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)
KL = 12 cm , LM = 12 cm , MK = 12 cm
(ii)
KL = 10 cm , LM = 19 cm , MK = 12 cm
(iii)
KL = 15 cm , LM = 12 cm , MK = 19.21 cm
(iv)
KL = 13 cm , LM = 12 cm , MK = 11 cm
Question
2
2.
Which of the following are measures of an isosceles right angled triangle ?
(i)
HI = 13 cm , IJ = 13 cm , JH = 13 cm
(ii)
HI = 15 cm , IJ = 25 cm , JH = 12 cm
(iii)
HI = 11 cm , IJ = 12 cm , JH = 15 cm
(iv)
HI = 14 cm , IJ = 10 cm , JH = 15 cm
(v)
HI = 10 cm , IJ = 10 cm , JH = 14.14 cm
Question
3
3.
Which of the following are measures of a right angled triangle ?
(i)
GH = 13 cm , HI = 14 cm , IG = 19.1 cm
(ii)
GH = 11 cm , HI = 18 cm , IG = 13 cm
(iii)
GH = 11 cm , HI = 15 cm , IG = 15 cm
(iv)
GH = 12 cm , HI = 15 cm , IG = 13 cm
(v)
GH = 14 cm , HI = 14 cm , IG = 14 cm
Question
4
4.
Which of the following are measures of an isosceles right angled triangle ?
(i)
HI = 10 cm , IJ = 10 cm , JH = 13 cm
(ii)
HI = 14 cm , IJ = 22 cm , JH = 12 cm
(iii)
HI = 11 cm , IJ = 11 cm , JH = 11 cm
(iv)
HI = 13 cm , IJ = 13 cm , JH = 18.38 cm
(v)
HI = 10 cm , IJ = 15 cm , JH = 12 cm
Question
5
5.
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)
22.00 cm
(iii)
23.00 cm
(iv)
26.00 cm
(v)
25.00 cm
Question
6
6.
In a right angled triangle, if the two non-hypotenuse sides are 6 cm and 8 cm, find the hypotenuse
(i)
8.00 cm
(ii)
12.00 cm
(iii)
11.00 cm
(iv)
9.00 cm
(v)
10.00 cm
Question
7
7.
In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. Which of the following are true?
a)
BC
2
=
AC
.
AD
b)
BD
2
=
AD
.
DC
c)
AB
2
=
CA
.
CD
d)
AB
2
=
AC
.
AD
e)
BC
2
=
CA
.
CD
(i)
{a,c,e}
(ii)
{a,b}
(iii)
{c,d}
(iv)
{b,d,e}
(v)
{a,b,d}
Question
8
8.
In the given figure, △ABC is an obtuse angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(ii)
AC
2
=
AB
2
+
BC
2
+
2
BD
.
CD
(iii)
AC
2
=
AB
2
+
BC
2
+
BD
2
(iv)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
(v)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
Question
9
9.
In the given figure, △EFG is an acute angled triangle and EH ⟂ FG. Then
(i)
EG
2
=
EF
2
+
FG
2
−
2
EF
.
FG
(ii)
EG
2
=
EF
2
+
FG
2
+
2
FG
.
FH
(iii)
EG
2
=
EF
2
+
FG
2
−
2
FG
.
FH
(iv)
EG
2
=
EF
2
+
FG
2
+
2
EF
.
FG
(v)
EG
2
=
EF
2
+
FG
2
−
EH
2
Question
10
10.
In the given figure, △EFG is a triangle with EH being the median of FG. Then
(i)
EF
2
+
EG
2
=
FG
2
(ii)
EF
2
+
EG
2
=
EH
2
(iii)
EF
2
+
EG
2
=
2
FH
2
+
2
EH
2
(iv)
EF
2
+
EG
2
=
2
FH
2
+
2
HG
2
(v)
EF
2
+
EG
2
=
2
HG
2
+
2
EH
2
Question
11
11.
In the given figure, △DEF is a triangle in which DE = DF and G is a point on EF. Then
(i)
DE
2
+
DG
2
=
EF
2
(ii)
DE
2
−
DG
2
=
DG
.
FG
(iii)
DE
2
−
DG
2
=
EG
.
FG
(iv)
DE
2
−
DG
2
=
DG
.
EG
(v)
DE
2
+
DG
2
=
EG
.
FG
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
=
OI
2
+
OH
2
+
OG
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
=
DE
2
+
GF
2
+
FD
2
−
EI
2
−
FG
2
−
HD
2
(iv)
DI
2
+
EG
2
+
FH
2
=
OD
2
+
OE
2
+
OF
2
+
OG
2
+
OH
2
+
OI
2
Question
13
13.
In the given figure, in △ABC, 'O' is a point inside the triangle. OD ⟂ BC, OE ⟂ AC and OF ⟂ AB. Then
(i)
AF
2
+
BD
2
+
CE
2
=
OA
.
OB
+
OB
.
OC
+
OC
.
OA
(ii)
AF
2
+
BD
2
+
CE
2
=
OF
.
OD
+
OD
.
OE
+
OE
.
OF
(iii)
AF
2
+
BD
2
+
CE
2
=
AE
2
+
CD
2
+
BF
2
(iv)
AF
2
+
BD
2
+
CE
2
=
OD
2
+
OE
2
+
OF
2
Question
14
14.
In the given figure,
△CED
is right-angled at
E
.
Q
is the mid-point of
CE
and
R
is the mid-point of
DE
.
Which of the following cases are true?
a)
4
DQ
2
=
4
CE
2
+
DE
2
b)
4
CR
2
=
4
DE
2
+
CE
2
c)
4
CR
2
=
4
CE
2
+
DE
2
d)
4 (
CR
2
+
DQ
2
) =
5
CD
2
e)
4
DQ
2
=
4
DE
2
+
CE
2
(i)
{a,c,d}
(ii)
{a,c}
(iii)
{c,d,e}
(iv)
{a,b,e}
(v)
{b,d}
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
−
DE
2
= 2
DE
.
BE
(iii)
CE
2
+
DE
2
= 2
DE
.
BE
(iv)
CE
2
+
BE
2
= 2
DE
.
BE
Question
16
16.
In the given figure, ABCD is a rhombus. Which of the following are true?
a)
4
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)
2
AB
2
=
AC
2
+
BD
2
e)
BC
2
+
CD
2
=
BD
2
(i)
{a,b}
(ii)
{e,c,a}
(iii)
{c,a}
(iv)
{d,b,a}
(v)
{d,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
−
GI
2
=
HJ
2
−
IJ
2
c)
GH
2
+
HJ
2
=
GI
2
+
IJ
2
d)
GJ
2
=
2
HJ
.
IJ
e)
GH
2
−
HJ
2
=
GI
2
−
IJ
2
(i)
{d,a,b}
(ii)
{b,e}
(iii)
{c,e,b}
(iv)
{a,b}
(v)
{c,e}
Question
18
18.
The altitude and area of an equilateral triangle of side 'a' is
(i)
√
3
a,
1
2
√
3
a
2
(ii)
1
2
√
3
a,
1
2
√
3
a
2
(iii)
1
2
√
3
a,
1
4
√
3
a
2
(iv)
√
3
a,
1
2
√
3
a
Question
19
19.
In the given figure, O is a point in the interior of the rectangle CDEF. Then
(i)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CD
2
+
DE
2
+
EF
2
+
FC
2
(ii)
OC
2
+
OE
2
=
OD
2
+
OF
2
(iii)
OC
2
−
OE
2
=
OD
2
−
OF
2
(iv)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CE
2
+
DF
2
Question
20
20.
In the given figure, △DEF , G is the mid-point of EF and DH ⟂ EF. Which of the following are true?
a)
DE
2
+
DF
2
= 2
DG
2
+
1
2
EF
2
b)
DE
2
=
DG
2
−
EF
.
GH
+
1
4
EF
2
c)
DF
2
=
DG
2
+
EF
.
GH
+
1
4
EF
2
d)
DE
2
=
DH
2
−
EF
.
GH
+
1
4
EF
2
e)
DF
2
=
DH
2
+
EF
.
GH
+
1
4
EF
2
(i)
{e,b}
(ii)
{d,a,b}
(iii)
{d,a}
(iv)
{a,b,c}
(v)
{d,e,c}
Question
21
21.
In the given figure, △ACB is right-angled at C, CD ⟂ AB.
AB
= c,
CB
= a,
AC
= b and
CD
= 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)
a
2
+
b
2
=
c
2
d)
ab
=
pc
e)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
(i)
{b,a,c}
(ii)
{b,a}
(iii)
{e,c}
(iv)
{a,c,d}
(v)
{b,e,d}
Question
22
22.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
3 AD
2
=
7 AB
2
(ii)
7 AD
2
=
9 AB
2
(iii)
7 AD
2
=
3 AB
2
(iv)
9 AD
2
=
7 AB
2
Question
23
23.
In the given figure, CDE is a triangle and 'O' is a point inside △CDE. The angular bisector of ∠DOC, ∠EOD & ∠COE meet CD, DE & EC at F, G & H respectively . Then
(i)
CF . DG . EH = FD . GE . HC
(ii)
CF . DG . EH = CD . DE . EC
(iii)
CF . DG . EH = FG . GH . HF
(iv)
CF . DG . EH = OF . OG . OH
(v)
CF . DG . EH = OC . OD . OE
Question
24
24.
A vehicle goes 10 km West and then 13 km North. How far is it from its starting point ?
(i)
17.40 km
(ii)
18.40 km
(iii)
14.40 km
(iv)
16.40 km
(v)
15.40 km
Question
25
25.
The foot of a ladder resting on a wall from the foot of the wall is 15 m. If the height of the top of the ladder from ground is 14 m, find the length of the ladder
(i)
20.52 m
(ii)
19.52 m
(iii)
18.52 m
(iv)
21.52 m
(v)
22.52 m
Question
26
26.
Two poles of heights 10 m and 14 m stand vertically on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
(i)
14.52 m
(ii)
17.52 m
(iii)
16.52 m
(iv)
15.52 m
(v)
13.52 m
Question
27
27.
A ladder reaches a window which is 8 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 16 m high. Find the width of the street if the length of the ladder is 18 m
(i)
25.37 m
(ii)
23.37 m
(iii)
22.37 m
(iv)
26.37 m
(v)
24.37 m
Assignment Key
1) (iii)
2) (v)
3) (i)
4) (iv)
5) (i)
6) (v)
7) (iv)
8) (i)
9) (iii)
10) (iii)
11) (iii)
12) (ii)
13) (iii)
14) (iii)
15) (ii)
16) (i)
17) (ii)
18) (iii)
19) (ii)
20) (iv)
21) (iv)
22) (iv)
23) (i)
24) (iv)
25) (i)
26) (iv)
27) (v)
