EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In a right angled triangle, if one of the sides is 4 cm and hypotenuse 5 cm, find the third side
(i)
5.00 cm
(ii)
1.00 cm
(iii)
4.00 cm
(iv)
3.00 cm
(v)
2.00 cm
Question
2
2.
In the given figure, in △FGH, 'O' is a point inside the triangle. OI ⟂ GH, OJ ⟂ FH and OK ⟂ FG. Then
(i)
FK
2
+
GI
2
+
HJ
2
=
OF
2
+
OG
2
+
OH
2
−
OI
2
−
OJ
2
−
OK
2
(ii)
FK
2
+
GI
2
+
HJ
2
=
OK
2
+
OJ
2
+
OI
2
(iii)
FK
2
+
GI
2
+
HJ
2
=
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
+
OK
2
(iv)
FK
2
+
GI
2
+
HJ
2
=
FG
2
+
IH
2
+
HF
2
−
GK
2
−
HI
2
−
JF
2
Question
3
3.
In the given figure,
△EGF
is right-angled at
G
.
R
is the mid-point of
EG
and
S
is the mid-point of
FG
.
Which of the following cases are true?
a)
4
FR
2
=
4
EG
2
+
FG
2
b)
4
FR
2
=
4
FG
2
+
EG
2
c)
4 (
ES
2
+
FR
2
) =
5
EF
2
d)
4
ES
2
=
4
FG
2
+
EG
2
e)
4
ES
2
=
4
EG
2
+
FG
2
(i)
{a,d,e}
(ii)
{b,c,e}
(iii)
{a,b,c}
(iv)
{d,c}
(v)
{a,b}
Question
4
4.
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 trapezium
KLNO
is
1
4
the area of
△JKL
b)
Area of trapezium KLNO is thrice the area of △JON
c)
All four small triangles have equal areas
d)
Area of
△JKL
=
1
3
area of
△MNO
e)
Area of △JKL = 4 times area of △MNO
(i)
{a,b}
(ii)
{a,d,e}
(iii)
{b,c,e}
(iv)
{d,c}
(v)
{a,b,c}
Question
5
5.
In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If JI = 9 cm, HJ = 12 cm, then find GJ.
(i)
16.00 cm
(ii)
14.00 cm
(iii)
15.00 cm
(iv)
18.00 cm
(v)
17.00 cm
Question
6
6.
Identify the property by which the two given triangles are similar
(i)
SAS Similarity
(ii)
not similar
(iii)
AAA Similarity
(iv)
SSS Similarity
Question
7
7.
In the given figure, RS ∥ CD , and median BE bisects RS.
If BC = 16 cm, BR = 8 cm and BF = 7.95 cm, BE =
(i)
16.90 cm
(ii)
15.90 cm
(iii)
14.90 cm
(iv)
17.90 cm
(v)
13.90 cm
Question
8
8.
In the given figure, the altitudes QG and HR of △FGH meet at P. ∠RGP =
(i)
∠PHQ
(ii)
∠QPH
(iii)
∠GPR
(iv)
∠PRG
(v)
∠HQP
Question
9
9.
In the given figure
△GHI
,
J
is the mid-point of
GH
and
JK
∥
HI
,
then
KI
=
(i)
GJ
(ii)
GK
(iii)
IG
(iv)
JH
(v)
GH
Question
10
10.
In the given figure, HIJK is a trapezium in which
HI ∥ JK
and the diagonals
IK
and
HJ
intersect at
L
.
If
LH
=
(
3
x
+
15
)
cm,
IL
=
(
2
x
+
22
)
cm,
LJ
=
(
2
x
+
10
)
cm and
KL
=
(
x
+
25
)
cm, find the value of x
(i)
(
-4
,
32
)
(ii)
(
-5
,
30
)
(iii)
(
-5
,
31
)
(iv)
(
33
,
-3
)
(v)
(
-2
,
31
)
Question
11
11.
In the given figure, △CDE, ST ∥ DE such that
area of
△CST
= area of
STED
. Find
CS
CD
(i)
1
2
√
2
(ii)
1
2
√
1
2
(iii)
1
(iv)
1
2
√
4
(v)
1
2
4
√
2
Question
12
12.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
3 AD
2
=
7 AB
2
(ii)
7 AD
2
=
3 AB
2
(iii)
9 AD
2
=
7 AB
2
(iv)
7 AD
2
=
9 AB
2
Question
13
13.
A vehicle goes 10 km East and then 12 km North. How far is it from its starting point ?
(i)
15.62 km
(ii)
17.62 km
(iii)
16.62 km
(iv)
13.62 km
(v)
14.62 km
Question
14
14.
In the given figure, the two circles touch each other internally.
Diameter
OB
passes through the centre of the smaller circle.
OX = 9 cm
,
OY = 21 cm
and radius of the inner circle is
5.3 cm
.
Find the radius of the outer circle.
(i)
11.37 cm
(ii)
10.37 cm
(iii)
14.37 cm
(iv)
13.37 cm
(v)
12.37 cm
Question
15
15.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
NL
=
(i)
MK
(ii)
KL
(iii)
KO
(iv)
OM
(v)
KN
Question
16
16.
Which of the following are true?
a)
Similarity is reflexive.
b)
Similarity is symmetric.
c)
Similarity is transitive.
d)
Similarity is anti symmetric.
(i)
{a,b,c}
(ii)
{d,b}
(iii)
{d,c}
(iv)
{d,a,b}
(v)
{d,a}
Question
17
17.
In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. Which of the following are true?
a)
CD
2
=
BD
.
BE
b)
BC
2
=
DB
.
DE
c)
CE
2
=
BE
.
ED
d)
CD
2
=
DB
.
DE
e)
BC
2
=
BD
.
BE
(i)
{a,c,d}
(ii)
{a,c}
(iii)
{a,b,e}
(iv)
{c,d,e}
(v)
{b,d}
Question
18
18.
In the given figure, if FG ∥ HI then
(i)
△FGJ ∼ △JHI
(ii)
△FGJ ∼ △IHJ
(iii)
△FGJ ∼ △JIH
(iv)
△JGF ∼ △JIH
(v)
△JFG ∼ △JHI
Question
19
19.
In the given △NOP, QR ∥ OP. If NQ : QO = 5.33 cm : 10.67 cm and NP = 15 cm, RP =
(i)
11.00 cm
(ii)
12.00 cm
(iii)
10.00 cm
(iv)
9.00 cm
(v)
8.00 cm
Question
20
20.
In the given figure
△CDE
,
F
is the mid-point of
CD
and
FG
∥
DE
,
then
CF
=
(i)
CG
(ii)
EC
(iii)
FD
(iv)
CD
(v)
GE
Question
21
21.
In the given figure, ABCD is a rhombus. Which of the following are true?
a)
2
AB
2
=
AC
2
+
BD
2
b)
AB
2
+
BC
2
+
CD
2
+
AD
2
=
AC
2
+
BD
2
c)
AB
2
+
BC
2
=
AC
2
d)
4
AB
2
=
AC
2
+
BD
2
e)
BC
2
+
CD
2
=
BD
2
(i)
{c,d,b}
(ii)
{a,b}
(iii)
{e,a,b}
(iv)
{c,d}
(v)
{b,d}
Question
22
22.
Which of the following are measures of an isosceles right angled triangle ?
(i)
PQ = 12 cm , QR = 12 cm , RP = 16.97 cm
(ii)
PQ = 10 cm , QR = 11 cm , RP = 13 cm
(iii)
PQ = 15 cm , QR = 15 cm , RP = 15 cm
(iv)
PQ = 10 cm , QR = 18 cm , RP = 13 cm
(v)
PQ = 15 cm , QR = 12 cm , RP = 12 cm
Question
23
23.
In the given figure, TU ∥ FG , and median EH bisects TU.
If EG = 20 cm, EI = 6.03 cm and EU = 6.67 cm, EH =
(i)
16.10 cm
(ii)
17.10 cm
(iii)
19.10 cm
(iv)
20.10 cm
(v)
18.10 cm
Question
24
24.
Which of the following are measures of a right angled triangle ?
(i)
JK = 13 cm , KL = 23 cm , LJ = 15 cm
(ii)
JK = 10 cm , KL = 10 cm , LJ = 10 cm
(iii)
JK = 14 cm , KL = 14 cm , LJ = 11 cm
(iv)
JK = 14 cm , KL = 15 cm , LJ = 20.52 cm
(v)
JK = 14 cm , KL = 11 cm , LJ = 13 cm
Question
25
25.
In the given figure
△FGH
,
I
is the mid-point of
FG
and
IJ
∥
GH
,
then
FJ
=
(i)
FI
(ii)
FG
2
(iii)
HF
2
(iv)
GH
2
(v)
GH
Assignment Key
1) (iv)
2) (i)
3) (ii)
4) (iii)
5) (i)
6) (iv)
7) (ii)
8) (i)
9) (ii)
10) (iii)
11) (i)
12) (iii)
13) (i)
14) (v)
15) (v)
16) (i)
17) (iv)
18) (ii)
19) (iii)
20) (iii)
21) (v)
22) (i)
23) (v)
24) (iv)
25) (iii)
