EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Triangles
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are measures of a right angled triangle ?
(i)
HI = 14 cm , IJ = 14 cm , JH = 14 cm
(ii)
HI = 11 cm , IJ = 15 cm , JH = 13 cm
(iii)
HI = 11 cm , IJ = 22 cm , JH = 14 cm
(iv)
HI = 15 cm , IJ = 10 cm , JH = 14 cm
(v)
HI = 15 cm , IJ = 12 cm , JH = 19.21 cm
Question
2
2.
Which of the following are measures of an isosceles right angled triangle ?
(i)
JK = 10 cm , KL = 13 cm , LJ = 11 cm
(ii)
JK = 12 cm , KL = 18 cm , LJ = 10 cm
(iii)
JK = 11 cm , KL = 11 cm , LJ = 11 cm
(iv)
JK = 13 cm , KL = 15 cm , LJ = 10 cm
(v)
JK = 15 cm , KL = 15 cm , LJ = 21.21 cm
Question
3
3.
Which of the following are measures of a right angled triangle ?
(i)
NO = 12 cm , OP = 13 cm , PN = 10 cm
(ii)
NO = 15 cm , OP = 12 cm , PN = 19.21 cm
(iii)
NO = 10 cm , OP = 10 cm , PN = 10 cm
(iv)
NO = 12 cm , OP = 23 cm , PN = 15 cm
(v)
NO = 13 cm , OP = 13 cm , PN = 15 cm
Question
4
4.
Which of the following are measures of an isosceles right angled triangle ?
(i)
EF = 12 cm , FG = 14 cm , GE = 13 cm
(ii)
EF = 15 cm , FG = 22 cm , GE = 14 cm
(iii)
EF = 12 cm , FG = 12 cm , GE = 16.97 cm
(iv)
EF = 13 cm , FG = 13 cm , GE = 13 cm
(v)
EF = 12 cm , FG = 14 cm , GE = 15 cm
Question
5
5.
In a right angled triangle, if one of the sides is 20 cm and hypotenuse 101 cm, find the third side
(i)
100.00 cm
(ii)
99.00 cm
(iii)
97.00 cm
(iv)
101.00 cm
(v)
98.00 cm
Question
6
6.
In a right angled triangle, if the two non-hypotenuse sides are 8 cm and 15 cm, find the hypotenuse
(i)
18.00 cm
(ii)
16.00 cm
(iii)
17.00 cm
(iv)
19.00 cm
(v)
15.00 cm
Question
7
7.
In the given figure, △CDE is right-angled at D. Also, DF ⟂ CE. Which of the following are true?
a)
DE
2
=
EC
.
EF
b)
CD
2
=
CE
.
CF
c)
CD
2
=
EC
.
EF
d)
DF
2
=
CF
.
FE
e)
DE
2
=
CE
.
CF
(i)
{c,a,b}
(ii)
{c,a}
(iii)
{e,b}
(iv)
{c,e,d}
(v)
{a,b,d}
Question
8
8.
In the given figure, △BCD is an obtuse angled triangle and BE ⟂ CD. Then
(i)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
(ii)
BD
2
=
BC
2
+
CD
2
+
CE
2
(iii)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
(iv)
BD
2
=
BC
2
+
CD
2
−
2
CD
.
CE
(v)
BD
2
=
BC
2
+
CD
2
+
2
CE
.
DE
Question
9
9.
In the given figure, △ABC is an acute angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
−
2
AB
.
BC
(ii)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(iii)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(iv)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
(v)
AC
2
=
AB
2
+
BC
2
−
AD
2
Question
10
10.
In the given figure, △CDE is a triangle with CF being the median of DE. Then
(i)
CD
2
+
CE
2
=
2
FE
2
+
2
CF
2
(ii)
CD
2
+
CE
2
=
2
DF
2
+
2
FE
2
(iii)
CD
2
+
CE
2
=
CF
2
(iv)
CD
2
+
CE
2
=
2
DF
2
+
2
CF
2
(v)
CD
2
+
CE
2
=
DE
2
Question
11
11.
In the given figure, △ABC is a triangle in which AB = AC and D is a point on BC. Then
(i)
AB
2
+
AD
2
=
BC
2
(ii)
AB
2
+
AD
2
=
BD
.
CD
(iii)
AB
2
−
AD
2
=
AD
.
BD
(iv)
AB
2
−
AD
2
=
AD
.
CD
(v)
AB
2
−
AD
2
=
BD
.
CD
Question
12
12.
In the given figure, in △DEF, 'O' is a point inside the triangle. OG ⟂ EF, OH ⟂ DF and OI ⟂ DE. Then
(i)
DI
2
+
EG
2
+
FH
2
=
OD
2
+
OE
2
+
OF
2
−
OG
2
−
OH
2
−
OI
2
(ii)
DI
2
+
EG
2
+
FH
2
=
OD
2
+
OE
2
+
OF
2
+
OG
2
+
OH
2
+
OI
2
(iii)
DI
2
+
EG
2
+
FH
2
=
OI
2
+
OH
2
+
OG
2
(iv)
DI
2
+
EG
2
+
FH
2
=
DE
2
+
GF
2
+
FD
2
−
EI
2
−
FG
2
−
HD
2
Question
13
13.
In the given figure, in △DEF, 'O' is a point inside the triangle. OG ⟂ EF, OH ⟂ DF and OI ⟂ DE. Then
(i)
DI
2
+
EG
2
+
FH
2
=
OI
.
OG
+
OG
.
OH
+
OH
.
OI
(ii)
DI
2
+
EG
2
+
FH
2
=
OD
.
OE
+
OE
.
OF
+
OF
.
OD
(iii)
DI
2
+
EG
2
+
FH
2
=
OG
2
+
OH
2
+
OI
2
(iv)
DI
2
+
EG
2
+
FH
2
=
DH
2
+
FG
2
+
EI
2
Question
14
14.
In the given figure,
△GIH
is right-angled at
I
.
S
is the mid-point of
GI
and
T
is the mid-point of
HI
.
Which of the following cases are true?
a)
4 (
GT
2
+
HS
2
) =
5
GH
2
b)
4
GT
2
=
4
HI
2
+
GI
2
c)
4
HS
2
=
4
HI
2
+
GI
2
d)
4
HS
2
=
4
GI
2
+
HI
2
e)
4
GT
2
=
4
GI
2
+
HI
2
(i)
{a,c,e}
(ii)
{b,a,c}
(iii)
{b,d,e}
(iv)
{d,c}
(v)
{b,a}
Question
15
15.
In the given figure, △BCD is isosceles with BC = BD and CE ⟂ BD. Then
(i)
CE
2
−
BE
2
= 2
DE
.
BE
(ii)
CE
2
+
BE
2
= 2
DE
.
BE
(iii)
CE
2
−
DE
2
= 2
DE
.
BE
(iv)
CE
2
+
DE
2
= 2
DE
.
BE
Question
16
16.
In the given figure, GHIJ is a rhombus. Which of the following are true?
a)
HI
2
+
IJ
2
=
HJ
2
b)
4
GH
2
=
GI
2
+
HJ
2
c)
GH
2
+
HI
2
=
GI
2
d)
2
GH
2
=
GI
2
+
HJ
2
e)
GH
2
+
HI
2
+
IJ
2
+
GJ
2
=
GI
2
+
HJ
2
(i)
{d,a,b}
(ii)
{c,e}
(iii)
{a,b}
(iv)
{b,e}
(v)
{c,e,b}
Question
17
17.
In the given figure, △GHI, GJ ⟂ HI. Which of the following are true?
a)
GH
2
−
GI
2
=
HJ
2
−
IJ
2
b)
GH
2
+
HJ
2
=
GI
2
+
IJ
2
c)
GH
2
−
HJ
2
=
GI
2
−
IJ
2
d)
GJ
2
=
2
HJ
.
IJ
e)
GH
2
+
GI
2
=
HJ
2
+
IJ
2
(i)
{d,c}
(ii)
{d,c,a}
(iii)
{e,b,a}
(iv)
{a,c}
(v)
{b,a}
Question
18
18.
The altitude and area of an equilateral triangle of side 'a' is
(i)
√
3
a,
1
2
√
3
a
(ii)
1
2
√
3
a,
1
4
√
3
a
2
(iii)
1
2
√
3
a,
1
2
√
3
a
2
(iv)
√
3
a,
1
2
√
3
a
2
Question
19
19.
In the given figure, O is a point in the interior of the rectangle BCDE. Then
(i)
OB
2
+
OC
2
+
OD
2
+
OE
2
=
BD
2
+
CE
2
(ii)
OB
2
+
OC
2
+
OD
2
+
OE
2
=
BC
2
+
CD
2
+
DE
2
+
EB
2
(iii)
OB
2
+
OD
2
=
OC
2
+
OE
2
(iv)
OB
2
−
OD
2
=
OC
2
−
OE
2
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
=
BF
2
−
CD
.
EF
+
1
4
CD
2
b)
BD
2
=
BF
2
+
CD
.
EF
+
1
4
CD
2
c)
BD
2
=
BE
2
+
CD
.
EF
+
1
4
CD
2
d)
BC
2
=
BE
2
−
CD
.
EF
+
1
4
CD
2
e)
BC
2
+
BD
2
= 2
BE
2
+
1
2
CD
2
(i)
{a,b,e}
(ii)
{a,c}
(iii)
{b,d}
(iv)
{c,d,e}
(v)
{a,c,d}
Question
21
21.
In the given figure, △EGF is right-angled at G, GH ⟂ EF.
EF
= c,
GF
= a,
EG
= b and
GH
= p.
Which of the following are true?
a)
1
a
2
+
1
b
2
=
1
p
2
b)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
c)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
d)
a
2
+
b
2
=
c
2
e)
ab
=
pc
(i)
{b,c,e}
(ii)
{c,d}
(iii)
{b,a}
(iv)
{a,d,e}
(v)
{b,a,d}
Question
22
22.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
9 AD
2
=
7 AB
2
(ii)
7 AD
2
=
3 AB
2
(iii)
3 AD
2
=
7 AB
2
(iv)
7 AD
2
=
9 AB
2
Question
23
23.
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 = OJ . OK . OL
(ii)
GJ . HK . IL = GH . HI . IG
(iii)
GJ . HK . IL = JH . KI . LG
(iv)
GJ . HK . IL = OG . OH . OI
(v)
GJ . HK . IL = JK . KL . LJ
Question
24
24.
A vehicle goes 13 km North and then 11 km West. How far is it from its starting point ?
(i)
17.03 km
(ii)
18.03 km
(iii)
15.03 km
(iv)
19.03 km
(v)
16.03 km
Question
25
25.
The foot of a ladder resting on a wall from the foot of the wall is 11 m. If the height of the top of the ladder from ground is 12 m, find the length of the ladder
(i)
16.28 m
(ii)
18.28 m
(iii)
14.28 m
(iv)
17.28 m
(v)
15.28 m
Question
26
26.
Two poles of heights 8 m and 17 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops
(i)
14.00 m
(ii)
16.00 m
(iii)
17.00 m
(iv)
13.00 m
(v)
15.00 m
Question
27
27.
A ladder reaches a window which is 10 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 14 m high. Find the width of the street if the length of the ladder is 17 m
(i)
21.39 m
(ii)
24.39 m
(iii)
25.39 m
(iv)
23.39 m
(v)
22.39 m
Assignment Key
1) (v)
2) (v)
3) (ii)
4) (iii)
5) (ii)
6) (iii)
7) (v)
8) (iii)
9) (ii)
10) (iv)
11) (v)
12) (i)
13) (iv)
14) (i)
15) (iii)
16) (iv)
17) (iv)
18) (ii)
19) (iii)
20) (iv)
21) (iv)
22) (i)
23) (iii)
24) (i)
25) (i)
26) (v)
27) (iv)
