EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Similar Triangles
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
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)
∠EHF
(iii)
∠ACF
(iv)
∠FDA
(v)
∠DAF
Question
2
2.
In the given figure, RS ∥ BC , and median AD bisects RS.
△AES ∼
(i)
△ABC
(ii)
△BCA
(iii)
△ABD
(iv)
△ARE
(v)
△ADC
Question
3
3.
In the given figure, the parallelogram HIJK and the triangle △LHI are on the same bases and between the same parallels.
The area of the
△LHI
is x sq.cm. The area of the parallelogram is
(i)
twice
the area of the triangle
(ii)
5
4
the area of the triangle
(iii)
3
2
the area of the triangle
(iv)
4
3
the area of the triangle
(v)
thrice
the area of the triangle
Question
4
4.
Which of the following are true?
a)
Similar and congruent are not synonymous.
b)
If two figures are congruent, then they are similar too.
c)
Congruent figures have same area.
d)
Similar figures have same area.
e)
If two figures are similar, then they are congruent too.
(i)
{d,a}
(ii)
{d,a,b}
(iii)
{e,b}
(iv)
{a,b,c}
(v)
{d,e,c}
Question
5
5.
A vehicle goes 14 km West and then 12 km South. How far is it from its starting point ?
(i)
18.44 km
(ii)
20.44 km
(iii)
16.44 km
(iv)
17.44 km
(v)
19.44 km
Question
6
6.
Identify the property by which the two given triangles are similar
(i)
not similar
(ii)
SSS Similarity
(iii)
SAS Similarity
(iv)
AAA Similarity
Question
7
7.
In the given figure, ∠FGH = 41.7°, find the value of y =
(i)
47.30°
(ii)
46.30°
(iii)
49.30°
(iv)
50.30°
(v)
48.30°
Question
8
8.
In the given figure, O is a point in the interior of the rectangle ABCD. Then
(i)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AB
2
+
BC
2
+
CD
2
+
DA
2
(ii)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AC
2
+
BD
2
(iii)
OA
2
+
OC
2
=
OB
2
+
OD
2
(iv)
OA
2
−
OC
2
=
OB
2
−
OD
2
Question
9
9.
In the given figure, the altitudes MF and GN of △EFG meet at L. ∠GML =
(i)
∠LNF
(ii)
∠LGM
(iii)
∠FLN
(iv)
∠NFL
(v)
∠MLG
Question
10
10.
The ratio of the bases of two triangles ABC and DEF is
8
:
5
.
If the triangles are equal in area, then the ratio of their heights is
(i)
5
:
8
(ii)
8
:
3
(iii)
7
:
5
(iv)
9
:
5
(v)
8
:
7
Question
11
11.
In the given figure, △DEF & △NOP are similar triangles. If the ratio of the heights DG : NQ = 11 : 15, then the ratio of their areas is
(i)
121
sq.cm
:
227
sq.cm
(ii)
122
sq.cm
:
225
sq.cm
(iii)
120
sq.cm
:
225
sq.cm
(iv)
121
sq.cm
:
222
sq.cm
(v)
121
sq.cm
:
225
sq.cm
Question
12
12.
In the given figure, QR ∥ HI , and median GJ bisects QR.
If GJ = 17.4 cm, GK = 7.91 cm and GR = 9.09 cm, GI =
(i)
18.00 cm
(ii)
19.00 cm
(iii)
22.00 cm
(iv)
20.00 cm
(v)
21.00 cm
Question
13
13.
In the given figure, △EFG ∼ △QRS and FG = 15 cm , RS = 21 cm and
QT
=
12.18 cm
,
find the area of the
△EFG
(i)
67.24 sq.cm
(ii)
64.24 sq.cm
(iii)
66.24 sq.cm
(iv)
65.24 sq.cm
(v)
63.24 sq.cm
Question
14
14.
Identify the property by which the two given triangles are similar
(i)
AAA Similarity
(ii)
SSS Similarity
(iii)
not similar
(iv)
SAS Similarity
Question
15
15.
In the given figure, BCDE is a rhombus. Which of the following are true?
a)
BC
2
+
CD
2
+
DE
2
+
BE
2
=
BD
2
+
CE
2
b)
CD
2
+
DE
2
=
CE
2
c)
4
BC
2
=
BD
2
+
CE
2
d)
2
BC
2
=
BD
2
+
CE
2
e)
BC
2
+
CD
2
=
BD
2
(i)
{a,c}
(ii)
{b,a}
(iii)
{d,c,a}
(iv)
{d,c}
(v)
{e,b,a}
Question
16
16.
A ladder reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 17 m high. Find the width of the street if the length of the ladder is 21 m
(i)
33.30 m
(ii)
29.30 m
(iii)
32.30 m
(iv)
30.30 m
(v)
31.30 m
Question
17
17.
In the given figure,
DE
∥
BC
.
If
AD
DB
=
1
1
and
AC
=
14.9 cm
, find
AE
(i)
8.45 cm
(ii)
7.45 cm
(iii)
6.45 cm
(iv)
5.45 cm
(v)
9.45 cm
Question
18
18.
In the given figure, K and L are points on the sides HI and HJ respectively of △HIJ.For which of the following cases, KL ∥ IJ
a)
HI = 16 cm, KI = 8 cm, HL = 11.5 cm and HJ = 19 cm
b)
HK = 8 cm, KI = 8 cm, HL = 9.5 cm and LJ = 9.5 cm
c)
HI = 16 cm, HK = 10 cm, HJ = 19 cm and LJ = 9.5 cm
d)
HI = 16 cm, KI = 8 cm, HJ = 19 cm and HL = 9.5 cm
(i)
{b,d}
(ii)
{a,d,b}
(iii)
{a,c,b}
(iv)
{a,b}
(v)
{c,d}
Question
19
19.
In the given figure, ∠DAB = ∠CAD and AD ∥ EC and AB = 16 cm, BD = 7 cm and DC = 8 cm. Find AE
(i)
18.29 cm
(ii)
19.29 cm
(iii)
17.29 cm
(iv)
16.29 cm
(v)
20.29 cm
Question
20
20.
In the given figure, △BCD , E is the mid-point of CD and BF ⟂ CD. Which of the following are true?
a)
BC
2
=
BE
2
−
CD
.
EF
+
1
4
CD
2
b)
BC
2
+
BD
2
= 2
BE
2
+
1
2
CD
2
c)
BD
2
=
BF
2
+
CD
.
EF
+
1
4
CD
2
d)
BD
2
=
BE
2
+
CD
.
EF
+
1
4
CD
2
e)
BC
2
=
BF
2
−
CD
.
EF
+
1
4
CD
2
(i)
{c,a,b}
(ii)
{c,e,d}
(iii)
{a,b,d}
(iv)
{c,a}
(v)
{e,b}
Question
21
21.
In the given figure, DEFG is a trapezium in which
DE ∥ FG
and the diagonals
EG
and
DF
intersect at
H
.
△HFG
∼
(i)
△HEF
(ii)
△HGD
(iii)
△GDE
(iv)
△HDE
(v)
△EFG
Question
22
22.
In the given figure, △GHI, GJ ⟂ HI. Which of the following are true?
a)
GH
2
+
HJ
2
=
GI
2
+
IJ
2
b)
GJ
2
=
2
HJ
.
IJ
c)
GH
2
−
HJ
2
=
GI
2
−
IJ
2
d)
GH
2
+
GI
2
=
HJ
2
+
IJ
2
e)
GH
2
−
GI
2
=
HJ
2
−
IJ
2
(i)
{b,e}
(ii)
{d,a,c}
(iii)
{a,c}
(iv)
{c,e}
(v)
{b,e,c}
Question
23
23.
In the given figure, △CDE is a triangle in which CF is the internal bisector of ∠C and EG ∥ FC meeting DC produced at G . ∠FCD =
(i)
∠DFC
(ii)
∠EGC
(iii)
∠FEC
(iv)
∠GCE
(v)
∠CFE
Question
24
24.
In the given figure, △FGH is right-angled at G. Also, GI ⟂ FH. If FI = 15.6 cm, GI = 12.49 cm, then find IH.
(i)
8.00 cm
(ii)
10.00 cm
(iii)
9.00 cm
(iv)
12.00 cm
(v)
11.00 cm
Question
25
25.
In the given figure, if BC ∥ DE then
(i)
△BCF ∼ △FDE
(ii)
△FCB ∼ △FED
(iii)
△BCF ∼ △EDF
(iv)
△BCF ∼ △FED
(v)
△FBC ∼ △FDE
Assignment Key
1) (iii)
2) (v)
3) (i)
4) (iv)
5) (i)
6) (iii)
7) (v)
8) (iii)
9) (i)
10) (i)
11) (v)
12) (iv)
13) (iv)
14) (i)
15) (i)
16) (v)
17) (ii)
18) (i)
19) (i)
20) (iii)
21) (iv)
22) (iv)
23) (ii)
24) (ii)
25) (iii)
