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, ∠DAB = ∠CAD and AD ∥ EC and AB = 17 cm, BD = 8 cm and DC = 8 cm. Find AE
(i)
18.00 cm
(ii)
17.00 cm
(iii)
19.00 cm
(iv)
15.00 cm
(v)
16.00 cm
Question
2
2.
In the given figure, if BC ∥ DE then
(i)
△FCB ∼ △FED
(ii)
△BCF ∼ △EDF
(iii)
△BCF ∼ △FDE
(iv)
△FBC ∼ △FDE
(v)
△BCF ∼ △FED
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.
∠HAB =
(i)
∠HFE
(ii)
∠FDA
(iii)
∠AFD
(iv)
∠FEH
(v)
∠FAC
Question
4
4.
In the given figure, △EFG & △PQR are similar triangles. If the ratio of the heights EH : PS = 8 : 11, then the ratio of their areas is
(i)
65
sq.cm
:
121
sq.cm
(ii)
64
sq.cm
:
118
sq.cm
(iii)
64
sq.cm
:
121
sq.cm
(iv)
64
sq.cm
:
124
sq.cm
(v)
63
sq.cm
:
121
sq.cm
Question
5
5.
In the given figure, △CDE and △RST are such that
∠D
=
∠S
and
∠E
=
∠T
.
Identify the property by which the two triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
6
6.
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)
∠FEH
(iii)
∠DAF
(iv)
∠ABH
(v)
∠ACF
Question
7
7.
From the given figure and values, find x
(i)
(
23
,
-2
)
(ii)
(
-4
,
20
)
(iii)
(
-4
,
21
)
(iv)
(
-3
,
22
)
(v)
(
-2
,
21
)
Question
8
8.
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 = JH . KI . LG
(ii)
GJ . HK . IL = GH . HI . IG
(iii)
GJ . HK . IL = OG . OH . OI
(iv)
GJ . HK . IL = JK . KL . LJ
(v)
GJ . HK . IL = OJ . OK . OL
Question
9
9.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
SSS Similarity
(iii)
AAA Similarity
(iv)
not similar
Question
10
10.
In the given figure, ∠DEF = 40.02°, find the value of y =
(i)
47.98°
(ii)
48.98°
(iii)
51.98°
(iv)
50.98°
(v)
49.98°
Question
11
11.
In the given △ABC, DE ∥ BC. If AD : DB = 11.11 cm : 8.89 cm and AC = 15 cm, AE =
(i)
9.33 cm
(ii)
10.33 cm
(iii)
8.33 cm
(iv)
7.33 cm
(v)
6.33 cm
Question
12
12.
In the given figure, ST ∥ CD , and median BE bisects ST.
If BC = 15 cm, BE = 15.1 cm and BS = 7.5 cm, SC =
(i)
5.50 cm
(ii)
6.50 cm
(iii)
9.50 cm
(iv)
8.50 cm
(v)
7.50 cm
Question
13
13.
The ratio of the bases of two triangles ABC and DEF is
3
:
4
.
If the triangles are equal in area, then the ratio of their heights is
(i)
4
:
3
(ii)
3
:
2
(iii)
3
:
6
(iv)
2
:
4
(v)
4
:
4
Question
14
14.
In the given figure, △FGH and △STU are such that
∠G
=
∠T
and
FG
ST
=
GH
TU
.
Identify the property by which the two triangles are similar
(i)
not similar
(ii)
AAA Similarity
(iii)
SAS Similarity
(iv)
SSS Similarity
Question
15
15.
In the given figure, △EFG ∼ △OPQ and FG = 14 cm , PQ = 19.6 cm and
OR
=
15.18 cm
,
find the area of the
△EFG
(i)
75.89 sq.cm
(ii)
77.89 sq.cm
(iii)
73.89 sq.cm
(iv)
76.89 sq.cm
(v)
74.89 sq.cm
Question
16
16.
In the given figure, EFGH is a trapezium in which
EF ∥ GH
and the diagonals
FH
and
EG
intersect at
I
.
△IGH
∼
(i)
△IEF
(ii)
△FGH
(iii)
△IHE
(iv)
△IFG
(v)
△HEF
Question
17
17.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 25 cm and AP = 10 cm. Find PB
(i)
13.00 cm
(ii)
14.00 cm
(iii)
15.00 cm
(iv)
16.00 cm
(v)
17.00 cm
Question
18
18.
The perimeters of two similar triangles are 35 cm and 15 cm respectively. If one side of the first triangle is 11 cm, find the length of the corresponding side of the second triangle.
(i)
6.71 cm
(ii)
4.71 cm
(iii)
5.71 cm
(iv)
3.71 cm
(v)
2.71 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.
△ACF ∼
(i)
△DAE
(ii)
△DCF
(iii)
△FEH
(iv)
△FDA
(v)
△ABH
Question
20
20.
In the given figure, points G , H and I are the mid-points of sides EF, FD and DE of △DEF. Which of the following are true?
a)
△GIH ∼ △DEF
b)
△IEG ∼ △DEF
c)
△DIH ∼ △DEF
d)
△HGF ∼ △DEF
e)
△GHI ∼ △DEF
(i)
{a,c}
(ii)
{a,e,b}
(iii)
{a,b}
(iv)
{a,d}
(v)
{b,c,d,e}
Question
21
21.
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)
2
3
of area of △GHI
(ii)
1
2
of area of △GHI
(iii)
3
4
of area of △GHI
(iv)
1
3
of area of △GHI
(v)
1
4
of area of △GHI
Question
22
22.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
23
23.
In the given figure, ∠CDF = 48.72°, find the value of x =
(i)
42.28°
(ii)
40.28°
(iii)
43.28°
(iv)
41.28°
(v)
39.28°
Question
24
24.
In the given figure, ST ∥ HI , and median GJ bisects ST.
△GJI ∼
(i)
△GKT
(ii)
△GSK
(iii)
△GHI
(iv)
△HIG
(v)
△GHJ
Question
25
25.
In the given figure, the parallelogram IJKL and the triangle △MIJ are on the same bases and between the same parallels.
The area of the
△MIJ
is x sq.cm. The area of the parallelogram is
(i)
twice
the area of the triangle
(ii)
thrice
the area of the triangle
(iii)
3
2
the area of the triangle
(iv)
5
4
the area of the triangle
(v)
4
3
the area of the triangle
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (iii)
5) (i)
6) (ii)
7) (iii)
8) (i)
9) (ii)
10) (v)
11) (iii)
12) (v)
13) (i)
14) (iii)
15) (i)
16) (i)
17) (iii)
18) (ii)
19) (v)
20) (v)
21) (v)
22) (i)
23) (iv)
24) (i)
25) (i)
