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
EF
.
EG
(ii)
DF
2
=
DE
2
+
EF
2
+
EG
2
(iii)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(iv)
DF
2
=
DE
2
+
EF
2
+
2
EF
.
EG
(v)
DF
2
=
DE
2
+
EF
2
+
2
EG
.
FG
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
DE
.
EF
(ii)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(iii)
DF
2
=
DE
2
+
EF
2
+
2
EF
.
EG
(iv)
DF
2
=
DE
2
+
EF
2
−
DG
2
(v)
DF
2
=
DE
2
+
EF
2
−
2
EF
.
EG
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
ED
2
+
2
BE
2
(iii)
BC
2
+
BD
2
=
CD
2
(iv)
BC
2
+
BD
2
=
2
CE
2
+
2
ED
2
(v)
BC
2
+
BD
2
=
2
CE
2
+
2
BE
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
=
GH
2
(iv)
FG
2
+
FI
2
=
GI
.
HI
(v)
FG
2
−
FI
2
=
FI
.
GI
Question
5
5.
In the given figure, in △FGH, 'O' is a point inside the triangle. OI ⟂ GH, OJ ⟂ FH and OK ⟂ FG. Then
(i)
FK
2
+
GI
2
+
HJ
2
=
OF
2
+
OG
2
+
OH
2
−
OI
2
−
OJ
2
−
OK
2
(ii)
FK
2
+
GI
2
+
HJ
2
=
OK
2
+
OJ
2
+
OI
2
(iii)
FK
2
+
GI
2
+
HJ
2
=
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
+
OK
2
(iv)
FK
2
+
GI
2
+
HJ
2
=
FG
2
+
IH
2
+
HF
2
−
GK
2
−
HI
2
−
JF
2
Question
6
6.
In the given figure, in △GHI, 'O' is a point inside the triangle. OJ ⟂ HI, OK ⟂ GI and OL ⟂ GH. Then
(i)
GL
2
+
HJ
2
+
IK
2
=
GK
2
+
IJ
2
+
HL
2
(ii)
GL
2
+
HJ
2
+
IK
2
=
OL
.
OJ
+
OJ
.
OK
+
OK
.
OL
(iii)
GL
2
+
HJ
2
+
IK
2
=
OG
.
OH
+
OH
.
OI
+
OI
.
OG
(iv)
GL
2
+
HJ
2
+
IK
2
=
OJ
2
+
OK
2
+
OL
2
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
DS
2
=
4
DE
2
+
CE
2
b)
4 (
CT
2
+
DS
2
) =
5
CD
2
c)
4
DS
2
=
4
CE
2
+
DE
2
d)
4
CT
2
=
4
DE
2
+
CE
2
e)
4
CT
2
=
4
CE
2
+
DE
2
(i)
{c,a}
(ii)
{a,b,e}
(iii)
{c,d,e}
(iv)
{d,b}
(v)
{c,a,b}
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, CDEF is a rhombus. Which of the following are true?
a)
2
CD
2
=
CE
2
+
DF
2
b)
CD
2
+
DE
2
+
EF
2
+
CF
2
=
CE
2
+
DF
2
c)
DE
2
+
EF
2
=
DF
2
d)
4
CD
2
=
CE
2
+
DF
2
e)
CD
2
+
DE
2
=
CE
2
(i)
{b,d}
(ii)
{c,d}
(iii)
{a,b}
(iv)
{e,a,b}
(v)
{c,d,b}
Question
10
10.
In the given figure, △GHI, GJ ⟂ HI. Which of the following are true?
a)
GH
2
+
GI
2
=
HJ
2
+
IJ
2
b)
GH
2
−
GI
2
=
HJ
2
−
IJ
2
c)
GH
2
−
HJ
2
=
GI
2
−
IJ
2
d)
GJ
2
=
2
HJ
.
IJ
e)
GH
2
+
HJ
2
=
GI
2
+
IJ
2
(i)
{d,c}
(ii)
{d,c,b}
(iii)
{e,a,b}
(iv)
{b,c}
(v)
{a,b}
Question
11
11.
The altitude and area of an equilateral triangle of side 'a' is
(i)
√
3
a,
1
2
√
3
a
2
(ii)
1
2
√
3
a,
1
4
√
3
a
2
(iii)
√
3
a,
1
2
√
3
a
(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 BCDE. Then
(i)
OB
2
+
OC
2
+
OD
2
+
OE
2
=
BC
2
+
CD
2
+
DE
2
+
EB
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
−
OD
2
=
OC
2
−
OE
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
=
BE
2
−
CD
.
EF
+
1
4
CD
2
b)
BD
2
=
BF
2
+
CD
.
EF
+
1
4
CD
2
c)
BC
2
=
BF
2
−
CD
.
EF
+
1
4
CD
2
d)
BD
2
=
BE
2
+
CD
.
EF
+
1
4
CD
2
e)
BC
2
+
BD
2
= 2
BE
2
+
1
2
CD
2
(i)
{c,d}
(ii)
{a,d,e}
(iii)
{b,c,e}
(iv)
{b,a,d}
(v)
{b,a}
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)
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)
a
2
+
b
2
=
c
2
d)
1
a
2
+
1
b
2
=
1
p
2
e)
ab
=
pc
(i)
{a,c}
(ii)
{c,d,e}
(iii)
{a,b,e}
(iv)
{a,c,d}
(v)
{b,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)
3 AD
2
=
7 AB
2
(iii)
9 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 = JK . KL . LJ
(ii)
GJ . HK . IL = OG . OH . OI
(iii)
GJ . HK . IL = OJ . OK . OL
(iv)
GJ . HK . IL = GH . HI . IG
(v)
GJ . HK . IL = JH . KI . LG
Question
17
17.
A vehicle goes 15 km West and then 13 km North. How far is it from its starting point ?
(i)
21.85 km
(ii)
19.85 km
(iii)
18.85 km
(iv)
20.85 km
(v)
17.85 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 14 m, find the length of the ladder
(i)
19.10 m
(ii)
20.10 m
(iii)
17.10 m
(iv)
21.10 m
(v)
18.10 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 14 m, find the distance between their tops
(i)
14.12 m
(ii)
16.12 m
(iii)
15.12 m
(iv)
17.12 m
(v)
18.12 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 21 m
(i)
33.49 m
(ii)
31.49 m
(iii)
30.49 m
(iv)
29.49 m
(v)
32.49 m
Question
21
21.
In a right angled triangle, if one of the sides is 8 cm and hypotenuse 17 cm, find the third side
(i)
13.00 cm
(ii)
17.00 cm
(iii)
15.00 cm
(iv)
16.00 cm
(v)
14.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 10 cm and 24 cm, find the hypotenuse
(i)
24.00 cm
(ii)
27.00 cm
(iii)
28.00 cm
(iv)
25.00 cm
(v)
26.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 39.81°, find the third angle
(i)
80.19°
(ii)
65.19°
(iii)
60.19°
(iv)
55.19°
(v)
50.19°
Question
24
24.
In a right angled triangle, if one of the angles is 47.49°, find the third angle
(i)
47.51°
(ii)
72.51°
(iii)
57.51°
(iv)
52.51°
(v)
42.51°
Assignment Key
1) (iv)
2) (v)
3) (v)
4) (ii)
5) (i)
6) (i)
7) (ii)
8) (i)
9) (i)
10) (iv)
11) (ii)
12) (ii)
13) (ii)
14) (ii)
15) (iii)
16) (v)
17) (ii)
18) (i)
19) (ii)
20) (ii)
21) (iii)
22) (v)
23) (v)
24) (v)
