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
BC
.
BD
(ii)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(iii)
AC
2
=
AB
2
+
BC
2
+
BD
2
(iv)
AC
2
=
AB
2
+
BC
2
+
2
BD
.
CD
(v)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
Question
2
2.
In the given figure, △ABC is an acute angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(ii)
AC
2
=
AB
2
+
BC
2
−
AD
2
(iii)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
(iv)
AC
2
=
AB
2
+
BC
2
−
2
AB
.
BC
(v)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
Question
3
3.
In the given figure, △BCD is a triangle with BE being the median of CD. Then
(i)
BC
2
+
BD
2
=
2
CE
2
+
2
BE
2
(ii)
BC
2
+
BD
2
=
2
ED
2
+
2
BE
2
(iii)
BC
2
+
BD
2
=
2
CE
2
+
2
ED
2
(iv)
BC
2
+
BD
2
=
BE
2
(v)
BC
2
+
BD
2
=
CD
2
Question
4
4.
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
=
CF
.
DF
(ii)
CD
2
−
CF
2
=
CF
.
EF
(iii)
CD
2
−
CF
2
=
DF
.
EF
(iv)
CD
2
+
CF
2
=
DF
.
EF
(v)
CD
2
+
CF
2
=
DE
2
Question
5
5.
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
=
BC
2
+
ED
2
+
DB
2
−
CG
2
−
DE
2
−
FB
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
=
OG
2
+
OF
2
+
OE
2
(iv)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
−
OE
2
−
OF
2
−
OG
2
Question
6
6.
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
=
EI
2
+
GH
2
+
FJ
2
(ii)
EJ
2
+
FH
2
+
GI
2
=
OE
.
OF
+
OF
.
OG
+
OG
.
OE
(iii)
EJ
2
+
FH
2
+
GI
2
=
OH
2
+
OI
2
+
OJ
2
(iv)
EJ
2
+
FH
2
+
GI
2
=
OJ
.
OH
+
OH
.
OI
+
OI
.
OJ
Question
7
7.
In the given figure,
△GIH
is right-angled at
I
.
T
is the mid-point of
GI
and
U
is the mid-point of
HI
.
Which of the following cases are true?
a)
4
GU
2
=
4
GI
2
+
HI
2
b)
4
HT
2
=
4
HI
2
+
GI
2
c)
4
GU
2
=
4
HI
2
+
GI
2
d)
4 (
GU
2
+
HT
2
) =
5
GH
2
e)
4
HT
2
=
4
GI
2
+
HI
2
(i)
{c,e,d}
(ii)
{e,b}
(iii)
{a,b,d}
(iv)
{c,a}
(v)
{c,a,b}
Question
8
8.
In the given figure, △CDE is isosceles with CD = CE and DF ⟂ CE. Then
(i)
DF
2
+
CF
2
= 2
EF
.
CF
(ii)
DF
2
−
EF
2
= 2
EF
.
CF
(iii)
DF
2
+
EF
2
= 2
EF
.
CF
(iv)
DF
2
−
CF
2
= 2
EF
.
CF
Question
9
9.
In the given figure, GHIJ is a rhombus. Which of the following are true?
a)
4
GH
2
=
GI
2
+
HJ
2
b)
GH
2
+
HI
2
=
GI
2
c)
GH
2
+
HI
2
+
IJ
2
+
GJ
2
=
GI
2
+
HJ
2
d)
HI
2
+
IJ
2
=
HJ
2
e)
2
GH
2
=
GI
2
+
HJ
2
(i)
{d,c,a}
(ii)
{b,a}
(iii)
{a,c}
(iv)
{e,b,a}
(v)
{d,c}
Question
10
10.
In the given figure, △DEF, DG ⟂ EF. Which of the following are true?
a)
DG
2
=
2
EG
.
FG
b)
DE
2
+
EG
2
=
DF
2
+
FG
2
c)
DE
2
−
DF
2
=
EG
2
−
FG
2
d)
DE
2
−
EG
2
=
DF
2
−
FG
2
e)
DE
2
+
DF
2
=
EG
2
+
FG
2
(i)
{b,d,c}
(ii)
{e,a,c}
(iii)
{a,c}
(iv)
{c,d}
(v)
{b,d}
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
2
√
3
a
2
(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 BCDE. Then
(i)
OB
2
−
OD
2
=
OC
2
−
OE
2
(ii)
OB
2
+
OD
2
=
OC
2
+
OE
2
(iii)
OB
2
+
OC
2
+
OD
2
+
OE
2
=
BD
2
+
CE
2
(iv)
OB
2
+
OC
2
+
OD
2
+
OE
2
=
BC
2
+
CD
2
+
DE
2
+
EB
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)
BD
2
=
BF
2
+
CD
.
EF
+
1
4
CD
2
b)
BC
2
+
BD
2
= 2
BE
2
+
1
2
CD
2
c)
BC
2
=
BE
2
−
CD
.
EF
+
1
4
CD
2
d)
BD
2
=
BE
2
+
CD
.
EF
+
1
4
CD
2
e)
BC
2
=
BF
2
−
CD
.
EF
+
1
4
CD
2
(i)
{e,c}
(ii)
{a,b}
(iii)
{a,b,c}
(iv)
{a,e,d}
(v)
{b,c,d}
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)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
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)
a
2
+
b
2
=
c
2
(i)
{b,d}
(ii)
{a,c}
(iii)
{c,d,e}
(iv)
{a,b,e}
(v)
{a,c,d}
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)
3 AD
2
=
7 AB
2
(iv)
9 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 = EF . FG . GE
(ii)
BE . CF . DG = OB . OC . OD
(iii)
BE . CF . DG = BC . CD . DB
(iv)
BE . CF . DG = OE . OF . OG
(v)
BE . CF . DG = EC . FD . GB
Question
17
17.
A vehicle goes 10 km West and then 15 km North. How far is it from its starting point ?
(i)
16.03 km
(ii)
18.03 km
(iii)
19.03 km
(iv)
20.03 km
(v)
17.03 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)
17.03 m
(iii)
16.03 m
(iv)
18.03 m
(v)
19.03 m
Question
19
19.
Two poles of heights 8 m and 13 m stand vertically on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
(i)
17.81 m
(ii)
16.81 m
(iii)
15.81 m
(iv)
14.81 m
(v)
13.81 m
Question
20
20.
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 15 m high. Find the width of the street if the length of the ladder is 19 m
(i)
28.90 m
(ii)
26.90 m
(iii)
27.90 m
(iv)
29.90 m
(v)
30.90 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)
61.00 cm
(iii)
62.00 cm
(iv)
65.00 cm
(v)
64.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 14 cm and 48 cm, find the hypotenuse
(i)
51.00 cm
(ii)
50.00 cm
(iii)
52.00 cm
(iv)
49.00 cm
(v)
48.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 36.25°, find the third angle
(i)
53.75°
(ii)
63.75°
(iii)
83.75°
(iv)
68.75°
(v)
58.75°
Question
24
24.
In a right angled triangle, if one of the angles is 42.71°, find the third angle
(i)
57.29°
(ii)
52.29°
(iii)
77.29°
(iv)
62.29°
(v)
47.29°
Assignment Key
1) (i)
2) (v)
3) (i)
4) (iii)
5) (iv)
6) (i)
7) (iii)
8) (ii)
9) (iii)
10) (iv)
11) (iv)
12) (ii)
13) (v)
14) (iii)
15) (iv)
16) (v)
17) (ii)
18) (iv)
19) (iii)
20) (i)
21) (i)
22) (ii)
23) (i)
24) (v)
