)
7.90 cm
(v)
10.90 cm
Question
50
50.
In the given figure, △BCD ∼ △NOP and BC = 12 cm, NO = 16.8 cm.
If the area of the
△NOP
=
137.7 sq.cm
, find the area of the
△BCD
(i)
69.26 sq.cm
(ii)
71.26 sq.cm
(iii)
70.26 sq.cm
(iv)
68.26 sq.cm
(v)
72.26 sq.cm
Question
51
51.
In the given figure, △ABC ∼ △NOP and BC = 14 cm , OP = 19.6 cm and
AD
=
10.5 cm
,
find the area of the
△NOP
(i)
146.03 sq.cm
(ii)
144.03 sq.cm
(iii)
142.03 sq.cm
(iv)
143.03 sq.cm
(v)
145.03 sq.cm
Question
52
52.
In the given figure, △BCD & △OPQ are similar triangles. If the ratio of the heights BE : OR = 10 : 14, then the ratio of their areas is
(i)
99
sq.cm
:
196
sq.cm
(ii)
100
sq.cm
:
198
sq.cm
(iii)
100
sq.cm
:
196
sq.cm
(iv)
100
sq.cm
:
193
sq.cm
(v)
101
sq.cm
:
196
sq.cm
Question
53
53.
In the given figure, points O , P and Q are the mid-points of sides MN, NL and LM of △LMN. Which of the following are true?
a)
Area of trapezium MNPQ is thrice the area of △LQP
b)
All four small triangles have equal areas
c)
Area of trapezium
MNPQ
is
1
4
the area of
△LMN
d)
Area of
△LMN
=
1
3
area of
△OPQ
e)
Area of △LMN = 4 times area of △OPQ
(i)
{c,a,b}
(ii)
{c,d,e}
(iii)
{c,a}
(iv)
{d,b}
(v)
{a,b,e}
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)
△KGI ∼ △FGH
b)
△JIH ∼ △FGH
c)
△IJK ∼ △FGH
d)
△FKJ ∼ △FGH
e)
△IKJ ∼ △FGH
(i)
{e,a}
(ii)
{a,b,c,d}
(iii)
{e,d,a}
(iv)
{e,b}
(v)
{e,c}
Question
55
55.
The perimeters of two similar triangles are 30 cm and 15 cm respectively. If one side of the first triangle is 10 cm, find the length of the corresponding side of the second triangle.
(i)
7.00 cm
(ii)
4.00 cm
(iii)
5.00 cm
(iv)
3.00 cm
(v)
6.00 cm
Question
56
56.
In the given figure, J is a point on side HI of △GHI such that ∠IGH = ∠GJI = 107° , ∠JIG = 28°. Find ∠IGJ
(i)
45°
(ii)
46°
(iii)
47°
(iv)
43°
(v)
44°
Question
57
57.
CDEF is a square and △CDG is an equilateral triangle. Also, △CEH is an equilateral triangle. If area of △CDG is 'a' sq.units, then the area of △CEH is
(i)
1
2
a sq.units
(ii)
2a sq.units
(iii)
1
2
√
3
a sq.units
(iv)
a
2
sq.units
(v)
√
3
a sq.units
Question
58
58.
IJKL is a cyclic trapezium. Diagonals JL and IK intersect at M. If LI = 16 cm, find JK
(i)
14 cm
(ii)
16 cm
(iii)
17 cm
(iv)
15 cm
(v)
18 cm
Question
59
59.
A vertical stick
15 m
long casts a shadow of
13 m
long on the ground.
At the same time, a tower casts the shadow
104 m
long on the ground.
Find the height of the tower.
(i)
119 m
(ii)
120 m
(iii)
121 m
(iv)
118 m
(v)
122 m
Question
60
60.
In the given figure, △BCD, ST ∥ CD such that
area of
△BST
= area of
STDC
. Find
BS
BC
(i)
1
2
√
5
(ii)
1
(iii)
1
2
√
1
2
(iv)
1
2
4
√
2
(v)
1
2
√
2
Question
61
61.
In the given figure, ∠HEF = ∠GEH and EH ∥ IG and EF = 15 cm, FH = 8 cm and HG = 10 cm. Find EI
(i)
16.75 cm
(ii)
18.75 cm
(iii)
17.75 cm
(iv)
19.75 cm
(v)
20.75 cm
Question
62
62.
In the given figure, DF is the angular bisector of
∠D
&
∠F
CD
=
20 cm
,
DE
=
21 cm
and
EF
=
22 cm
.
Find
FC
(i)
19.95 cm
(ii)
20.95 cm
(iii)
21.95 cm
(iv)
22.95 cm
(v)
18.95 cm
Question
63
63.
In the given figure, FGH is a triangle and 'O' is a point inside △FGH. The angular bisector of ∠GOF, ∠HOG & ∠FOH meet FG, GH & HF at I, J & K respectively . Then
(i)
FI . GJ . HK = OF . OG . OH
(ii)
FI . GJ . HK = FG . GH . HF
(iii)
FI . GJ . HK = IJ . JK . KI
(iv)
FI . GJ . HK = IG . JH . KF
(v)
FI . GJ . HK = OI . OJ . OK
Question
64
64.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 23 cm and AP = 9 cm. Find PB
(i)
14.00 cm
(ii)
16.00 cm
(iii)
13.00 cm
(iv)
12.00 cm
(v)
15.00 cm
Question
65
65.
From the given figure and values, find x
(i)
(
-10
,
58
)
(ii)
(
60
,
-8
)
(iii)
(
-9
,
59
)
(iv)
(
-10
,
57
)
(v)
(
-7
,
58
)
Question
66
66.
The ratio of the bases of two triangles ABC and DEF is
5
:
10
.
If the triangles are equal in area, then the ratio of their heights is
(i)
6
:
10
(ii)
4
:
10
(iii)
5
:
13
(iv)
5
:
8
(v)
10
:
5
Question
67
67.
If the measures are as shown in the given figure, find EF
(i)
21.0 cm
(ii)
20.0 cm
(iii)
24.0 cm
(iv)
23.0 cm
(v)
22.0 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 = 20 cm
and radius of the inner circle is
5.4 cm
.
Find the radius of the outer circle.
(i)
10.00 cm
(ii)
11.00 cm
(iii)
14.00 cm
(iv)
13.00 cm
(v)
12.00 cm
Assignment Key
1) (iv)
2) (ii)
3) (iii)
4) (ii)
5) (iii)
6) (v)
7) (iii)
8) (i)
9) (iv)
10) (iv)
11) (ii)
12) (i)
13) (ii)
14) (v)
15) (ii)
16) (i)
17) (ii)
18) (i)
19) (iii)
20) (i)
21) (iii)
22) (i)
23) (v)
24) (v)
25) (iv)
26) (v)
27) (v)
28) (v)
29) (i)
30) (ii)
31) (i)
32) (i)
33) (i)
34) (iii)
35) (v)
36) (v)
37) (i)
38) (iv)
39) (v)
40) (i)
41) (ii)
42) (v)
43) (ii)
44) (iv)
45) (iii)
46) (i)
47) (v)
48) (i)
49) (ii)
50) (iii)
51) (ii)
52) (iii)
53) (v)
54) (ii)
55) (iii)
56) (i)
57) (ii)
58) (ii)
59) (ii)
60) (v)
61) (ii)
62) (ii)
63) (iv)
64) (i)
65) (i)
66) (v)
67) (v)
68) (v)
