EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Pythagoras Theorem
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In the given figure, △BCD is an obtuse angled triangle and BE ⟂ CD. Then
(i)
BD
2
=
BC
2
+
CD
2
+
CE
2
(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
CE
.
DE
(v)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
Question
2
2.
In the given figure, △CDE is an acute angled triangle and CF ⟂ DE. Then
(i)
CE
2
=
CD
2
+
DE
2
+
2
DE
.
DF
(ii)
CE
2
=
CD
2
+
DE
2
+
2
CD
.
DE
(iii)
CE
2
=
CD
2
+
DE
2
−
2
CD
.
DE
(iv)
CE
2
=
CD
2
+
DE
2
−
CF
2
(v)
CE
2
=
CD
2
+
DE
2
−
2
DE
.
DF
Question
3
3.
In the given figure, △CDE is a triangle with CF being the median of DE. Then
(i)
CD
2
+
CE
2
=
DE
2
(ii)
CD
2
+
CE
2
=
2
DF
2
+
2
CF
2
(iii)
CD
2
+
CE
2
=
2
DF
2
+
2
FE
2
(iv)
CD
2
+
CE
2
=
CF
2
(v)
CD
2
+
CE
2
=
2
FE
2
+
2
CF
2
Question
4
4.
In the given figure, △GHI is a triangle in which GH = GI and J is a point on HI. Then
(i)
GH
2
−
GJ
2
=
GJ
.
HJ
(ii)
GH
2
+
GJ
2
=
HJ
.
IJ
(iii)
GH
2
−
GJ
2
=
GJ
.
IJ
(iv)
GH
2
−
GJ
2
=
HJ
.
IJ
(v)
GH
2
+
GJ
2
=
HI
2
Question
5
5.
In the given figure, in △EFG, 'O' is a point inside the triangle. OH ⟂ FG, OI ⟂ EG and OJ ⟂ EF. Then
(i)
EJ
2
+
FH
2
+
GI
2
=
EF
2
+
HG
2
+
GE
2
−
FJ
2
−
GH
2
−
IE
2
(ii)
EJ
2
+
FH
2
+
GI
2
=
OE
2
+
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
(iii)
EJ
2
+
FH
2
+
GI
2
=
OE
2
+
OF
2
+
OG
2
−
OH
2
−
OI
2
−
OJ
2
(iv)
EJ
2
+
FH
2
+
GI
2
=
OJ
2
+
OI
2
+
OH
2
Question
6
6.
In the given figure, in △CDE, 'O' is a point inside the triangle. OF ⟂ DE, OG ⟂ CE and OH ⟂ CD. Then
(i)
CH
2
+
DF
2
+
EG
2
=
OH
.
OF
+
OF
.
OG
+
OG
.
OH
(ii)
CH
2
+
DF
2
+
EG
2
=
CG
2
+
EF
2
+
DH
2
(iii)
CH
2
+
DF
2
+
EG
2
=
OC
.
OD
+
OD
.
OE
+
OE
.
OC
(iv)
CH
2
+
DF
2
+
EG
2
=
OF
2
+
OG
2
+
OH
2
Question
7
7.
In the given figure,
△BDC
is right-angled at
D
.
S
is the mid-point of
BD
and
T
is the mid-point of
CD
.
Which of the following cases are true?
a)
4 (
BT
2
+
CS
2
) =
5
BC
2
b)
4
BT
2
=
4
BD
2
+
CD
2
c)
4
BT
2
=
4
CD
2
+
BD
2
d)
4
CS
2
=
4
BD
2
+
CD
2
e)
4
CS
2
=
4
CD
2
+
BD
2
(i)
{d,b}
(ii)
{a,b,e}
(iii)
{c,a,b}
(iv)
{c,d,e}
(v)
{c,a}
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
−
CD
2
= 2
CD
.
AD
(iv)
BD
2
+
AD
2
= 2
CD
.
AD
Question
9
9.
In the given figure, FGHI is a rhombus. Which of the following are true?
a)
2
FG
2
=
FH
2
+
GI
2
b)
FG
2
+
GH
2
=
FH
2
c)
4
FG
2
=
FH
2
+
GI
2
d)
GH
2
+
HI
2
=
GI
2
e)
FG
2
+
GH
2
+
HI
2
+
FI
2
=
FH
2
+
GI
2
(i)
{a,c}
(ii)
{b,e,c}
(iii)
{b,e}
(iv)
{c,e}
(v)
{d,a,c}
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
+
AC
2
=
BD
2
+
CD
2
c)
AB
2
−
BD
2
=
AC
2
−
CD
2
d)
AB
2
−
AC
2
=
BD
2
−
CD
2
e)
AD
2
=
2
BD
.
CD
(i)
{c,d}
(ii)
{e,a,c}
(iii)
{b,d,c}
(iv)
{b,d}
(v)
{a,c}
Question
11
11.
The altitude and area of an equilateral triangle of side 'a' is
(i)
1
2
√
3
a,
1
4
√
3
a
2
(ii)
1
2
√
3
a,
1
2
√
3
a
2
(iii)
√
3
a,
1
2
√
3
a
2
(iv)
√
3
a,
1
2
√
3
a
Question
12
12.
In the given figure, O is a point in the interior of the rectangle ABCD. Then
(i)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AB
2
+
BC
2
+
CD
2
+
DA
2
(ii)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AC
2
+
BD
2
(iii)
OA
2
−
OC
2
=
OB
2
−
OD
2
(iv)
OA
2
+
OC
2
=
OB
2
+
OD
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
=
CF
2
−
DE
.
FG
+
1
4
DE
2
c)
CE
2
=
CF
2
+
DE
.
FG
+
1
4
DE
2
d)
CD
2
=
CG
2
−
DE
.
FG
+
1
4
DE
2
e)
CD
2
+
CE
2
= 2
CF
2
+
1
2
DE
2
(i)
{a,b,c}
(ii)
{a,d,e}
(iii)
{d,c}
(iv)
{b,c,e}
(v)
{a,b}
Question
14
14.
In the given figure, △DFE is right-angled at F, FG ⟂ DE.
DE
= c,
FE
= a,
DF
= b and
FG
= 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
p
2
e)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
(i)
{b,e,d}
(ii)
{e,c}
(iii)
{b,a}
(iv)
{a,c,d}
(v)
{b,a,c}
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, BCD is a triangle and 'O' is a point inside △BCD. The angular bisector of ∠COB, ∠DOC & ∠BOD meet BC, CD & DB at E, F & G respectively . Then
(i)
BE . CF . DG = OB . OC . OD
(ii)
BE . CF . DG = EF . FG . GE
(iii)
BE . CF . DG = OE . OF . OG
(iv)
BE . CF . DG = BC . CD . DB
(v)
BE . CF . DG = EC . FD . GB
Question
17
17.
A vehicle goes 15 km West and then 11 km South. How far is it from its starting point ?
(i)
19.60 km
(ii)
18.60 km
(iii)
17.60 km
(iv)
20.60 km
(v)
16.60 km
Question
18
18.
The foot of a ladder resting on a wall from the foot of the wall is 10 m. If the height of the top of the ladder from ground is 12 m, find the length of the ladder
(i)
16.62 m
(ii)
15.62 m
(iii)
14.62 m
(iv)
17.62 m
(v)
13.62 m
Question
19
19.
Two poles of heights 9 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)
10.65 m
(ii)
14.65 m
(iii)
11.65 m
(iv)
13.65 m
(v)
12.65 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 14 m high. Find the width of the street if the length of the ladder is 17 m
(i)
21.61 m
(ii)
24.61 m
(iii)
20.61 m
(iv)
22.61 m
(v)
23.61 m
Question
21
21.
In a right angled triangle, if one of the sides is 16 cm and hypotenuse 65 cm, find the third side
(i)
63.00 cm
(ii)
62.00 cm
(iii)
65.00 cm
(iv)
61.00 cm
(v)
64.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 20 cm and 99 cm, find the hypotenuse
(i)
99.00 cm
(ii)
103.00 cm
(iii)
102.00 cm
(iv)
101.00 cm
(v)
100.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 40.6°, find the third angle
(i)
64.4°
(ii)
79.4°
(iii)
49.4°
(iv)
59.4°
(v)
54.4°
Question
24
24.
In a right angled triangle, if one of the angles is 38.66°, find the third angle
(i)
61.34°
(ii)
66.34°
(iii)
81.34°
(iv)
56.34°
(v)
51.34°
Assignment Key
1) (v)
2) (v)
3) (ii)
4) (iv)
5) (iii)
6) (ii)
7) (ii)
8) (iii)
9) (iv)
10) (i)
11) (i)
12) (iv)
13) (iv)
14) (iv)
15) (iii)
16) (v)
17) (ii)
18) (ii)
19) (v)
20) (iv)
21) (i)
22) (iv)
23) (iii)
24) (v)
