EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Similarity of Triangles
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
AAA Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
2
2.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
AAA Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
3
3.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
SAS Similarity
(iv)
not similar
Question
4
4.
In the given figure, △ABC and △TUV are such that
∠B
=
∠U
and
AB
TU
=
BC
UV
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
SAS Similarity
(iii)
SSS Similarity
(iv)
AAA Similarity
Question
5
5.
In the given figure, △DEF and △PQR are such that
∠E
=
∠Q
and
∠F
=
∠R
.
Identify the property by which the two triangles are similar
(i)
SAS Similarity
(ii)
AAA Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
6
6.
In the given figure, △GHI and △STU are such that
GH
ST
=
HI
TU
=
IG
US
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
SAS Similarity
(iii)
SSS Similarity
(iv)
AAA Similarity
Question
7
7.
In the given figure,
QR
∥
OP
.
If
NQ
QO
=
5
3
and
NP
=
11.2 cm
, find
NR
(i)
8.00 cm
(ii)
9.00 cm
(iii)
5.00 cm
(iv)
7.00 cm
(v)
6.00 cm
Question
8
8.
In the given figure,
EF
∥
CD
.
If
BE
=
4.54 cm
,
BC
=
12.1 cm
and
BD
=
14.8 cm
, find
BF
(i)
4.55 cm
(ii)
7.55 cm
(iii)
5.55 cm
(iv)
3.55 cm
(v)
6.55 cm
Question
9
9.
In the given figure, ST ∥ EF and DT = 12.6 cm, DF = 21 cm and EF = 22 cm, find ST
(i)
14.2 cm
(ii)
12.2 cm
(iii)
13.2 cm
(iv)
15.2 cm
(v)
11.2 cm
Question
10
10.
In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠P =
(i)
∠U
(ii)
∠R
(iii)
∠T
(iv)
∠Q
(v)
∠S
Question
11
11.
In the given figure, △OPQ is isosceles right-angled at P and PR ⟂ QO. ∠OPQ =
(i)
∠OPR
(ii)
∠PRO
(iii)
∠RPQ
(iv)
∠PQR
(v)
∠ROP
Question
12
12.
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)
△FEH
(ii)
△DCF
(iii)
△DAE
(iv)
△FDA
(v)
△ACF
Question
13
13.
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.
∠AFD =
(i)
∠HAB
(ii)
∠FDA
(iii)
∠FAC
(iv)
∠FEH
(v)
∠HFE
Question
14
14.
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)
∠EHF
(iii)
∠FEH
(iv)
∠DAF
(v)
∠ABH
Question
15
15.
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)
∠HFE
(ii)
∠CFA
(iii)
∠DAF
(iv)
∠BHA
(v)
∠AFD
Question
16
16.
In the given figure, ABCD is a trapezium in which
AB ∥ CD
and the diagonals
BD
and
AC
intersect at
E
.
If
EA
=
(
2
x
+
16
)
cm,
BE
=
(
5
x
+
10
)
cm,
EC
=
(
x
+
13
)
cm and
DE
=
(
3
x
+
6
)
cm, find the value of x
(i)
(
18
,
-1
)
(ii)
(
17
,
-3
)
(iii)
(
17
,
-2
)
(iv)
(
0
,
19
)
(v)
(
19
,
-2
)
Question
17
17.
In the given figure, DEFG is a trapezium in which
DE ∥ FG
and the diagonals
EG
and
DF
intersect at
H
.
△HDE
∼
(i)
△HFG
(ii)
△HEF
(iii)
△EFG
(iv)
△HGD
(v)
△GDE
Question
18
18.
In the given figure, the altitudes SG and HT of △FGH meet at R. △TGH ∼
(i)
△RGH
(ii)
△SHG
(iii)
△TGR
(iv)
△SHR
(v)
△RTS
Question
19
19.
In the given figure, the altitudes SC and DT of △BCD meet at R. ∠DSR =
(i)
∠RDS
(ii)
∠TCR
(iii)
∠RTC
(iv)
∠CRT
(v)
∠SRD
Question
20
20.
In the given figure, QR ∥ EF , and median DG bisects QR.
If DG = 15.9 cm, DQ = 9.6 cm and DH = 9.54 cm, DE =
(i)
15.00 cm
(ii)
18.00 cm
(iii)
16.00 cm
(iv)
14.00 cm
(v)
17.00 cm
Question
21
21.
In the given figure, TU ∥ EF , and median DG bisects TU.
If DG = 14.5 cm, DF = 16 cm and DH = 4.83 cm, UF =
(i)
11.67 cm
(ii)
10.67 cm
(iii)
8.67 cm
(iv)
12.67 cm
(v)
9.67 cm
Question
22
22.
In the given figure, RS ∥ IJ , and median HK bisects RS.
△HIK ∼
(i)
△HRL
(ii)
△HIJ
(iii)
△HKJ
(iv)
△HLS
(v)
△IJH
Question
23
23.
In the given figure, △DEF is a triangle in which DG is the internal bisector of ∠D and FH ∥ GD meeting ED produced at H . ∠DFH =
(i)
∠FDG
(ii)
∠EGD
(iii)
∠GFD
(iv)
∠HDF
(v)
∠DGF
Question
24
24.
In the given figure, D and E are points on the sides AB and AC respectively of △ABC.For which of the following cases, DE ∥ BC
a)
AD = 9.14 cm, DB = 6.86 cm, AE = 8.57 cm and EC = 6.43 cm
b)
AB = 16 cm, AD = 11.14 cm, AC = 15 cm and EC = 6.43 cm
c)
AB = 16 cm, DB = 6.86 cm, AE = 10.57 cm and AC = 15 cm
d)
AB = 16 cm, DB = 6.86 cm, AC = 15 cm and AE = 8.57 cm
(i)
{a,d}
(ii)
{b,d,a}
(iii)
{b,a}
(iv)
{c,d}
(v)
{b,c,a}
Question
25
25.
In the given figure, the area of the △GHI is x sq.cm. J,K,L are the mid-points of the sides HI , IG and GH respectively. The area of the △JKL is
(i)
1
2
of area of △GHI
(ii)
1
4
of area of △GHI
(iii)
2
3
of area of △GHI
(iv)
1
3
of area of △GHI
(v)
3
4
of area of △GHI
Question
26
26.
In the given figure, the parallelogram ABCD and the triangle △EAB are on the same bases and between the same parallels.
The area of the
△EAB
is x sq.cm. The area of the parallelogram is
(i)
thrice
the area of the triangle
(ii)
twice
the area of the triangle
(iii)
5
4
the area of the triangle
(iv)
4
3
the area of the triangle
(v)
3
2
the area of the triangle
Question
27
27.
If the ratio of the bases of two triangles is J : K and the ratio of the corresponding heights is L : M , the ratio of their areas in the same order is
(i)
JM : KL
(ii)
KL : JM
(iii)
JK : LM
(iv)
JL : KM
(v)
LM : JK
Question
28
28.
In the given △FGH, IJ ∥ GH. If FI : IG = 9 cm : 9 cm and FH = 20 cm, FJ =
(i)
12.00 cm
(ii)
10.00 cm
(iii)
9.00 cm
(iv)
8.00 cm
(v)
11.00 cm
Question
29
29.
In the given two similar triangles, if j = 19 cm, k = 18 cm, l = 20 cm, m = 11.4 cm, find n
(i)
11.80 cm
(ii)
9.80 cm
(iii)
12.80 cm
(iv)
10.80 cm
(v)
8.80 cm
Question
30
30.
In the given figure, given ∠HEF = ∠GEH, x : y = 7.5 cm : 7.5 cm and p = 17 cm, find q =
(i)
16.00 cm
(ii)
19.00 cm
(iii)
18.00 cm
(iv)
15.00 cm
(v)
17.00 cm
Question
31
31.
In the given figure, given ∠KHI = ∠JHK, p = 8.26 cm, q = 7.74 cm and IJ = 16 cm, find IK =
(i)
6.26 cm
(ii)
7.26 cm
(iii)
10.26 cm
(iv)
9.26 cm
(v)
8.26 cm
Question
32
32.
In the given figure, DEFG is a trapezium where OD = 12 cm , OF = 4 cm and OG = 4 cm . Find OE =
(i)
14 cm
(ii)
10 cm
(iii)
13 cm
(iv)
12 cm
(v)
11 cm
Question
33
33.
In the given figure, ∠FGI = 46.62°, find the value of x =
(i)
45.38°
(ii)
42.38°
(iii)
43.38°
(iv)
44.38°
(v)
41.38°
Question
34
34.
In the given figure, ∠BCD = 42.93°, find the value of y =
(i)
47.07°
(ii)
49.07°
(iii)
46.07°
(iv)
45.07°
(v)
48.07°
Question
35
35.
In the given figure, if GH ∥ IJ then
(i)
△GHK ∼ △JIK
(ii)
△GHK ∼ △KIJ
(iii)
△GHK ∼ △KJI
(iv)
△KGH ∼ △KIJ
(v)
△KHG ∼ △KJI
Question
36
36.
In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. Which of the following are true?
a)
HI
2
=
GI
.
GJ
b)
HJ
2
=
GJ
.
JI
c)
HI
2
=
IG
.
IJ
d)
GH
2
=
IG
.
IJ
e)
GH
2
=
GI
.
GJ
(i)
{a,b,c}
(ii)
{d,c}
(iii)
{a,b}
(iv)
{a,d,e}
(v)
{b,c,e}
Question
37
37.
In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If EF = 20 cm, EG = 13.77 cm, then find DE.
(i)
18.00 cm
(ii)
20.00 cm
(iii)
19.00 cm
(iv)
21.00 cm
(v)
17.00 cm
Question
38
38.
In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If AD = 14.9 cm, DC = 9.3 cm, then find BD.
(i)
13.77 cm
(ii)
11.77 cm
(iii)
12.77 cm
(iv)
9.77 cm
(v)
10.77 cm
Question
39
39.
In the given figure, △CDE ∼ △MNO and CD = 14 cm, MN = 19.6 cm.
If the area of the
△CDE
=
54.64 sq.cm
, find the area of the
△MNO
(i)
108.10 sq.cm
(ii)
109.10 sq.cm
(iii)
105.10 sq.cm
(iv)
107.10 sq.cm
(v)
106.10 sq.cm
Question
40
40.
In the given figure, △ABC ∼ △OPQ and BC = 10 cm , PQ = 14 cm and
AD
=
11.76 cm
,
find the area of the
△OPQ
(i)
115.22 sq.cm
(ii)
116.22 sq.cm
(iii)
114.22 sq.cm
(iv)
117.22 sq.cm
(v)
113.22 sq.cm
Question
41
41.
In the given figure, △ABC & △QRS are similar triangles. If the ratio of the heights AD : QT = 8 : 11, then the ratio of their areas is
(i)
64
sq.cm
:
124
sq.cm
(ii)
64
sq.cm
:
119
sq.cm
(iii)
64
sq.cm
:
121
sq.cm
(iv)
63
sq.cm
:
121
sq.cm
(v)
65
sq.cm
:
121
sq.cm
Question
42
42.
In the given figure, points E , F and G are the mid-points of sides CD, DB and BC of △BCD. Which of the following are true?
a)
Area of trapezium CDFG is thrice the area of △BGF
b)
All four small triangles have equal areas
c)
Area of trapezium
CDFG
is
1
4
the area of
△BCD
d)
Area of
△BCD
=
1
3
area of
△EFG
e)
Area of △BCD = 4 times area of △EFG
(i)
{c,d,e}
(ii)
{a,b,e}
(iii)
{d,b}
(iv)
{c,a,b}
(v)
{c,a}
Question
43
43.
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)
△NML ∼ △JKL
b)
△JON ∼ △JKL
c)
△MON ∼ △JKL
d)
△OKM ∼ △JKL
e)
△MNO ∼ △JKL
(i)
{c,a}
(ii)
{c,b}
(iii)
{a,b,d,e}
(iv)
{c,e,a}
(v)
{c,d}
Question
44
44.
The perimeters of two similar triangles are 30 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)
4.93 cm
(ii)
7.93 cm
(iii)
6.93 cm
(iv)
8.93 cm
(v)
5.93 cm
Question
45
45.
In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 102° , ∠GFD = 28°. Find ∠FDG
(i)
51°
(ii)
49°
(iii)
50°
(iv)
48°
(v)
52°
Question
46
46.
KLMN is a square and △KLO is an equilateral triangle. Also, △KMP is an equilateral triangle. If area of △KLO is 'a' sq.units, then the area of △KMP is
(i)
1
2
√
3
a sq.units
(ii)
a
2
sq.units
(iii)
1
2
a sq.units
(iv)
2a sq.units
(v)
√
3
a sq.units
Question
47
47.
CDEF is a cyclic trapezium. Diagonals DF and CE intersect at G. If FC = 16 cm, find DE
(i)
18 cm
(ii)
14 cm
(iii)
17 cm
(iv)
16 cm
(v)
15 cm
Question
48
48.
A vertical stick
13 m
long casts a shadow of
16 m
long on the ground.
At the same time, a tower casts the shadow
128 m
long on the ground.
Find the height of the tower.
(i)
106 m
(ii)
104 m
(iii)
103 m
(iv)
105 m
(v)
102 m
Question
49
49.
In the given figure, △FGH, RS ∥ GH such that
area of
△FRS
= area of
RSHG
. Find
FR
FG
(i)
1
2
√
2
(ii)
1
(iii)
1
2
4
√
2
(iv)
1
2
√
1
2
(v)
1
2
√
5
Question
50
50.
In the given figure, ∠DAB = ∠CAD and AD ∥ EC and AB = 16 cm, BD = 8 cm and DC = 7 cm. Find AE
(i)
13.00 cm
(ii)
14.00 cm
(iii)
15.00 cm
(iv)
16.00 cm
(v)
12.00 cm
Question
51
51.
In the given figure, IK is the angular bisector of
∠I
&
∠K
HI
=
20 cm
,
IJ
=
21 cm
and
JK
=
18 cm
.
Find
KH
(i)
16.14 cm
(ii)
17.14 cm
(iii)
19.14 cm
(iv)
18.14 cm
(v)
15.14 cm
Question
52
52.
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 = OJ . OK . OL
(iv)
GJ . HK . IL = JH . KI . LG
(v)
GJ . HK . IL = GH . HI . IG
Question
53
53.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 23 cm. Find AP
(i)
8.20 cm
(ii)
11.20 cm
(iii)
10.20 cm
(iv)
7.20 cm
(v)
9.20 cm
Question
54
54.
From the given figure and values, find x
(i)
(
0
,
8
)
(ii)
(
9
,
1
)
(iii)
(
-1
,
6
)
(iv)
(
-1
,
7
)
(v)
(
1
,
7
)
Question
55
55.
If the measures are as shown in the given figure, find DE
(i)
24.0 cm
(ii)
25.0 cm
(iii)
22.0 cm
(iv)
26.0 cm
(v)
23.0 cm
Question
56
56.
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
6.1 cm
.
Find the radius of the outer circle.
(i)
12.64 cm
(ii)
14.64 cm
(iii)
15.64 cm
(iv)
16.64 cm
(v)
13.64 cm
Assignment Key
1) (i)
2) (ii)
3) (ii)
4) (ii)
5) (ii)
6) (iii)
7) (iv)
8) (iii)
9) (iii)
10) (ii)
11) (ii)
12) (v)
13) (v)
14) (v)
15) (iii)
16) (iii)
17) (i)
18) (ii)
19) (iii)
20) (iii)
21) (ii)
22) (i)
23) (i)
24) (i)
25) (ii)
26) (ii)
27) (iv)
28) (ii)
29) (iv)
30) (v)
31) (v)
32) (iv)
33) (iii)
34) (i)
35) (i)
36) (v)
37) (iii)
38) (ii)
39) (iv)
40) (i)
41) (iii)
42) (ii)
43) (iii)
44) (iii)
45) (iii)
46) (iv)
47) (iv)
48) (ii)
49) (i)
50) (ii)
51) (ii)
52) (iv)
53) (v)
54) (iv)
55) (i)
56) (ii)