EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Triangles
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Which of the following are measures of an isosceles triangle ?
(i)
∠H = 59.49° , ∠I = 67.38° , ∠J = 53.13°
(ii)
∠H = 60° , ∠I = 60° , ∠J = 60°
(iii)
∠H = 64.78° , ∠I = 57.61° , ∠J = 57.61°
(iv)
∠H = 56.31° , ∠I = 90° , ∠J = 33.69°
(v)
∠H = 61.28° , ∠I = 69.98° , ∠J = 48.74°
Question
2
2.
In the given figure , if GD ⟂ EF and ∠DEG = 43.63°, find ∠FDG
(i)
32.18°
(ii)
31.18°
(iii)
34.18°
(iv)
33.18°
(v)
30.18°
Question
3
3.
The altitude corresponding to the side
OM
(i)
MP
(ii)
MQ
(iii)
OR
(iv)
NQ
(v)
MN
Question
4
4.
Each of the two equal angles of an isosceles triangle is half the third angle. Find the angles of the triangle
(i)
X
=
45°
,
Y
=
88°
,
Z
=
47°
(ii)
X
=
45°
,
Y
=
90°
,
Z
=
45°
(iii)
X
=
43°
,
Y
=
92°
,
Z
=
45°
(iv)
X
=
43°
,
Y
=
90°
,
Z
=
47°
(v)
X
=
47°
,
Y
=
90°
,
Z
=
43°
Question
5
5.
How many diagonals does a triangle have?
(i)
2
(ii)
0
(iii)
4
(iv)
1
(v)
3
Question
6
6.
The point of intersection of the bisectors of the interior angles of a triangle is called
(i)
altitude
(ii)
centroid
(iii)
median
(iv)
excentre
(v)
incentre
Question
7
7.
In the given figure, which of the following is true?
(i)
△EGH ≅ △EFG
(ii)
△EHG ≅ △FGE
(iii)
△EGH ≅ △GEF
(iv)
△EGH ≅ △EGF
(v)
△EHG ≅ △EFG
Question
8
8.
With the given data in the figure, △KJM ≅ △LIM by which property?
(i)
SSS Congruency
(ii)
ASA Congruency
(iii)
not congruent
(iv)
SAS Congruency
(v)
RHS Congruency
Question
9
9.
Which of the following are measures of a scalene triangle ?
(i)
∠P = 60° , ∠Q = 60° , ∠R = 60°
(ii)
∠P = 66.12° , ∠Q = 56.94° , ∠R = 56.94°
(iii)
∠P = 48.37° , ∠Q = 76.33° , ∠R = 55.3°
(iv)
∠P = 45° , ∠Q = 90° , ∠R = 45°
(v)
∠P = 79.04° , ∠Q = 50.48° , ∠R = 50.48°
Question
10
10.
With the data in the figure, △ABD ≅ △CBD by which property?
(i)
ASA Congruency
(ii)
RHS Congruency
(iii)
SAS Congruency
(iv)
not congruent
(v)
SSS Congruency
Question
11
11.
With the data in the given figure, △TOP ≅ △SPO by which property?
(i)
not congruent
(ii)
SAS Congruency
(iii)
SSS Congruency
(iv)
ASA Congruency
(v)
RHS Congruency
Question
12
12.
Which of the following are measures of an isosceles right angled triangle ?
(i)
∠O = 60° , ∠P = 60° , ∠Q = 60°
(ii)
∠O = 55.83° , ∠P = 49.32° , ∠Q = 74.85°
(iii)
∠O = 45° , ∠P = 90° , ∠Q = 45°
(iv)
∠O = 137.17° , ∠P = 20.64° , ∠Q = 22.19°
(v)
∠O = 62.18° , ∠P = 55.64° , ∠Q = 62.18°
Question
13
13.
If the ratio of the bases of two triangles is I : J and the ratio of the corresponding heights is K : L , the ratio of their areas in the same order is
(i)
KL : IJ
(ii)
IK : JL
(iii)
JK : IL
(iv)
IL : JK
(v)
IJ : KL
Question
14
14.
In the given figure, find the values of x and y
(i)
x
=
49.68°
,
y
=
50.02°
(ii)
x
=
48.68°
,
y
=
49.02°
(iii)
x
=
47.68°
,
y
=
48.02°
(iv)
x
=
46.68°
,
y
=
47.02°
(v)
x
=
50.68°
,
y
=
51.02°
Question
15
15.
With the data in the figure, △FGI ≅ △GFH by which property?
(i)
SAS Congruency
(ii)
RHS Congruency
(iii)
ASA Congruency
(iv)
not congruent
(v)
SSS Congruency
Question
16
16.
Which of the following are measures of an isosceles right angled triangle ?
(i)
∠H = 52.62° , ∠I = 59.41° , ∠J = 67.97°
(ii)
∠H = 95.22° , ∠I = 44.66° , ∠J = 40.12°
(iii)
∠H = 60° , ∠I = 60° , ∠J = 60°
(iv)
∠H = 45° , ∠I = 90° , ∠J = 45°
(v)
∠H = 49.32° , ∠I = 74.85° , ∠J = 55.83°
Question
17
17.
In the given figure, the area of the △KLM is x sq.cm. N,O,P are the mid-points of the sides LM , MK and KL respectively. The area of the △NOP is
(i)
1
4
of area of △KLM
(ii)
3
4
of area of △KLM
(iii)
1
2
of area of △KLM
(iv)
2
3
of area of △KLM
(v)
1
3
of area of △KLM
Question
18
18.
In the given figure, find ∠JHI
(i)
104°
(ii)
102°
(iii)
105°
(iv)
103°
(v)
106°
Question
19
19.
Find the measures of the three sides suitable to form a triangle?
(i)
KL = 13 cm , LM = 13 cm , MK = 10 cm
(ii)
KL = 9 cm , LM = 19 cm , MK = 8 cm
(iii)
KL = 19 cm , LM = 5 cm , MK = 13 cm
(iv)
KL = 17 cm , LM = 5 cm , MK = 9 cm
(v)
KL = 7 cm , LM = 16 cm , MK = 5 cm
Question
20
20.
Which of the following are true?
a)
Similar figures have same area.
b)
If two figures are congruent, then they are similar too.
c)
Congruent figures have same area.
d)
Similar and congruent are not synonymous.
e)
If two figures are similar, then they are congruent too.
(i)
{e,c}
(ii)
{a,b,c}
(iii)
{a,e,d}
(iv)
{a,b}
(v)
{b,c,d}
Question
21
21.
Find the angles of the triangle
(i)
B
=
62°
,
C
=
45°
,
D
=
73°
(ii)
B
=
60°
,
C
=
43°
,
D
=
77°
(iii)
B
=
60°
,
C
=
45°
,
D
=
75°
(iv)
B
=
58°
,
C
=
45°
,
D
=
77°
(v)
B
=
58°
,
C
=
47°
,
D
=
75°
Question
22
22.
Which of the following are measures of an obtuse angled triangle ?
(i)
EF = 10 cm , FG = 10 cm , GE = 10 cm
(ii)
EF = 13 cm , FG = 24 cm , GE = 15 cm
(iii)
EF = 15 cm , FG = 12 cm , GE = 14 cm
(iv)
EF = 14 cm , FG = 14 cm , GE = 19.8 cm
(v)
EF = 13 cm , FG = 11 cm , GE = 17.03 cm
Question
23
23.
In the given figure, if NK = LN and KO = OM , find the value of x.
(i)
x
=
68°
(ii)
x
=
67°
(iii)
x
=
66°
(iv)
x
=
64°
(v)
x
=
65°
Question
24
24.
Find the unknown marked angles in the following figure
(i)
x
=
97°
,
y
=
123°
(ii)
x
=
93°
,
y
=
119°
(iii)
x
=
94°
,
y
=
120°
(iv)
x
=
96°
,
y
=
122°
(v)
x
=
95°
,
y
=
121°
Question
25
25.
In the given figure,
△DEF
is a triangle in which
∠D
=
∠E
=
∠F
.
This bisectors of
∠E
and
∠F
intersect at
G
.
Find
∠G
=
(i)
122°
(ii)
121°
(iii)
120°
(iv)
118°
(v)
119°
Assignment Key
1) (iii)
2) (i)
3) (iv)
4) (ii)
5) (ii)
6) (v)
7) (iii)
8) (ii)
9) (iii)
10) (iv)
11) (v)
12) (iii)
13) (ii)
14) (ii)
15) (iv)
16) (iv)
17) (i)
18) (i)
19) (i)
20) (v)
21) (iii)
22) (ii)
23) (iii)
24) (v)
25) (iii)
