EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FJ
=
(i)
FI
(ii)
HF
2
(iii)
GH
(iv)
GH
2
(v)
FG
2
Question
2
2.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FI
=
(i)
GH
(ii)
FJ
(iii)
HF
2
(iv)
FG
2
(v)
GH
2
Question
3
3.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CF
=
(i)
EC
(ii)
FD
(iii)
GE
(iv)
CD
(v)
CG
Question
4
4.
In the given figure
△EFG
,
H
is the mid-point of
EF
and
HI
∥
FG
,
then
HF
=
(i)
EI
(ii)
EH
(iii)
GE
(iv)
EF
(v)
IG
Question
5
5.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AE
=
(i)
CA
(ii)
DB
(iii)
AD
(iv)
AB
(v)
EC
Question
6
6.
In the given figure
△HIJ
,
K
is the mid-point of
HI
and
KL
∥
IJ
,
then
LJ
=
(i)
JH
(ii)
HK
(iii)
HL
(iv)
HI
(v)
KI
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
8
8.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
AAA Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
not similar
(ii)
AAA Similarity
(iii)
SSS Similarity
(iv)
SAS Similarity
Question
10
10.
In the given figure, △GHI and △RST are such that
∠H
=
∠S
and
GH
RS
=
HI
ST
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
SAS Similarity
(iii)
SSS Similarity
(iv)
not similar
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)
SAS Similarity
(ii)
SSS Similarity
(iii)
AAA Similarity
(iv)
not similar
Question
12
12.
In the given figure, △FGH and △RST are such that
FG
RS
=
GH
ST
=
HF
TR
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
AAA Similarity
(iii)
SSS Similarity
(iv)
SAS Similarity
Question
13
13.
In the given figure,
MN
∥
KL
.
If
JM
MK
=
2
3
and
JL
=
12.3 cm
, find
JN
(i)
4.92 cm
(ii)
2.92 cm
(iii)
5.92 cm
(iv)
6.92 cm
(v)
3.92 cm
Question
14
14.
In the given figure,
JK
∥
HI
.
If
GJ
=
6.81 cm
,
GH
=
10.9 cm
and
GI
=
15.6 cm
, find
GK
(i)
10.75 cm
(ii)
7.75 cm
(iii)
8.75 cm
(iv)
9.75 cm
(v)
11.75 cm
Question
15
15.
In the given figure, TU ∥ DE and CT = 13.8 cm, TU = 15 cm and DE = 25 cm, find CD
(i)
23.0 cm
(ii)
24.0 cm
(iii)
22.0 cm
(iv)
25.0 cm
(v)
21.0 cm
Question
16
16.
In the given figure, △KLM is isosceles right-angled at L and LN ⟂ MK. ∠L =
(i)
∠K
(ii)
∠N
(iii)
∠O
(iv)
∠P
(v)
∠M
Question
17
17.
In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠RSQ =
(i)
∠SQR
(ii)
∠SPQ
(iii)
∠PQS
(iv)
∠QRS
(v)
∠QSP
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)
△FDA
(ii)
△DAE
(iii)
△DCF
(iv)
△ABH
(v)
△FEH
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)
∠AFD
(ii)
∠FAC
(iii)
∠HAB
(iv)
∠FEH
(v)
∠FDA
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)
∠FEH
(iii)
∠DAF
(iv)
∠EHF
(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.
∠CFA =
(i)
∠EHF
(ii)
∠AFD
(iii)
∠DAF
(iv)
∠HFE
(v)
∠BHA
Question
22
22.
In the given figure, EFGH is a trapezium in which
EF ∥ GH
and the diagonals
FH
and
EG
intersect at
I
.
If
IE
=
(
12
x
+
8
)
cm,
FI
=
(
8
x
+
3
)
cm,
IG
=
(
3
x
+
7
)
cm and
HI
=
(
2
x
+
4
)
cm, find the value of x
(i)
(
13
,
13
)
(ii)
(
14
,
11
)
(iii)
(
12
,
12
)
(iv)
(
11
,
10
)
(v)
(
11
,
11
)
Question
23
23.
In the given figure, GHIJ is a trapezium in which
GH ∥ IJ
and the diagonals
HJ
and
GI
intersect at
K
.
△KIJ
∼
(i)
△KGH
(ii)
△KHI
(iii)
△KJG
(iv)
△HIJ
(v)
△JGH
Question
24
24.
In the given figure, the altitudes MC and DN of △BCD meet at L. △MDL ∼
(i)
△MDC
(ii)
△LCD
(iii)
△NCD
(iv)
△LNM
(v)
△NCL
Question
25
25.
In the given figure, the altitudes NE and FO of △DEF meet at M. ∠FNM =
(i)
∠OEM
(ii)
∠MOE
(iii)
∠MFN
(iv)
∠NMF
(v)
∠EMO
Question
26
26.
In the given figure, QR ∥ CD , and median BE bisects QR.
If BE = 19.1 cm, BQ = 8.44 cm and BF = 8.49 cm, BC =
(i)
21.00 cm
(ii)
19.00 cm
(iii)
17.00 cm
(iv)
20.00 cm
(v)
18.00 cm
Question
27
27.
In the given figure, RS ∥ EF , and median DG bisects RS.
If DG = 17.1 cm, DF = 20 cm and DH = 9.5 cm, SF =
(i)
10.89 cm
(ii)
9.89 cm
(iii)
8.89 cm
(iv)
6.89 cm
(v)
7.89 cm
Question
28
28.
In the given figure, ST ∥ DE , and median CF bisects ST.
△CGT ∼
(i)
△CFE
(ii)
△DEC
(iii)
△CDE
(iv)
△CSG
(v)
△CDF
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 . ∠EGC =
(i)
∠DFC
(ii)
∠GCE
(iii)
∠FEC
(iv)
∠CFE
(v)
∠CEG
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 = 19 cm, GJ = 13.4 cm, GI = 19 cm and KI = 7.6 cm
b)
GH = 19 cm, JH = 7.6 cm, GK = 13.4 cm and GI = 19 cm
c)
GH = 19 cm, JH = 7.6 cm, GI = 19 cm and GK = 11.4 cm
d)
GJ = 11.4 cm, JH = 7.6 cm, GK = 11.4 cm and KI = 7.6 cm
(i)
{a,b,c}
(ii)
{a,c}
(iii)
{b,d}
(iv)
{c,d}
(v)
{a,d,c}
Question
31
31.
Which of the following are true?
a)
Any two squares are similar.
b)
Any two squares are congruent.
c)
Any two triangles are congruent.
d)
Any two circles are similar.
e)
Any two circles are congruent.
f)
Any two triangles are similar.
(i)
{b,d,a}
(ii)
{b,a}
(iii)
{c,d}
(iv)
{e,f,a}
(v)
{a,d}
Question
32
32.
Which of the following are true?
a)
A circle is a polygonal region.
b)
A sector is a polygonal region.
c)
A square is a polygonal region.
d)
A triangle is a polygonal region.
e)
A semi-circle is a polygonal region.
(i)
{b,d,c}
(ii)
{e,a,c}
(iii)
{b,d}
(iv)
{a,c}
(v)
{c,d}
Question
33
33.
Which of the following are true?
a)
If two figures are congruent, then they are similar too.
b)
Similar and congruent are not synonymous.
c)
Congruent figures have same area.
d)
Similar figures have same area.
e)
If two figures are similar, then they are congruent too.
(i)
{d,a}
(ii)
{d,a,b}
(iii)
{d,e,c}
(iv)
{e,b}
(v)
{a,b,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)
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,b,a}
(ii)
{a,b}
(iii)
{c,d,a}
(iv)
{d,b}
(v)
{c,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,d,c}
(iv)
{a,b,c}
(v)
{c,d}
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,b}
(ii)
{b,c,d}
(iii)
{a,c}
(iv)
{a,b,c}
(v)
{a,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 triangles are similar if the corresponding sides are proportional.
c)
Any two quadrilaterals are similar if the corresponding sides are proportional.
d)
Any two quadrilaterals are similar if the corresponding angles are equal.
(i)
{d,a}
(ii)
{d,c}
(iii)
{d,a,b}
(iv)
{d,b}
(v)
{a,b,c}
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
2
of area of △IJK
(ii)
2
3
of area of △IJK
(iii)
1
4
of area of △IJK
(iv)
3
4
of area of △IJK
(v)
1
3
of area of △IJK
Question
39
39.
In the given figure, the parallelogram GHIJ and the triangle △KGH are on the same bases and between the same parallels.
The area of the
△KGH
is x sq.cm. The area of the parallelogram is
(i)
thrice
the area of the triangle
(ii)
5
4
the area of the triangle
(iii)
3
2
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 △FGH, IJ ∥ GH. If FI : IG = 7.73 cm : 9.27 cm and FH = 18 cm, FJ =
(i)
9.18 cm
(ii)
8.18 cm
(iii)
7.18 cm
(iv)
10.18 cm
(v)
6.18 cm
Question
41
41.
In the given two similar triangles, if m = 16 cm, n = 20 cm, o = 17 cm, q = 12 cm, find r
(i)
11.20 cm
(ii)
9.20 cm
(iii)
12.20 cm
(iv)
8.20 cm
(v)
10.20 cm
Question
42
42.
In the given figure, given ∠DAB = ∠CAD, x : y = 8.76 cm : 9.24 cm and p = 18 cm, find q =
(i)
17.00 cm
(ii)
20.00 cm
(iii)
18.00 cm
(iv)
19.00 cm
(v)
21.00 cm
Question
43
43.
In the given figure, given ∠HEF = ∠GEH, p = 9.19 cm, q = 10.81 cm and FG = 20 cm, find HG =
(i)
11.81 cm
(ii)
12.81 cm
(iii)
8.81 cm
(iv)
10.81 cm
(v)
9.81 cm
Question
44
44.
In the given figure, IJKL is a trapezium where OJ = 14 cm , OK = 5 cm and OL = 5 cm . Find OI =
(i)
16 cm
(ii)
14 cm
(iii)
15 cm
(iv)
13 cm
(v)
12 cm
Question
45
45.
In the given figure, ∠HEF = 44.07°, find the value of x =
(i)
43.93°
(ii)
45.93°
(iii)
47.93°
(iv)
44.93°
(v)
46.93°
Question
46
46.
In the given figure, ∠JHI = 42.77°, find the value of y =
(i)
48.23°
(ii)
49.23°
(iii)
47.23°
(iv)
46.23°
(v)
45.23°
Question
47
47.
In the given figure, if FG ∥ HI then
(i)
△FGJ ∼ △JIH
(ii)
△FGJ ∼ △JHI
(iii)
△FGJ ∼ △IHJ
(iv)
△JFG ∼ △JHI
(v)
△JGF ∼ △JIH
Question
48
48.
In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FG = 15 cm, GH = 19 cm, then find GI.
(i)
11.77 cm
(ii)
10.77 cm
(iii)
13.77 cm
(iv)
12.77 cm
(v)
9.77 cm
Question
49
49.
In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If IH = 13.1 cm, GI = 12.38 cm, then find FI.
(i)
9.70 cm
(ii)
13.70 cm
(iii)
11.70 cm
(iv)
10.70 cm
(v)
12.70 cm
Question
50
50.
In the given figure, △DEF ∼ △NOP and DE = 12 cm, NO = 16.8 cm.
If the area of the
△NOP
=
94.08 sq.cm
, find the area of the
△DEF
(i)
47.00 sq.cm
(ii)
50.00 sq.cm
(iii)
48.00 sq.cm
(iv)
49.00 sq.cm
(v)
46.00 sq.cm
Question
51
51.
In the given figure, △ABC ∼ △NOP and BC = 14 cm , OP = 19.6 cm and
AD
=
11.28 cm
,
find the area of the
△NOP
(i)
154.70 sq.cm
(ii)
155.70 sq.cm
(iii)
156.70 sq.cm
(iv)
153.70 sq.cm
(v)
152.70 sq.cm
Question
52
52.
In the given figure, △ABC & △QRS are similar triangles. If the ratio of the heights AD : QT = 12 : 16, then the ratio of their areas is
(i)
143
sq.cm
:
256
sq.cm
(ii)
145
sq.cm
:
256
sq.cm
(iii)
144
sq.cm
:
256
sq.cm
(iv)
144
sq.cm
:
258
sq.cm
(v)
144
sq.cm
:
254
sq.cm
Question
53
53.
In the given figure, points D , E and F are the mid-points of sides BC, CA and AB of △ABC. Which of the following are true?
a)
All four small triangles have equal areas
b)
Area of
△ABC
=
1
3
area of
△DEF
c)
Area of △ABC = 4 times area of △DEF
d)
Area of trapezium
BCEF
is
1
4
the area of
△ABC
e)
Area of trapezium BCEF is thrice the area of △AFE
(i)
{a,c,e}
(ii)
{b,a}
(iii)
{b,d,e}
(iv)
{b,a,c}
(v)
{d,c}
Question
54
54.
In the given figure, points N , O and P are the mid-points of sides LM, MK and KL of △KLM. Which of the following are true?
a)
△NOP ∼ △KLM
b)
△ONM ∼ △KLM
c)
△KPO ∼ △KLM
d)
△PLN ∼ △KLM
e)
△NPO ∼ △KLM
(i)
{e,d,a}
(ii)
{e,a}
(iii)
{e,c}
(iv)
{e,b}
(v)
{a,b,c,d}
Question
55
55.
The perimeters of two similar triangles are 27 cm and 24 cm respectively. If one side of the first triangle is 11 cm, find the length of the corresponding side of the second triangle.
(i)
9.78 cm
(ii)
11.78 cm
(iii)
7.78 cm
(iv)
10.78 cm
(v)
8.78 cm
Question
56
56.
In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 107° , ∠GFD = 20°. Find ∠FDG
(i)
54°
(ii)
52°
(iii)
51°
(iv)
53°
(v)
55°
Question
57
57.
IJKL is a square and △IJM is an equilateral triangle. Also, △IKN is an equilateral triangle. If area of △IJM is 'a' sq.units, then the area of △IKN is
(i)
1
2
a sq.units
(ii)
√
3
a sq.units
(iii)
a
2
sq.units
(iv)
1
2
√
3
a sq.units
(v)
2a sq.units
Question
58
58.
BCDE is a cyclic trapezium. Diagonals CE and BD intersect at F. If EB = 18 cm, find CD
(i)
16 cm
(ii)
20 cm
(iii)
17 cm
(iv)
18 cm
(v)
19 cm
Question
59
59.
A vertical stick
15 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)
118 m
(ii)
121 m
(iii)
122 m
(iv)
119 m
(v)
120 m
Question
60
60.
In the given figure, △EFG, TU ∥ FG such that
area of
△ETU
= area of
TUGF
. Find
ET
EF
(i)
1
2
√
5
(ii)
1
2
√
-1
(iii)
1
(iv)
1
2
4
√
2
(v)
1
2
√
2
Question
61
61.
In the given figure, ∠JGH = ∠IGJ and GJ ∥ KI and GH = 17 cm, HJ = 11 cm and JI = 9 cm. Find GK
(i)
15.91 cm
(ii)
12.91 cm
(iii)
11.91 cm
(iv)
13.91 cm
(v)
14.91 cm
Question
62
62.
In the given figure, MO is the angular bisector of
∠M
&
∠O
LM
=
20 cm
,
MN
=
20 cm
and
NO
=
21 cm
.
Find
OL
(i)
19.00 cm
(ii)
22.00 cm
(iii)
20.00 cm
(iv)
21.00 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 = OE . OF . OG
(ii)
EH . FI . GJ = OH . OI . OJ
(iii)
EH . FI . GJ = HF . IG . JE
(iv)
EH . FI . GJ = HI . IJ . JH
(v)
EH . FI . GJ = EF . FG . GE
Question
64
64.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 27 cm. Find AP
(i)
10.80 cm
(ii)
9.80 cm
(iii)
12.80 cm
(iv)
11.80 cm
(v)
8.80 cm
Question
65
65.
From the given figure and values, find x
(i)
(
22
,
-3
)
(ii)
(
0
,
24
)
(iii)
(
23
,
-1
)
(iv)
(
22
,
-2
)
(v)
(
24
,
-2
)
Question
66
66.
The ratio of the bases of two triangles ABC and DEF is
9
:
3
.
If the triangles are equal in area, then the ratio of their heights is
(i)
9
:
0
(ii)
10
:
3
(iii)
8
:
3
(iv)
9
:
5
(v)
3
:
9
Question
67
67.
If the measures are as shown in the given figure, find HI
(i)
21.0 cm
(ii)
20.0 cm
(iii)
19.0 cm
(iv)
18.0 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
5.5 cm
.
Find the radius of the outer circle.
(i)
11.22 cm
(ii)
13.22 cm
(iii)
12.22 cm
(iv)
10.22 cm
(v)
14.22 cm
Assignment Key
1) (ii)
2) (iv)
3) (ii)
4) (ii)
5) (v)
6) (iii)
7) (iii)
8) (ii)
9) (iii)
10) (ii)
11) (iii)
12) (iii)
13) (i)
14) (iv)
15) (i)
16) (ii)
17) (v)
18) (iv)
19) (i)
20) (ii)
21) (v)
22) (v)
23) (i)
24) (v)
25) (ii)
26) (ii)
27) (iii)
28) (i)
29) (v)
30) (iv)
31) (v)
32) (v)
33) (v)
34) (ii)
35) (v)
36) (ii)
37) (v)
38) (iii)
39) (v)
40) (ii)
41) (v)
42) (iv)
43) (iv)
44) (ii)
45) (ii)
46) (iii)
47) (iii)
48) (i)
49) (iii)
50) (iii)
51) (i)
52) (iii)
53) (i)
54) (v)
55) (i)
56) (iv)
57) (v)
58) (iv)
59) (v)
60) (v)
61) (iv)
62) (iv)
63) (iii)
64) (i)
65) (iv)
66) (v)
67) (ii)
68) (iii)
