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
−
2
CD
.
CE
(ii)
BD
2
=
BC
2
+
CD
2
+
2
CE
.
DE
(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
+
CE
2
Question
2
2.
In the given figure, △EFG is an acute angled triangle and EH ⟂ FG. Then
(i)
EG
2
=
EF
2
+
FG
2
+
2
EF
.
FG
(ii)
EG
2
=
EF
2
+
FG
2
−
2
EF
.
FG
(iii)
EG
2
=
EF
2
+
FG
2
−
EH
2
(iv)
EG
2
=
EF
2
+
FG
2
+
2
FG
.
FH
(v)
EG
2
=
EF
2
+
FG
2
−
2
FG
.
FH
Question
3
3.
In the given figure, △ABC is a triangle with AD being the median of BC. Then
(i)
AB
2
+
AC
2
=
AD
2
(ii)
AB
2
+
AC
2
=
BC
2
(iii)
AB
2
+
AC
2
=
2
BD
2
+
2
AD
2
(iv)
AB
2
+
AC
2
=
2
DC
2
+
2
AD
2
(v)
AB
2
+
AC
2
=
2
BD
2
+
2
DC
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
=
DF
.
EF
(ii)
CD
2
−
CF
2
=
CF
.
EF
(iii)
CD
2
+
CF
2
=
DE
2
(iv)
CD
2
−
CF
2
=
CF
.
DF
(v)
CD
2
−
CF
2
=
DF
.
EF
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
=
OE
2
+
OF
2
+
OG
2
−
OH
2
−
OI
2
−
OJ
2
(ii)
EJ
2
+
FH
2
+
GI
2
=
OJ
2
+
OI
2
+
OH
2
(iii)
EJ
2
+
FH
2
+
GI
2
=
EF
2
+
HG
2
+
GE
2
−
FJ
2
−
GH
2
−
IE
2
(iv)
EJ
2
+
FH
2
+
GI
2
=
OE
2
+
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
Question
6
6.
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
=
OE
2
+
OF
2
+
OG
2
(ii)
BG
2
+
CE
2
+
DF
2
=
OB
.
OC
+
OC
.
OD
+
OD
.
OB
(iii)
BG
2
+
CE
2
+
DF
2
=
BF
2
+
DE
2
+
CG
2
(iv)
BG
2
+
CE
2
+
DF
2
=
OG
.
OE
+
OE
.
OF
+
OF
.
OG
Question
7
7.
In the given figure,
△CED
is right-angled at
E
.
S
is the mid-point of
CE
and
T
is the mid-point of
DE
.
Which of the following cases are true?
a)
4 (
CT
2
+
DS
2
) =
5
CD
2
b)
4
DS
2
=
4
CE
2
+
DE
2
c)
4
CT
2
=
4
DE
2
+
CE
2
d)
4
CT
2
=
4
CE
2
+
DE
2
e)
4
DS
2
=
4
DE
2
+
CE
2
(i)
{a,d,e}
(ii)
{b,a,d}
(iii)
{b,c,e}
(iv)
{b,a}
(v)
{c,d}
Question
8
8.
In the given figure, △EFG is isosceles with EF = EG and FH ⟂ EG. Then
(i)
FH
2
−
GH
2
= 2
GH
.
EH
(ii)
FH
2
+
GH
2
= 2
GH
.
EH
(iii)
FH
2
−
EH
2
= 2
GH
.
EH
(iv)
FH
2
+
EH
2
= 2
GH
.
EH
Question
9
9.
In the given figure, EFGH is a rhombus. Which of the following are true?
a)
4
EF
2
=
EG
2
+
FH
2
b)
FG
2
+
GH
2
=
FH
2
c)
2
EF
2
=
EG
2
+
FH
2
d)
EF
2
+
FG
2
=
EG
2
e)
EF
2
+
FG
2
+
GH
2
+
EH
2
=
EG
2
+
FH
2
(i)
{d,b,a}
(ii)
{a,e}
(iii)
{b,a}
(iv)
{c,e,a}
(v)
{c,e}
Question
10
10.
In the given figure, △ABC, AD ⟂ BC. Which of the following are true?
a)
AB
2
+
AC
2
=
BD
2
+
CD
2
b)
AB
2
+
BD
2
=
AC
2
+
CD
2
c)
AD
2
=
2
BD
.
CD
d)
AB
2
−
BD
2
=
AC
2
−
CD
2
e)
AB
2
−
AC
2
=
BD
2
−
CD
2
(i)
{c,a,d}
(ii)
{a,d}
(iii)
{d,e}
(iv)
{b,e}
(v)
{b,e,d}
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 CDEF. Then
(i)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CE
2
+
DF
2
(ii)
OC
2
+
OE
2
=
OD
2
+
OF
2
(iii)
OC
2
−
OE
2
=
OD
2
−
OF
2
(iv)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CD
2
+
DE
2
+
EF
2
+
FC
2
Question
13
13.
In the given figure, △FGH , I is the mid-point of GH and FJ ⟂ GH. Which of the following are true?
a)
FG
2
=
FI
2
−
GH
.
IJ
+
1
4
GH
2
b)
FG
2
=
FJ
2
−
GH
.
IJ
+
1
4
GH
2
c)
FH
2
=
FI
2
+
GH
.
IJ
+
1
4
GH
2
d)
FG
2
+
FH
2
= 2
FI
2
+
1
2
GH
2
e)
FH
2
=
FJ
2
+
GH
.
IJ
+
1
4
GH
2
(i)
{b,a}
(ii)
{e,c}
(iii)
{a,c,d}
(iv)
{b,e,d}
(v)
{b,a,c}
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)
1
a
2
+
1
b
2
=
1
p
2
b)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
c)
ab
=
pc
d)
a
2
+
b
2
=
c
2
e)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
(i)
{e,c}
(ii)
{a,c,d}
(iii)
{b,e,d}
(iv)
{b,a,c}
(v)
{b,a}
Question
15
15.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
9 AD
2
=
7 AB
2
(ii)
3 AD
2
=
7 AB
2
(iii)
7 AD
2
=
3 AB
2
(iv)
7 AD
2
=
9 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 = OF . OG . OH
(iii)
CF . DG . EH = FG . GH . HF
(iv)
CF . DG . EH = OC . OD . OE
(v)
CF . DG . EH = CD . DE . EC
Question
17
17.
A vehicle goes 11 km East and then 13 km South. How far is it from its starting point ?
(i)
17.03 km
(ii)
15.03 km
(iii)
18.03 km
(iv)
19.03 km
(v)
16.03 km
Question
18
18.
The foot of a ladder resting on a wall from the foot of the wall is 15 m. If the height of the top of the ladder from ground is 10 m, find the length of the ladder
(i)
17.03 m
(ii)
20.03 m
(iii)
18.03 m
(iv)
19.03 m
(v)
16.03 m
Question
19
19.
Two poles of heights 8 m and 15 m stand vertically on a plane ground. If the distance between their feet is 10 m, find the distance between their tops
(i)
10.21 m
(ii)
11.21 m
(iii)
14.21 m
(iv)
12.21 m
(v)
13.21 m
Question
20
20.
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 15 m high. Find the width of the street if the length of the ladder is 18 m
(i)
25.37 m
(ii)
21.37 m
(iii)
23.37 m
(iv)
22.37 m
(v)
24.37 m
Question
21
21.
In a right angled triangle, if one of the sides is 12 cm and hypotenuse 37 cm, find the third side
(i)
37.00 cm
(ii)
33.00 cm
(iii)
36.00 cm
(iv)
34.00 cm
(v)
35.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 12 cm and 35 cm, find the hypotenuse
(i)
35.00 cm
(ii)
38.00 cm
(iii)
37.00 cm
(iv)
36.00 cm
(v)
39.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 35.54°, find the third angle
(i)
69.46°
(ii)
64.46°
(iii)
54.46°
(iv)
84.46°
(v)
59.46°
Question
24
24.
In a right angled triangle, if one of the angles is 52.43°, find the third angle
(i)
37.57°
(ii)
52.57°
(iii)
42.57°
(iv)
67.57°
(v)
47.57°
Assignment Key
1) (iii)
2) (v)
3) (iii)
4) (v)
5) (i)
6) (iii)
7) (i)
8) (i)
9) (ii)
10) (iii)
11) (iv)
12) (ii)
13) (iii)
14) (ii)
15) (i)
16) (i)
17) (i)
18) (iii)
19) (iv)
20) (iii)
21) (v)
22) (iii)
23) (iii)
24) (i)
