EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Pythagoras Theorem
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
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
+
2
EG
.
FG
(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
+
EG
2
Question
2
2.
In the given figure, △BCD is an acute angled triangle and BE ⟂ CD. Then
(i)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
(ii)
BD
2
=
BC
2
+
CD
2
−
2
BC
.
CD
(iii)
BD
2
=
BC
2
+
CD
2
−
2
CD
.
CE
(iv)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
(v)
BD
2
=
BC
2
+
CD
2
−
BE
2
Question
3
3.
In the given figure, △ABC is a triangle with AD being the median of BC. Then
(i)
AB
2
+
AC
2
=
BC
2
(ii)
AB
2
+
AC
2
=
2
BD
2
+
2
DC
2
(iii)
AB
2
+
AC
2
=
2
DC
2
+
2
AD
2
(iv)
AB
2
+
AC
2
=
2
BD
2
+
2
AD
2
(v)
AB
2
+
AC
2
=
AD
2
Question
4
4.
In the given figure, △FGH is a triangle in which FG = FH and I is a point on GH. Then
(i)
FG
2
−
FI
2
=
FI
.
HI
(ii)
FG
2
−
FI
2
=
GI
.
HI
(iii)
FG
2
−
FI
2
=
FI
.
GI
(iv)
FG
2
+
FI
2
=
GI
.
HI
(v)
FG
2
+
FI
2
=
GH
2
Question
5
5.
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
2
+
OB
2
+
OC
2
−
OD
2
−
OE
2
−
OF
2
(ii)
AF
2
+
BD
2
+
CE
2
=
OA
2
+
OB
2
+
OC
2
+
OD
2
+
OE
2
+
OF
2
(iii)
AF
2
+
BD
2
+
CE
2
=
OF
2
+
OE
2
+
OD
2
(iv)
AF
2
+
BD
2
+
CE
2
=
AB
2
+
DC
2
+
CA
2
−
BF
2
−
CD
2
−
EA
2
Question
6
6.
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
=
AE
2
+
CD
2
+
BF
2
(ii)
AF
2
+
BD
2
+
CE
2
=
OA
.
OB
+
OB
.
OC
+
OC
.
OA
(iii)
AF
2
+
BD
2
+
CE
2
=
OF
.
OD
+
OD
.
OE
+
OE
.
OF
(iv)
AF
2
+
BD
2
+
CE
2
=
OD
2
+
OE
2
+
OF
2
Question
7
7.
In the given figure,
△ACB
is right-angled at
C
.
P
is the mid-point of
AC
and
Q
is the mid-point of
BC
.
Which of the following cases are true?
a)
4 (
AQ
2
+
BP
2
) =
5
AB
2
b)
4
BP
2
=
4
BC
2
+
AC
2
c)
4
BP
2
=
4
AC
2
+
BC
2
d)
4
AQ
2
=
4
AC
2
+
BC
2
e)
4
AQ
2
=
4
BC
2
+
AC
2
(i)
{c,a,b}
(ii)
{a,b,d}
(iii)
{c,e,d}
(iv)
{c,a}
(v)
{e,b}
Question
8
8.
In the given figure, △ABC is isosceles with AB = AC and BD ⟂ AC. Then
(i)
BD
2
+
AD
2
= 2
CD
.
AD
(ii)
BD
2
+
CD
2
= 2
CD
.
AD
(iii)
BD
2
−
AD
2
= 2
CD
.
AD
(iv)
BD
2
−
CD
2
= 2
CD
.
AD
Question
9
9.
In the given figure, IJKL is a rhombus. Which of the following are true?
a)
IJ
2
+
JK
2
=
IK
2
b)
IJ
2
+
JK
2
+
KL
2
+
IL
2
=
IK
2
+
JL
2
c)
JK
2
+
KL
2
=
JL
2
d)
4
IJ
2
=
IK
2
+
JL
2
e)
2
IJ
2
=
IK
2
+
JL
2
(i)
{a,b}
(ii)
{e,a,b}
(iii)
{c,d}
(iv)
{c,d,b}
(v)
{b,d}
Question
10
10.
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
+
BD
2
=
AC
2
+
CD
2
c)
AD
2
=
2
BD
.
CD
d)
AB
2
−
AC
2
=
BD
2
−
CD
2
e)
AB
2
+
AC
2
=
BD
2
+
CD
2
(i)
{e,b,a}
(ii)
{c,d}
(iii)
{a,d}
(iv)
{b,a}
(v)
{c,d,a}
Question
11
11.
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
12
12.
In the given figure, O is a point in the interior of the rectangle DEFG. Then
(i)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DF
2
+
EG
2
(ii)
OD
2
−
OF
2
=
OE
2
−
OG
2
(iii)
OD
2
+
OF
2
=
OE
2
+
OG
2
(iv)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DE
2
+
EF
2
+
FG
2
+
GD
2
Question
13
13.
In the given figure, △CDE , F is the mid-point of DE and CG ⟂ DE. Which of the following are true?
a)
CE
2
=
CG
2
+
DE
.
FG
+
1
4
DE
2
b)
CD
2
+
CE
2
= 2
CF
2
+
1
2
DE
2
c)
CD
2
=
CG
2
−
DE
.
FG
+
1
4
DE
2
d)
CE
2
=
CF
2
+
DE
.
FG
+
1
4
DE
2
e)
CD
2
=
CF
2
−
DE
.
FG
+
1
4
DE
2
(i)
{b,d,e}
(ii)
{a,c,e}
(iii)
{c,d}
(iv)
{a,b,d}
(v)
{a,b}
Question
14
14.
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)
a
2
+
b
2
=
c
2
b)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
c)
ab
=
pc
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,c}
(ii)
{a,c,e}
(iii)
{d,c}
(iv)
{b,a}
(v)
{b,d,e}
Question
15
15.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
3 AB
2
(ii)
7 AD
2
=
9 AB
2
(iii)
9 AD
2
=
7 AB
2
(iv)
3 AD
2
=
7 AB
2
Question
16
16.
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 = CD . DE . EC
(iv)
CF . DG . EH = OF . OG . OH
(v)
CF . DG . EH = FG . GH . HF
Question
17
17.
A vehicle goes 15 km South and then 14 km East. How far is it from its starting point ?
(i)
22.52 km
(ii)
21.52 km
(iii)
20.52 km
(iv)
18.52 km
(v)
19.52 km
Question
18
18.
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 10 m, find the length of the ladder
(i)
20.03 m
(ii)
18.03 m
(iii)
16.03 m
(iv)
17.03 m
(v)
19.03 m
Question
19
19.
Two poles of heights 5 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)
16.97 m
(ii)
18.97 m
(iii)
15.97 m
(iv)
14.97 m
(v)
17.97 m
Question
20
20.
A ladder reaches a window which is 11 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)
21.49 m
(ii)
23.49 m
(iii)
20.49 m
(iv)
24.49 m
(v)
22.49 m
Question
21
21.
In a right angled triangle, if one of the sides is 18 cm and hypotenuse 82 cm, find the third side
(i)
79.00 cm
(ii)
80.00 cm
(iii)
78.00 cm
(iv)
81.00 cm
(v)
82.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 8 cm and 15 cm, find the hypotenuse
(i)
15.00 cm
(ii)
19.00 cm
(iii)
18.00 cm
(iv)
17.00 cm
(v)
16.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 42.27°, find the third angle
(i)
57.73°
(ii)
52.73°
(iii)
77.73°
(iv)
62.73°
(v)
47.73°
Question
24
24.
In a right angled triangle, if one of the angles is 40.91°, find the third angle
(i)
49.09°
(ii)
54.09°
(iii)
59.09°
(iv)
79.09°
(v)
64.09°
Assignment Key
1) (iv)
2) (iii)
3) (iv)
4) (ii)
5) (i)
6) (i)
7) (ii)
8) (iv)
9) (v)
10) (iii)
11) (iii)
12) (iii)
13) (i)
14) (ii)
15) (iii)
16) (i)
17) (iii)
18) (ii)
19) (i)
20) (v)
21) (ii)
22) (iv)
23) (v)
24) (i)
