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, ST ∥ BC , and median AD bisects ST.
If AD = 17.3 cm, AC = 20 cm and AE = 7.41 cm, ED =
(i)
9.89 cm
(ii)
11.89 cm
(iii)
10.89 cm
(iv)
8.89 cm
(v)
7.89 cm
Question
2
2.
In the given figure, the altitudes TI and JU of △HIJ meet at S. △UIS ∼
(i)
△TJI
(ii)
△SIJ
(iii)
△TJS
(iv)
△SUT
(v)
△UIJ
Question
3
3.
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)
∠DAF
(iii)
∠ACF
(iv)
∠EHF
(v)
∠FDA
Question
4
4.
In the given figure,
FG
∥
DE
.
If
CF
FD
=
5
2
and
CE
=
12.5 cm
, find
CG
(i)
10.93 cm
(ii)
9.93 cm
(iii)
8.93 cm
(iv)
6.93 cm
(v)
7.93 cm
Question
5
5.
The perimeters of two similar triangles are 34 cm and 16 cm respectively. If one side of the first triangle is 12 cm, find the length of the corresponding side of the second triangle.
(i)
6.65 cm
(ii)
3.65 cm
(iii)
7.65 cm
(iv)
5.65 cm
(v)
4.65 cm
Question
6
6.
In the given figure, given ∠KHI = ∠JHK, x : y = 8.44 cm : 10.56 cm and p = 16 cm, find q =
(i)
20.00 cm
(ii)
18.00 cm
(iii)
22.00 cm
(iv)
19.00 cm
(v)
21.00 cm
Question
7
7.
In the given figure, △PQR is isosceles right-angled at Q and QS ⟂ RP. ∠QSP =
(i)
∠PQS
(ii)
∠QRS
(iii)
∠PQR
(iv)
∠SQR
(v)
∠SPQ
Question
8
8.
In the given figure, △CDE ∼ △PQR and DE = 15 cm , QR = 21 cm and
PS
=
16.4 cm
,
find the area of the
△CDE
(i)
87.87 sq.cm
(ii)
89.87 sq.cm
(iii)
85.87 sq.cm
(iv)
86.87 sq.cm
(v)
88.87 sq.cm
Question
9
9.
In the given figure, the altitudes RB and CS of △ABC meet at Q. ∠CRQ =
(i)
∠SBQ
(ii)
∠BQS
(iii)
∠RQC
(iv)
∠QCR
(v)
∠QSB
Question
10
10.
In the given figure, PQ ∥ GH and FG = 20 cm, PQ = 15 cm and GH = 25 cm, find FP
(i)
12.0 cm
(ii)
13.0 cm
(iii)
11.0 cm
(iv)
10.0 cm
(v)
14.0 cm
Question
11
11.
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
+
29
)
cm,
EH
=
(
3
x
+
13
)
cm,
HF
=
(
2
x
+
30
)
cm and
GH
=
(
2
x
+
18
)
cm, find the value of x
(i)
(
34
,
34
)
(ii)
(
35
,
35
)
(iii)
(
36
,
33
)
(iv)
(
33
,
32
)
(v)
(
33
,
33
)
Question
12
12.
In the given figure, PQ ∥ HI , and median GJ bisects PQ.
If GH = 18 cm, GJ = 17.9 cm and GP = 8.18 cm, PH =
(i)
10.82 cm
(ii)
8.82 cm
(iii)
9.82 cm
(iv)
7.82 cm
(v)
11.82 cm
Question
13
13.
In the given △MNO, PQ ∥ NO. If MP : PN = 12.5 cm : 7.5 cm and MO = 18 cm, QO =
(i)
7.75 cm
(ii)
8.75 cm
(iii)
5.75 cm
(iv)
4.75 cm
(v)
6.75 cm
Question
14
14.
In the given figure, △HIJ and △QRS are such that
∠I
=
∠R
and
∠J
=
∠S
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
SSS Similarity
(iii)
AAA Similarity
(iv)
SAS Similarity
Question
15
15.
In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. If GF = 9 cm, EG = 12 cm, then find DG.
(i)
17.00 cm
(ii)
18.00 cm
(iii)
16.00 cm
(iv)
14.00 cm
(v)
15.00 cm
Question
16
16.
In the given figure, G is a point on side EF of △DEF such that ∠FDE = ∠DGF = 103° , ∠GFD = 25°. Find ∠FDG
(i)
50°
(ii)
51°
(iii)
53°
(iv)
52°
(v)
54°
Question
17
17.
In the given figure, ST ∥ DE , and median CF bisects ST.
△CSG ∼
(i)
△CGT
(ii)
△CFE
(iii)
△DEC
(iv)
△CDF
(v)
△CDE
Question
18
18.
In the given figure, △ABC ∼ △OPQ and AB = 14 cm, OP = 19.6 cm.
If the area of the
△ABC
=
65.38 sq.cm
, find the area of the
△OPQ
(i)
127.15 sq.cm
(ii)
128.15 sq.cm
(iii)
129.15 sq.cm
(iv)
126.15 sq.cm
(v)
130.15 sq.cm
Question
19
19.
In the given figure, △CDE & △PQR are similar triangles. If the ratio of the heights CF : PS = 9 : 13, then the ratio of their areas is
(i)
81
sq.cm
:
166
sq.cm
(ii)
82
sq.cm
:
169
sq.cm
(iii)
80
sq.cm
:
169
sq.cm
(iv)
81
sq.cm
:
169
sq.cm
(v)
81
sq.cm
:
172
sq.cm
Question
20
20.
In the given figure, △FGH is isosceles right-angled at G and GI ⟂ HF. ∠G =
(i)
∠J
(ii)
∠I
(iii)
∠H
(iv)
∠K
(v)
∠F
Question
21
21.
GHIJ is a square and △GHK is an equilateral triangle. Also, △GIL is an equilateral triangle. If area of △GHK is 'a' sq.units, then the area of △GIL is
(i)
1
2
√
3
a sq.units
(ii)
2a sq.units
(iii)
√
3
a sq.units
(iv)
a
2
sq.units
(v)
1
2
a sq.units
Question
22
22.
In the given figure, R and S are points on the sides OP and OQ respectively of △OPQ.For which of the following cases, RS ∥ PQ
a)
OP = 20 cm, OR = 12 cm, OQ = 17 cm and SQ = 8.5 cm
b)
OR = 10 cm, RP = 10 cm, OS = 8.5 cm and SQ = 8.5 cm
c)
OP = 20 cm, RP = 10 cm, OQ = 17 cm and OS = 8.5 cm
d)
OP = 20 cm, RP = 10 cm, OS = 10.5 cm and OQ = 17 cm
(i)
{d,c}
(ii)
{b,c}
(iii)
{a,d,b}
(iv)
{a,b}
(v)
{a,c,b}
Question
23
23.
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)
∠FAC
(ii)
∠FEH
(iii)
∠HFE
(iv)
∠FDA
(v)
∠HAB
Question
24
24.
In the given figure, points K , L and M are the mid-points of sides IJ, JH and HI of △HIJ. Which of the following are true?
a)
△LKJ ∼ △HIJ
b)
△MIK ∼ △HIJ
c)
△KML ∼ △HIJ
d)
△HML ∼ △HIJ
e)
△KLM ∼ △HIJ
(i)
{c,b}
(ii)
{a,b,d,e}
(iii)
{c,d}
(iv)
{c,a}
(v)
{c,e,a}
Question
25
25.
In the given figure,
NO
∥
LM
.
If
KN
=
10.13 cm
,
KL
=
15.2 cm
and
KM
=
12.1 cm
, find
KO
(i)
6.07 cm
(ii)
9.07 cm
(iii)
7.07 cm
(iv)
8.07 cm
(v)
10.07 cm
Assignment Key
1) (i)
2) (iii)
3) (iii)
4) (iii)
5) (iv)
6) (i)
7) (iii)
8) (i)
9) (v)
10) (i)
11) (v)
12) (iii)
13) (v)
14) (iii)
15) (iii)
16) (iv)
17) (iv)
18) (ii)
19) (iv)
20) (ii)
21) (ii)
22) (ii)
23) (iii)
24) (ii)
25) (iv)
