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, I and J are points on the sides FG and FH respectively of △FGH.For which of the following cases, IJ ∥ GH
a)
FG = 20 cm, FI = 10.89 cm, FH = 19 cm and JH = 10.56 cm
b)
FG = 20 cm, IG = 11.11 cm, FH = 19 cm and FJ = 8.44 cm
c)
FI = 8.89 cm, IG = 11.11 cm, FJ = 8.44 cm and JH = 10.56 cm
d)
FG = 20 cm, IG = 11.11 cm, FJ = 10.44 cm and FH = 19 cm
(i)
{d,c}
(ii)
{b,c}
(iii)
{a,d,b}
(iv)
{a,c,b}
(v)
{a,b}
Question
2
2.
In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FG = 15 cm, GI = 11.52 cm, then find GH.
(i)
17.00 cm
(ii)
18.00 cm
(iii)
20.00 cm
(iv)
16.00 cm
(v)
19.00 cm
Question
3
3.
In the given figure, the two circles touch each other internally.
Diameter
OB
passes through the centre of the smaller circle.
OX = 11 cm
,
OY = 26 cm
and radius of the inner circle is
6.1 cm
.
Find the radius of the outer circle.
(i)
13.42 cm
(ii)
14.42 cm
(iii)
15.42 cm
(iv)
16.42 cm
(v)
12.42 cm
Question
4
4.
In the given figure, ∠IGH = 38.52°, find the value of y =
(i)
52.48°
(ii)
49.48°
(iii)
53.48°
(iv)
50.48°
(v)
51.48°
Question
5
5.
In the given figure, △EFG and △STU are such that
∠F
=
∠T
and
∠G
=
∠U
.
Identify the property by which the two triangles are similar
(i)
SAS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SSS Similarity
Question
6
6.
From the given figure and values, find x
(i)
(
23
,
-3
)
(ii)
(
-5
,
21
)
(iii)
(
-5
,
20
)
(iv)
(
-4
,
22
)
(v)
(
-2
,
21
)
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.
In the given figure, if CD ∥ EF then
(i)
△CDG ∼ △FEG
(ii)
△GDC ∼ △GFE
(iii)
△CDG ∼ △GFE
(iv)
△GCD ∼ △GEF
(v)
△CDG ∼ △GEF
Question
9
9.
In the given figure, PQ ∥ EF , and median DG bisects PQ.
△DPH ∼
(i)
△DHQ
(ii)
△DEG
(iii)
△EFD
(iv)
△DEF
(v)
△DGF
Question
10
10.
In the given two similar triangles, if i = 19 cm, j = 17 cm, k = 15 cm, n = 9 cm, find l
(i)
13.40 cm
(ii)
10.40 cm
(iii)
12.40 cm
(iv)
9.40 cm
(v)
11.40 cm
Question
11
11.
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
12
12.
In the given figure, the altitudes RF and GS of △EFG meet at Q. △SFQ ∼
(i)
△SFG
(ii)
△RGQ
(iii)
△QFG
(iv)
△QSR
(v)
△RGF
Question
13
13.
In the given figure, △GHI, TU ∥ HI such that
area of
△GTU
= area of
TUIH
. Find
GT
GH
(i)
1
2
4
√
2
(ii)
1
2
√
2
(iii)
1
2
√
1
2
(iv)
1
2
√
5
(v)
1
Question
14
14.
A vertical stick
11 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)
90 m
(ii)
89 m
(iii)
86 m
(iv)
87 m
(v)
88 m
Question
15
15.
In the given figure, CDEF is a trapezium where OC = 13 cm , OD = 13 cm and OF = 4 cm . Find OE =
(i)
3 cm
(ii)
2 cm
(iii)
6 cm
(iv)
5 cm
(v)
4 cm
Question
16
16.
In the given figure, given ∠IFG = ∠HFI, x : y = 7.94 cm : 7.06 cm and q = 16 cm, find p =
(i)
17.00 cm
(ii)
16.00 cm
(iii)
19.00 cm
(iv)
18.00 cm
(v)
20.00 cm
Question
17
17.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
AAA Similarity
(iii)
SSS Similarity
(iv)
not similar
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.
∠AFD =
(i)
∠FEH
(ii)
∠HAB
(iii)
∠HFE
(iv)
∠FDA
(v)
∠FAC
Question
19
19.
In the given figure,
ST
∥
QR
.
If
PS
=
9.53 cm
,
PQ
=
14.3 cm
and
PR
=
14.8 cm
, find
PT
(i)
8.87 cm
(ii)
11.87 cm
(iii)
10.87 cm
(iv)
7.87 cm
(v)
9.87 cm
Question
20
20.
The ratio of the bases of two triangles ABC and DEF is
6
:
7
.
If the triangles are equal in area, then the ratio of their heights is
(i)
6
:
9
(ii)
6
:
5
(iii)
7
:
6
(iv)
5
:
7
(v)
7
:
7
Question
21
21.
In the given figure, the altitudes QC and DR of △BCD meet at P. ∠DQP =
(i)
∠PDQ
(ii)
∠CPR
(iii)
∠QPD
(iv)
∠RCP
(v)
∠PRC
Question
22
22.
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)
△DAE
(ii)
△FDA
(iii)
△ABH
(iv)
△DCF
(v)
△FEH
Question
23
23.
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)
Area of △JKL = 4 times area of △MNO
b)
Area of
△JKL
=
1
3
area of
△MNO
c)
All four small triangles have equal areas
d)
Area of trapezium KLNO is thrice the area of △JON
e)
Area of trapezium
KLNO
is
1
4
the area of
△JKL
(i)
{b,a}
(ii)
{e,c}
(iii)
{b,e,d}
(iv)
{b,a,c}
(v)
{a,c,d}
Question
24
24.
In the given figure, DEFG is a trapezium in which
DE ∥ FG
and the diagonals
EG
and
DF
intersect at
H
.
If
HD
=
(
3
x
+
15
)
cm,
EH
=
(
3
x
+
6
)
cm,
HF
=
(
x
+
22
)
cm and
GH
=
(
x
+
18
)
cm, find the value of x
(i)
(
48
,
48
)
(ii)
(
48
,
46
)
(iii)
(
47
,
47
)
(iv)
(
46
,
46
)
(v)
(
46
,
45
)
Question
25
25.
In the given figure, EG is the angular bisector of
∠E
&
∠G
DE
=
20 cm
,
EF
=
20 cm
and
FG
=
21 cm
.
Find
GD
(i)
23.00 cm
(ii)
21.00 cm
(iii)
20.00 cm
(iv)
19.00 cm
(v)
22.00 cm
Assignment Key
1) (ii)
2) (ii)
3) (ii)
4) (v)
5) (iii)
6) (ii)
7) (i)
8) (i)
9) (ii)
10) (v)
11) (iii)
12) (ii)
13) (ii)
14) (v)
15) (v)
16) (iv)
17) (ii)
18) (iii)
19) (v)
20) (iii)
21) (v)
22) (iii)
23) (v)
24) (iv)
25) (ii)
