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)
GH = 15 cm , HI = 13 cm , IG = 11 cm
(ii)
GH = 13 cm , HI = 12 cm , IG = 17.69 cm
(iii)
GH = 11 cm , HI = 15 cm , IG = 10 cm
(iv)
GH = 15 cm , HI = 15 cm , IG = 15 cm
(v)
GH = 13 cm , HI = 15 cm , IG = 11 cm
Question
2
2.
Which of the following are measures of an isosceles right angled triangle ?
(i)
EF = 13 cm , FG = 15 cm , GE = 14 cm
(ii)
EF = 10 cm , FG = 10 cm , GE = 14.14 cm
(iii)
EF = 14 cm , FG = 14 cm , GE = 14 cm
(iv)
EF = 13 cm , FG = 21 cm , GE = 14 cm
(v)
EF = 13 cm , FG = 13 cm , GE = 13 cm
Question
3
3.
Which of the following are measures of a right angled triangle ?
(i)
CD = 13 cm , DE = 15 cm , EC = 19.85 cm
(ii)
CD = 11 cm , DE = 18 cm , EC = 12 cm
(iii)
CD = 10 cm , DE = 11 cm , EC = 10 cm
(iv)
CD = 13 cm , DE = 12 cm , EC = 10 cm
(v)
CD = 15 cm , DE = 15 cm , EC = 15 cm
Question
4
4.
Which of the following are measures of an isosceles right angled triangle ?
(i)
GH = 13 cm , HI = 13 cm , IG = 13 cm
(ii)
GH = 12 cm , HI = 12 cm , IG = 16.97 cm
(iii)
GH = 11 cm , HI = 14 cm , IG = 11 cm
(iv)
GH = 10 cm , HI = 17 cm , IG = 10 cm
(v)
GH = 11 cm , HI = 14 cm , IG = 13 cm
Question
5
5.
In a right angled triangle, if one of the sides is 4 cm and hypotenuse 5 cm, find the third side
(i)
1.00 cm
(ii)
5.00 cm
(iii)
4.00 cm
(iv)
2.00 cm
(v)
3.00 cm
Question
6
6.
In a right angled triangle, if the two non-hypotenuse sides are 14 cm and 48 cm, find the hypotenuse
(i)
50.00 cm
(ii)
48.00 cm
(iii)
51.00 cm
(iv)
52.00 cm
(v)
49.00 cm
Question
7
7.
In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. Which of the following are true?
a)
CD
2
=
DB
.
DE
b)
CD
2
=
BD
.
BE
c)
BC
2
=
BD
.
BE
d)
CE
2
=
BE
.
ED
e)
BC
2
=
DB
.
DE
(i)
{a,c,d}
(ii)
{b,e,d}
(iii)
{b,a}
(iv)
{b,a,c}
(v)
{e,c}
Question
8
8.
In the given figure, △DEF is an obtuse angled triangle and DG ⟂ EF. Then
(i)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(ii)
DF
2
=
DE
2
+
EF
2
+
EG
2
(iii)
DF
2
=
DE
2
+
EF
2
−
2
EF
.
EG
(iv)
DF
2
=
DE
2
+
EF
2
+
2
EF
.
EG
(v)
DF
2
=
DE
2
+
EF
2
+
2
EG
.
FG
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
−
AD
2
(iii)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(iv)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(v)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
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
DF
2
+
2
FE
2
(ii)
CD
2
+
CE
2
=
2
FE
2
+
2
CF
2
(iii)
CD
2
+
CE
2
=
DE
2
(iv)
CD
2
+
CE
2
=
2
DF
2
+
2
CF
2
(v)
CD
2
+
CE
2
=
CF
2
Question
11
11.
In the given figure, △CDE is a triangle in which CD = CE and F is a point on DE. Then
(i)
CD
2
+
CF
2
=
DE
2
(ii)
CD
2
−
CF
2
=
CF
.
EF
(iii)
CD
2
−
CF
2
=
CF
.
DF
(iv)
CD
2
−
CF
2
=
DF
.
EF
(v)
CD
2
+
CF
2
=
DF
.
EF
Question
12
12.
In the given figure, in △BCD, 'O' is a point inside the triangle. OE ⟂ CD, OF ⟂ BD and OG ⟂ BC. Then
(i)
BG
2
+
CE
2
+
DF
2
=
OG
2
+
OF
2
+
OE
2
(ii)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
+
OE
2
+
OF
2
+
OG
2
(iii)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
−
OE
2
−
OF
2
−
OG
2
(iv)
BG
2
+
CE
2
+
DF
2
=
BC
2
+
ED
2
+
DB
2
−
CG
2
−
DE
2
−
FB
2
Question
13
13.
In the given figure, in △GHI, 'O' is a point inside the triangle. OJ ⟂ HI, OK ⟂ GI and OL ⟂ GH. Then
(i)
GL
2
+
HJ
2
+
IK
2
=
OJ
2
+
OK
2
+
OL
2
(ii)
GL
2
+
HJ
2
+
IK
2
=
OG
.
OH
+
OH
.
OI
+
OI
.
OG
(iii)
GL
2
+
HJ
2
+
IK
2
=
GK
2
+
IJ
2
+
HL
2
(iv)
GL
2
+
HJ
2
+
IK
2
=
OL
.
OJ
+
OJ
.
OK
+
OK
.
OL
Question
14
14.
In the given figure,
△DFE
is right-angled at
F
.
Q
is the mid-point of
DF
and
R
is the mid-point of
EF
.
Which of the following cases are true?
a)
4 (
DR
2
+
EQ
2
) =
5
DE
2
b)
4
DR
2
=
4
DF
2
+
EF
2
c)
4
EQ
2
=
4
EF
2
+
DF
2
d)
4
DR
2
=
4
EF
2
+
DF
2
e)
4
EQ
2
=
4
DF
2
+
EF
2
(i)
{d,a}
(ii)
{d,a,b}
(iii)
{d,e,c}
(iv)
{a,b,c}
(v)
{e,b}
Question
15
15.
In the given figure, △EFG is isosceles with EF = EG and FH ⟂ EG. Then
(i)
FH
2
+
EH
2
= 2
GH
.
EH
(ii)
FH
2
−
GH
2
= 2
GH
.
EH
(iii)
FH
2
+
GH
2
= 2
GH
.
EH
(iv)
FH
2
−
EH
2
= 2
GH
.
EH
Question
16
16.
In the given figure, CDEF is a rhombus. Which of the following are true?
a)
DE
2
+
EF
2
=
DF
2
b)
4
CD
2
=
CE
2
+
DF
2
c)
2
CD
2
=
CE
2
+
DF
2
d)
CD
2
+
DE
2
=
CE
2
e)
CD
2
+
DE
2
+
EF
2
+
CF
2
=
CE
2
+
DF
2
(i)
{c,e,b}
(ii)
{a,b}
(iii)
{d,a,b}
(iv)
{b,e}
(v)
{c,e}
Question
17
17.
In the given figure, △ABC, AD ⟂ BC. Which of the following are true?
a)
AB
2
+
BD
2
=
AC
2
+
CD
2
b)
AB
2
+
AC
2
=
BD
2
+
CD
2
c)
AB
2
−
BD
2
=
AC
2
−
CD
2
d)
AD
2
=
2
BD
.
CD
e)
AB
2
−
AC
2
=
BD
2
−
CD
2
(i)
{d,a,c}
(ii)
{b,e,c}
(iii)
{c,e}
(iv)
{b,e}
(v)
{a,c}
Question
18
18.
The altitude and area of an equilateral triangle of side 'a' is
(i)
√
3
a,
1
2
√
3
a
2
(ii)
√
3
a,
1
2
√
3
a
(iii)
1
2
√
3
a,
1
4
√
3
a
2
(iv)
1
2
√
3
a,
1
2
√
3
a
2
Question
19
19.
In the given figure, O is a point in the interior of the rectangle CDEF. Then
(i)
OC
2
+
OE
2
=
OD
2
+
OF
2
(ii)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CD
2
+
DE
2
+
EF
2
+
FC
2
(iii)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CE
2
+
DF
2
(iv)
OC
2
−
OE
2
=
OD
2
−
OF
2
Question
20
20.
In the given figure, △ABC , D is the mid-point of BC and AE ⟂ BC. Which of the following are true?
a)
AC
2
=
AE
2
+
BC
.
DE
+
1
4
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)
AB
2
+
AC
2
= 2
AD
2
+
1
2
BC
2
(i)
{b,c,e}
(ii)
{d,c}
(iii)
{a,b}
(iv)
{a,d,e}
(v)
{a,b,c}
Question
21
21.
In the given figure, △BDC is right-angled at D, DE ⟂ BC.
BC
= c,
DC
= a,
BD
= b and
DE
= p.
Which of the following are true?
a)
ab
=
pc
b)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
c)
a
2
+
b
2
=
c
2
d)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
e)
1
a
2
+
1
b
2
=
1
p
2
(i)
{b,a}
(ii)
{d,c}
(iii)
{b,a,c}
(iv)
{b,d,e}
(v)
{a,c,e}
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
=
3 AB
2
(iii)
9 AD
2
=
7 AB
2
(iv)
7 AD
2
=
9 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 = OC . OD . OE
(iii)
CF . DG . EH = OF . OG . OH
(iv)
CF . DG . EH = FG . GH . HF
(v)
CF . DG . EH = CD . DE . EC
Question
24
24.
A vehicle goes 15 km South and then 14 km East. How far is it from its starting point ?
(i)
19.52 km
(ii)
18.52 km
(iii)
20.52 km
(iv)
21.52 km
(v)
22.52 km
Question
25
25.
The foot of a ladder resting on a wall from the foot of the wall is 14 m. If the height of the top of the ladder from ground is 15 m, find the length of the ladder
(i)
19.52 m
(ii)
20.52 m
(iii)
21.52 m
(iv)
22.52 m
(v)
18.52 m
Question
26
26.
Two poles of heights 6 m and 13 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops
(i)
15.89 m
(ii)
13.89 m
(iii)
11.89 m
(iv)
14.89 m
(v)
12.89 m
Question
27
27.
A ladder reaches a window which is 12 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 17 m
(i)
15.79 m
(ii)
19.79 m
(iii)
17.79 m
(iv)
16.79 m
(v)
18.79 m
Assignment Key
1) (ii)
2) (ii)
3) (i)
4) (ii)
5) (v)
6) (i)
7) (i)
8) (iv)
9) (iv)
10) (iv)
11) (iv)
12) (iii)
13) (iii)
14) (iv)
15) (ii)
16) (iv)
17) (iii)
18) (iii)
19) (i)
20) (i)
21) (v)
22) (iii)
23) (i)
24) (iii)
25) (ii)
26) (ii)
27) (iii)
