EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Similarity of Triangles
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure, △KLM is a triangle in which KN is the internal bisector of ∠K and MO ∥ NK meeting LK produced at O . ∠MKN =
(i)
∠LNK
(ii)
∠KNM
(iii)
∠NKL
(iv)
∠NMK
(v)
∠OKM
Question
2
2.
In the given figure, K is a point on side IJ of △HIJ such that ∠JHI = ∠HKJ = 106° , ∠KJH = 22°. Find ∠JHK
(i)
52°
(ii)
53°
(iii)
51°
(iv)
54°
(v)
50°
Question
3
3.
In the given figure, △FGH is isosceles right-angled at G and GI ⟂ HF. ∠HIG =
(i)
∠FGI
(ii)
∠IFG
(iii)
∠GHI
(iv)
∠GIF
(v)
∠IGH
Question
4
4.
In the given figure, DEF is a triangle and 'O' is a point inside △DEF. The angular bisector of ∠EOD, ∠FOE & ∠DOF meet DE, EF & FD at G, H & I respectively . Then
(i)
DG . EH . FI = OG . OH . OI
(ii)
DG . EH . FI = GH . HI . IG
(iii)
DG . EH . FI = OD . OE . OF
(iv)
DG . EH . FI = DE . EF . FD
(v)
DG . EH . FI = GE . HF . ID
Question
5
5.
In the given figure, △BCD and △STU are such that
∠C
=
∠T
and
BC
ST
=
CD
TU
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
not similar
(iii)
SAS Similarity
(iv)
SSS Similarity
Question
6
6.
Identify the property by which the two given triangles are similar
(i)
SSS Similarity
(ii)
SAS Similarity
(iii)
not similar
(iv)
AAA Similarity
Question
7
7.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SAS Similarity
(iii)
not similar
(iv)
SSS Similarity
Question
8
8.
In the given figure, ∠JHI = 50.01°, find the value of y =
(i)
37.99°
(ii)
38.99°
(iii)
39.99°
(iv)
41.99°
(v)
40.99°
Question
9
9.
From the given figure and values, find x
(i)
(
42
,
41
)
(ii)
(
42
,
42
)
(iii)
(
44
,
44
)
(iv)
(
44
,
42
)
(v)
(
43
,
43
)
Question
10
10.
In the given figure, △ABC, ST ∥ BC such that
area of
△AST
= area of
STCB
. Find
AS
AB
(i)
1
2
√
-1
(ii)
1
2
√
2
(iii)
1
2
√
4
(iv)
1
2
4
√
2
(v)
1
Question
11
11.
In the given △GHI, JK ∥ HI. If GJ : JH = 9 cm : 9 cm and GI = 19 cm, GK =
(i)
11.50 cm
(ii)
10.50 cm
(iii)
8.50 cm
(iv)
9.50 cm
(v)
7.50 cm
Question
12
12.
A vertical stick
11 m
long casts a shadow of
15 m
long on the ground.
At the same time, a tower casts the shadow
120 m
long on the ground.
Find the height of the tower.
(i)
89 m
(ii)
86 m
(iii)
90 m
(iv)
88 m
(v)
87 m
Question
13
13.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
not similar
(iii)
SSS Similarity
(iv)
AAA Similarity
Question
14
14.
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
6.4 cm
.
Find the radius of the outer circle.
(i)
15.36 cm
(ii)
13.36 cm
(iii)
17.36 cm
(iv)
16.36 cm
(v)
14.36 cm
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.
∠BHA =
(i)
∠EHF
(ii)
∠AFD
(iii)
∠HFE
(iv)
∠CFA
(v)
∠DAF
Question
16
16.
In the given figure, △EFG and △UVW are such that
∠F
=
∠V
and
∠G
=
∠W
.
Identify the property by which the two triangles are similar
(i)
SSS Similarity
(ii)
SAS Similarity
(iii)
not similar
(iv)
AAA Similarity
Question
17
17.
In the given figure, TU ∥ EF and DU = 13.8 cm, DF = 23 cm and TU = 13.8 cm, find EF
(i)
22.0 cm
(ii)
25.0 cm
(iii)
21.0 cm
(iv)
23.0 cm
(v)
24.0 cm
Question
18
18.
In the given figure,
LM
∥
JK
.
If
IL
LJ
=
5
4
and
IK
=
11.3 cm
, find
IM
(i)
4.28 cm
(ii)
8.28 cm
(iii)
6.28 cm
(iv)
5.28 cm
(v)
7.28 cm
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.
∠FDA =
(i)
∠EHF
(ii)
∠ACF
(iii)
∠FEH
(iv)
∠DAF
(v)
∠ABH
Question
20
20.
In the given figure, CDEF is a trapezium in which
CD ∥ EF
and the diagonals
DF
and
CE
intersect at
G
.
△GCD
∼
(i)
△GFC
(ii)
△GEF
(iii)
△GDE
(iv)
△FCD
(v)
△DEF
Question
21
21.
In the given figure, given ∠GDE = ∠FDG, x : y = 8.74 cm : 8.26 cm and p = 18 cm, find q =
(i)
15.00 cm
(ii)
19.00 cm
(iii)
17.00 cm
(iv)
18.00 cm
(v)
16.00 cm
Question
22
22.
In the given figure, △CDE ∼ △OPQ and DE = 11 cm , PQ = 15.4 cm and
CF
=
9.53 cm
,
find the area of the
△OPQ
(i)
103.69 sq.cm
(ii)
100.69 sq.cm
(iii)
101.69 sq.cm
(iv)
104.69 sq.cm
(v)
102.69 sq.cm
Question
23
23.
In the given figure, G and H are points on the sides DE and DF respectively of △DEF.For which of the following cases, GH ∥ EF
a)
DE = 15 cm, DG = 8 cm, DF = 17 cm and HF = 10.2 cm
b)
DG = 6 cm, GE = 9 cm, DH = 6.8 cm and HF = 10.2 cm
c)
DE = 15 cm, GE = 9 cm, DH = 8.8 cm and DF = 17 cm
d)
DE = 15 cm, GE = 9 cm, DF = 17 cm and DH = 6.8 cm
(i)
{a,d,b}
(ii)
{a,b}
(iii)
{a,c,b}
(iv)
{c,d}
(v)
{b,d}
Question
24
24.
In the given figure, ∠HEF = 36.87°, find the value of x =
(i)
54.13°
(ii)
51.13°
(iii)
52.13°
(iv)
55.13°
(v)
53.13°
Question
25
25.
If the ratio of the bases of two triangles is G : H and the ratio of the corresponding heights is I : J , the ratio of their areas in the same order is
(i)
GJ : HI
(ii)
GH : IJ
(iii)
HI : GJ
(iv)
GI : HJ
(v)
IJ : GH
Assignment Key
1) (iii)
2) (i)
3) (iv)
4) (v)
5) (iii)
6) (ii)
7) (iv)
8) (iii)
9) (ii)
10) (ii)
11) (iv)
12) (iv)
13) (iv)
14) (i)
15) (iv)
16) (iv)
17) (iv)
18) (iii)
19) (iii)
20) (ii)
21) (iii)
22) (v)
23) (v)
24) (v)
25) (iv)
