EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure, △CDE, CF ⟂ DE. Which of the following are true?
a)
CD
2
−
DF
2
=
CE
2
−
EF
2
b)
CF
2
=
2
DF
.
EF
c)
CD
2
+
DF
2
=
CE
2
+
EF
2
d)
CD
2
+
CE
2
=
DF
2
+
EF
2
e)
CD
2
−
CE
2
=
DF
2
−
EF
2
(i)
{d,b,a}
(ii)
{c,e}
(iii)
{c,e,a}
(iv)
{b,a}
(v)
{a,e}
Question
2
2.
In a right angled triangle, if one of the sides is 10 cm and hypotenuse 26 cm, find the third side
(i)
24.00 cm
(ii)
23.00 cm
(iii)
26.00 cm
(iv)
25.00 cm
(v)
22.00 cm
Question
3
3.
Two poles of heights 5 m and 15 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops
(i)
16.62 m
(ii)
17.62 m
(iii)
13.62 m
(iv)
14.62 m
(v)
15.62 m
Question
4
4.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
9 AB
2
(ii)
7 AD
2
=
3 AB
2
(iii)
3 AD
2
=
7 AB
2
(iv)
9 AD
2
=
7 AB
2
Question
5
5.
Which of the following are true?
a)
A circle is a polygonal region.
b)
A sector is a polygonal region.
c)
A square is a polygonal region.
d)
A triangle is a polygonal region.
e)
A semi-circle is a polygonal region.
(i)
{c,d}
(ii)
{e,a,c}
(iii)
{b,d}
(iv)
{a,c}
(v)
{b,d,c}
Question
6
6.
In the given figure, the area of the △LMN is x sq.cm. O,P,Q are the mid-points of the sides MN , NL and LM respectively. The area of the △OPQ is
(i)
1
3
of area of △LMN
(ii)
1
4
of area of △LMN
(iii)
1
2
of area of △LMN
(iv)
3
4
of area of △LMN
(v)
2
3
of area of △LMN
Question
7
7.
Which of the following are true?
a)
Any two quadrilaterals are similar if the corresponding sides are proportional.
b)
Any two triangles are similar if the corresponding sides are proportional.
c)
Any two triangles are similar if the corresponding angles are equal.
d)
Any two quadrilaterals are similar if the corresponding angles are equal.
(i)
{d,a,b}
(ii)
{d,c}
(iii)
{d,a}
(iv)
{d,b}
(v)
{a,b,c}
Question
8
8.
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)
∠HFE
(ii)
∠HAB
(iii)
∠FEH
(iv)
∠FAC
(v)
∠FDA
Question
9
9.
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)
△ACF
(ii)
△FEH
(iii)
△ABH
(iv)
△DCF
(v)
△DAE
Question
10
10.
In the given figure, IJKL is a trapezium in which
IJ ∥ KL
and the diagonals
JL
and
IK
intersect at
M
.
If
MI
=
(
x
+
14
)
cm,
JM
=
(
x
+
32
)
cm,
MK
=
(
x
+
3
)
cm and
LM
=
(
x
+
18
)
cm, find the value of x
(i)
(
53
,
53
)
(ii)
(
52
,
52
)
(iii)
(
52
,
51
)
(iv)
(
54
,
54
)
(v)
(
54
,
52
)
Question
11
11.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
AD
=
(i)
CA
2
(ii)
BC
2
(iii)
BC
(iv)
AB
2
(v)
AE
Question
12
12.
In the given figure, △ABC , D is the mid-point of BC and AE ⟂ BC. Which of the following are true?
a)
AB
2
+
AC
2
= 2
AD
2
+
1
2
BC
2
b)
AB
2
=
AD
2
−
BC
.
DE
+
1
4
BC
2
c)
AC
2
=
AD
2
+
BC
.
DE
+
1
4
BC
2
d)
AB
2
=
AE
2
−
BC
.
DE
+
1
4
BC
2
e)
AC
2
=
AE
2
+
BC
.
DE
+
1
4
BC
2
(i)
{d,e,c}
(ii)
{d,a,b}
(iii)
{e,b}
(iv)
{a,b,c}
(v)
{d,a}
Question
13
13.
In the given figure, O is a point in the interior of the rectangle EFGH. Then
(i)
OE
2
−
OG
2
=
OF
2
−
OH
2
(ii)
OE
2
+
OG
2
=
OF
2
+
OH
2
(iii)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EG
2
+
FH
2
(iv)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EF
2
+
FG
2
+
GH
2
+
HE
2
Question
14
14.
In the given figure,
△BDC
is right-angled at
D
.
S
is the mid-point of
BD
and
T
is the mid-point of
CD
.
Which of the following cases are true?
a)
4
CS
2
=
4
CD
2
+
BD
2
b)
4
BT
2
=
4
CD
2
+
BD
2
c)
4
CS
2
=
4
BD
2
+
CD
2
d)
4 (
BT
2
+
CS
2
) =
5
BC
2
e)
4
BT
2
=
4
BD
2
+
CD
2
(i)
{b,a,d}
(ii)
{c,d}
(iii)
{b,a}
(iv)
{b,c,e}
(v)
{a,d,e}
Question
15
15.
In the given figure, △DEF, ST ∥ EF such that
area of
△DST
= area of
STFE
. Find
DS
DE
(i)
1
2
√
-1
(ii)
1
(iii)
1
2
√
2
(iv)
1
2
√
4
(v)
1
2
4
√
2
Question
16
16.
In the given △IJK, LM ∥ JK. If IL : LJ = 7.6 cm : 11.4 cm and IK = 17 cm, MK =
(i)
10.20 cm
(ii)
12.20 cm
(iii)
11.20 cm
(iv)
9.20 cm
(v)
8.20 cm
Question
17
17.
In the given figure
△KLM
,
N
is the mid-point of
KL
and
NO
∥
LM
,
then
KN
=
(i)
MK
(ii)
OM
(iii)
KO
(iv)
KL
(v)
NL
Question
18
18.
In the given figure, QR ∥ GH , and median FI bisects QR.
If FI = 14.6 cm, FJ = 8.34 cm and FR = 10.29 cm, FH =
(i)
18.00 cm
(ii)
19.00 cm
(iii)
20.00 cm
(iv)
16.00 cm
(v)
17.00 cm
Question
19
19.
In the given figure
△ABC
,
D
is the mid-point of
AB
and
DE
∥
BC
,
then
DB
=
(i)
AD
(ii)
EC
(iii)
AB
(iv)
AE
(v)
CA
Question
20
20.
In the given figure, O and P are points on the sides LM and LN respectively of △LMN.For which of the following cases, OP ∥ MN
a)
LM = 18 cm, OM = 11.25 cm, LN = 19 cm and LP = 7.12 cm
b)
LM = 18 cm, OM = 11.25 cm, LP = 9.12 cm and LN = 19 cm
c)
LM = 18 cm, LO = 8.75 cm, LN = 19 cm and PN = 11.88 cm
d)
LO = 6.75 cm, OM = 11.25 cm, LP = 7.12 cm and PN = 11.88 cm
(i)
{b,a}
(ii)
{c,d}
(iii)
{b,c,a}
(iv)
{a,d}
(v)
{b,d,a}
Question
21
21.
In the given figure, EFGH is a rhombus. Which of the following are true?
a)
EF
2
+
FG
2
=
EG
2
b)
EF
2
+
FG
2
+
GH
2
+
EH
2
=
EG
2
+
FH
2
c)
FG
2
+
GH
2
=
FH
2
d)
2
EF
2
=
EG
2
+
FH
2
e)
4
EF
2
=
EG
2
+
FH
2
(i)
{b,e}
(ii)
{a,b}
(iii)
{c,e,b}
(iv)
{c,e}
(v)
{d,a,b}
Question
22
22.
In the given figure,
FG
∥
DE
.
If
CF
FD
=
5
4
and
CE
=
12.8 cm
, find
CG
(i)
5.11 cm
(ii)
7.11 cm
(iii)
9.11 cm
(iv)
6.11 cm
(v)
8.11 cm
Question
23
23.
In the given figure, the parallelogram DEFG and the triangle △HDE are on the same bases and between the same parallels.
The area of the
△HDE
is x sq.cm. The area of the parallelogram is
(i)
5
4
the area of the triangle
(ii)
thrice
the area of the triangle
(iii)
3
2
the area of the triangle
(iv)
twice
the area of the triangle
(v)
4
3
the area of the triangle
Question
24
24.
In the given figure, LMNO is a trapezium in which
LM ∥ NO
and the diagonals
MO
and
LN
intersect at
P
.
△PNO
∼
(i)
△PLM
(ii)
△POL
(iii)
△MNO
(iv)
△PMN
(v)
△OLM
Question
25
25.
From the given figure and values, find x
(i)
(
-13
,
25
)
(ii)
(
-13
,
26
)
(iii)
(
28
,
-11
)
(iv)
(
-12
,
27
)
(v)
(
-10
,
26
)
Assignment Key
1) (v)
2) (i)
3) (v)
4) (iv)
5) (i)
6) (ii)
7) (v)
8) (i)
9) (ii)
10) (ii)
11) (iv)
12) (iv)
13) (ii)
14) (v)
15) (iii)
16) (i)
17) (v)
18) (i)
19) (i)
20) (iv)
21) (i)
22) (ii)
23) (iv)
24) (i)
25) (ii)
