EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Pythagoras Theorem
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In the given figure, △ABC is an obtuse 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
+
BD
2
(v)
AC
2
=
AB
2
+
BC
2
+
2
BD
.
CD
Question
2
2.
In the given figure, △DEF is an acute angled triangle and DG ⟂ EF. Then
(i)
DF
2
=
DE
2
+
EF
2
−
2
EF
.
EG
(ii)
DF
2
=
DE
2
+
EF
2
+
2
EF
.
EG
(iii)
DF
2
=
DE
2
+
EF
2
−
DG
2
(iv)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(v)
DF
2
=
DE
2
+
EF
2
−
2
DE
.
EF
Question
3
3.
In the given figure, △BCD is a triangle with BE being the median of CD. Then
(i)
BC
2
+
BD
2
=
BE
2
(ii)
BC
2
+
BD
2
=
2
CE
2
+
2
ED
2
(iii)
BC
2
+
BD
2
=
2
CE
2
+
2
BE
2
(iv)
BC
2
+
BD
2
=
CD
2
(v)
BC
2
+
BD
2
=
2
ED
2
+
2
BE
2
Question
4
4.
In the given figure, △HIJ is a triangle in which HI = HJ and K is a point on IJ. Then
(i)
HI
2
−
HK
2
=
HK
.
JK
(ii)
HI
2
+
HK
2
=
IJ
2
(iii)
HI
2
+
HK
2
=
IK
.
JK
(iv)
HI
2
−
HK
2
=
IK
.
JK
(v)
HI
2
−
HK
2
=
HK
.
IK
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
=
AB
2
+
DC
2
+
CA
2
−
BF
2
−
CD
2
−
EA
2
(iii)
AF
2
+
BD
2
+
CE
2
=
OF
2
+
OE
2
+
OD
2
(iv)
AF
2
+
BD
2
+
CE
2
=
OA
2
+
OB
2
+
OC
2
−
OD
2
−
OE
2
−
OF
2
Question
6
6.
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
=
DH
2
+
FG
2
+
EI
2
(ii)
DI
2
+
EG
2
+
FH
2
=
OG
2
+
OH
2
+
OI
2
(iii)
DI
2
+
EG
2
+
FH
2
=
OD
.
OE
+
OE
.
OF
+
OF
.
OD
(iv)
DI
2
+
EG
2
+
FH
2
=
OI
.
OG
+
OG
.
OH
+
OH
.
OI
Question
7
7.
In the given figure,
△DFE
is right-angled at
F
.
P
is the mid-point of
DF
and
Q
is the mid-point of
EF
.
Which of the following cases are true?
a)
4
DQ
2
=
4
EF
2
+
DF
2
b)
4
DQ
2
=
4
DF
2
+
EF
2
c)
4
EP
2
=
4
DF
2
+
EF
2
d)
4
EP
2
=
4
EF
2
+
DF
2
e)
4 (
DQ
2
+
EP
2
) =
5
DE
2
(i)
{c,d}
(ii)
{a,c,e}
(iii)
{a,b}
(iv)
{b,d,e}
(v)
{a,b,d}
Question
8
8.
In the given figure, △ABC is isosceles with AB = AC and BD ⟂ AC. Then
(i)
BD
2
+
CD
2
= 2
CD
.
AD
(ii)
BD
2
+
AD
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, HIJK is a rhombus. Which of the following are true?
a)
HI
2
+
IJ
2
=
HJ
2
b)
HI
2
+
IJ
2
+
JK
2
+
HK
2
=
HJ
2
+
IK
2
c)
4
HI
2
=
HJ
2
+
IK
2
d)
2
HI
2
=
HJ
2
+
IK
2
e)
IJ
2
+
JK
2
=
IK
2
(i)
{e,a,b}
(ii)
{d,c,b}
(iii)
{a,b}
(iv)
{d,c}
(v)
{b,c}
Question
10
10.
In the given figure, △GHI, GJ ⟂ HI. Which of the following are true?
a)
GH
2
+
HJ
2
=
GI
2
+
IJ
2
b)
GJ
2
=
2
HJ
.
IJ
c)
GH
2
−
HJ
2
=
GI
2
−
IJ
2
d)
GH
2
+
GI
2
=
HJ
2
+
IJ
2
e)
GH
2
−
GI
2
=
HJ
2
−
IJ
2
(i)
{d,a,c}
(ii)
{b,e}
(iii)
{b,e,c}
(iv)
{c,e}
(v)
{a,c}
Question
11
11.
The altitude and area of an equilateral triangle of side 'a' is
(i)
1
2
√
3
a,
1
2
√
3
a
2
(ii)
√
3
a,
1
2
√
3
a
2
(iii)
√
3
a,
1
2
√
3
a
(iv)
1
2
√
3
a,
1
4
√
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
+
OF
2
=
OE
2
+
OG
2
(ii)
OD
2
−
OF
2
=
OE
2
−
OG
2
(iii)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DF
2
+
EG
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, △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)
BC
2
+
BD
2
= 2
BE
2
+
1
2
CD
2
d)
BC
2
=
BE
2
−
CD
.
EF
+
1
4
CD
2
e)
BD
2
=
BE
2
+
CD
.
EF
+
1
4
CD
2
(i)
{a,c,d}
(ii)
{b,d}
(iii)
{a,b,e}
(iv)
{a,c}
(v)
{c,d,e}
Question
14
14.
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)
ab
=
pc
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)
1
a
2
+
1
b
2
=
1
p
2
e)
a
2
+
b
2
=
c
2
(i)
{b,c,e}
(ii)
{b,a,d}
(iii)
{a,d,e}
(iv)
{c,d}
(v)
{b,a}
Question
15
15.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
3 AB
2
(ii)
9 AD
2
=
7 AB
2
(iii)
3 AD
2
=
7 AB
2
(iv)
7 AD
2
=
9 AB
2
Question
16
16.
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 = JH . KI . LG
(iii)
GJ . HK . IL = OG . OH . OI
(iv)
GJ . HK . IL = GH . HI . IG
(v)
GJ . HK . IL = JK . KL . LJ
Question
17
17.
A vehicle goes 11 km South and then 13 km West. How far is it from its starting point ?
(i)
18.03 km
(ii)
17.03 km
(iii)
19.03 km
(iv)
15.03 km
(v)
16.03 km
Question
18
18.
The foot of a ladder resting on a wall from the foot of the wall is 13 m. If the height of the top of the ladder from ground is 15 m, find the length of the ladder
(i)
17.85 m
(ii)
18.85 m
(iii)
20.85 m
(iv)
21.85 m
(v)
19.85 m
Question
19
19.
Two poles of heights 8 m and 16 m stand vertically on a plane ground. If the distance between their feet is 11 m, find the distance between their tops
(i)
14.60 m
(ii)
12.60 m
(iii)
11.60 m
(iv)
15.60 m
(v)
13.60 m
Question
20
20.
A ladder reaches a window which is 9 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)
22.07 m
(ii)
26.07 m
(iii)
23.07 m
(iv)
25.07 m
(v)
24.07 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)
78.00 cm
(ii)
79.00 cm
(iii)
82.00 cm
(iv)
81.00 cm
(v)
80.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 4 cm and 3 cm, find the hypotenuse
(i)
6.00 cm
(ii)
4.00 cm
(iii)
7.00 cm
(iv)
5.00 cm
(v)
3.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 49.09°, find the third angle
(i)
40.91°
(ii)
70.91°
(iii)
55.91°
(iv)
50.91°
(v)
45.91°
Question
24
24.
In a right angled triangle, if one of the angles is 53.75°, find the third angle
(i)
36.25°
(ii)
41.25°
(iii)
66.25°
(iv)
46.25°
(v)
51.25°
Assignment Key
1) (ii)
2) (i)
3) (iii)
4) (iv)
5) (iv)
6) (i)
7) (iv)
8) (iv)
9) (v)
10) (iv)
11) (iv)
12) (i)
13) (v)
14) (iii)
15) (ii)
16) (ii)
17) (ii)
18) (v)
19) (v)
20) (v)
21) (v)
22) (iv)
23) (i)
24) (i)
