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
+
2
EF
.
EG
(iii)
DF
2
=
DE
2
+
EF
2
+
2
EG
.
FG
(iv)
DF
2
=
DE
2
+
EF
2
+
EG
2
(v)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
Question
2
2.
In the given figure, △CDE is an acute angled triangle and CF ⟂ DE. Then
(i)
CE
2
=
CD
2
+
DE
2
−
CF
2
(ii)
CE
2
=
CD
2
+
DE
2
−
2
DE
.
DF
(iii)
CE
2
=
CD
2
+
DE
2
+
2
DE
.
DF
(iv)
CE
2
=
CD
2
+
DE
2
+
2
CD
.
DE
(v)
CE
2
=
CD
2
+
DE
2
−
2
CD
.
DE
Question
3
3.
In the given figure, △EFG is a triangle with EH being the median of FG. Then
(i)
EF
2
+
EG
2
=
FG
2
(ii)
EF
2
+
EG
2
=
EH
2
(iii)
EF
2
+
EG
2
=
2
FH
2
+
2
HG
2
(iv)
EF
2
+
EG
2
=
2
HG
2
+
2
EH
2
(v)
EF
2
+
EG
2
=
2
FH
2
+
2
EH
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
=
GI
.
HI
(ii)
FG
2
−
FI
2
=
FI
.
HI
(iii)
FG
2
−
FI
2
=
FI
.
GI
(iv)
FG
2
+
FI
2
=
GH
2
(v)
FG
2
+
FI
2
=
GI
.
HI
Question
5
5.
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
=
OD
2
+
OE
2
+
OF
2
+
OG
2
+
OH
2
+
OI
2
(ii)
DI
2
+
EG
2
+
FH
2
=
OI
2
+
OH
2
+
OG
2
(iii)
DI
2
+
EG
2
+
FH
2
=
OD
2
+
OE
2
+
OF
2
−
OG
2
−
OH
2
−
OI
2
(iv)
DI
2
+
EG
2
+
FH
2
=
DE
2
+
GF
2
+
FD
2
−
EI
2
−
FG
2
−
HD
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
=
OD
.
OE
+
OE
.
OF
+
OF
.
OD
(ii)
DI
2
+
EG
2
+
FH
2
=
DH
2
+
FG
2
+
EI
2
(iii)
DI
2
+
EG
2
+
FH
2
=
OI
.
OG
+
OG
.
OH
+
OH
.
OI
(iv)
DI
2
+
EG
2
+
FH
2
=
OG
2
+
OH
2
+
OI
2
Question
7
7.
In the given figure,
△GIH
is right-angled at
I
.
Q
is the mid-point of
GI
and
R
is the mid-point of
HI
.
Which of the following cases are true?
a)
4 (
GR
2
+
HQ
2
) =
5
GH
2
b)
4
GR
2
=
4
GI
2
+
HI
2
c)
4
HQ
2
=
4
GI
2
+
HI
2
d)
4
HQ
2
=
4
HI
2
+
GI
2
e)
4
GR
2
=
4
HI
2
+
GI
2
(i)
{c,a}
(ii)
{c,e,d}
(iii)
{c,a,b}
(iv)
{e,b}
(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
+
CD
2
= 2
CD
.
AD
(iv)
BD
2
+
AD
2
= 2
CD
.
AD
Question
9
9.
In the given figure, EFGH is a rhombus. Which of the following are true?
a)
2
EF
2
=
EG
2
+
FH
2
b)
EF
2
+
FG
2
+
GH
2
+
EH
2
=
EG
2
+
FH
2
c)
4
EF
2
=
EG
2
+
FH
2
d)
EF
2
+
FG
2
=
EG
2
e)
FG
2
+
GH
2
=
FH
2
(i)
{d,c,b}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{e,a,b}
(v)
{d,c}
Question
10
10.
In the given figure, △BCD, BE ⟂ CD. Which of the following are true?
a)
BC
2
−
CE
2
=
BD
2
−
DE
2
b)
BC
2
+
CE
2
=
BD
2
+
DE
2
c)
BC
2
−
BD
2
=
CE
2
−
DE
2
d)
BC
2
+
BD
2
=
CE
2
+
DE
2
e)
BE
2
=
2
CE
.
DE
(i)
{a,c}
(ii)
{b,a}
(iii)
{d,c}
(iv)
{d,c,a}
(v)
{e,b,a}
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
(iii)
√
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
+
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)
BD
2
=
BE
2
+
CD
.
EF
+
1
4
CD
2
b)
BC
2
+
BD
2
= 2
BE
2
+
1
2
CD
2
c)
BD
2
=
BF
2
+
CD
.
EF
+
1
4
CD
2
d)
BC
2
=
BE
2
−
CD
.
EF
+
1
4
CD
2
e)
BC
2
=
BF
2
−
CD
.
EF
+
1
4
CD
2
(i)
{c,a}
(ii)
{c,e,d}
(iii)
{e,b}
(iv)
{c,a,b}
(v)
{a,b,d}
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)
a
2
+
b
2
=
c
2
c)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
d)
ab
=
pc
e)
1
a
2
+
1
b
2
=
1
p
2
(i)
{a,b,d}
(ii)
{b,d,e}
(iii)
{a,b}
(iv)
{a,c,e}
(v)
{c,d}
Question
15
15.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
9 AB
2
(ii)
3 AD
2
=
7 AB
2
(iii)
7 AD
2
=
3 AB
2
(iv)
9 AD
2
=
7 AB
2
Question
16
16.
In the given figure, EFG is a triangle and 'O' is a point inside △EFG. The angular bisector of ∠FOE, ∠GOF & ∠EOG meet EF, FG & GE at H, I & J respectively . Then
(i)
EH . FI . GJ = HI . IJ . JH
(ii)
EH . FI . GJ = OE . OF . OG
(iii)
EH . FI . GJ = EF . FG . GE
(iv)
EH . FI . GJ = OH . OI . OJ
(v)
EH . FI . GJ = HF . IG . JE
Question
17
17.
A vehicle goes 14 km North and then 11 km East. How far is it from its starting point ?
(i)
19.80 km
(ii)
17.80 km
(iii)
16.80 km
(iv)
18.80 km
(v)
15.80 km
Question
18
18.
The foot of a ladder resting on a wall from the foot of the wall is 11 m. If the height of the top of the ladder from ground is 12 m, find the length of the ladder
(i)
16.28 m
(ii)
18.28 m
(iii)
14.28 m
(iv)
15.28 m
(v)
17.28 m
Question
19
19.
Two poles of heights 10 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)
13.53 m
(ii)
12.53 m
(iii)
10.53 m
(iv)
11.53 m
(v)
14.53 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)
24.07 m
(ii)
26.07 m
(iii)
23.07 m
(iv)
25.07 m
(v)
22.07 m
Question
21
21.
In a right angled triangle, if one of the sides is 20 cm and hypotenuse 101 cm, find the third side
(i)
101.00 cm
(ii)
97.00 cm
(iii)
98.00 cm
(iv)
99.00 cm
(v)
100.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 6 cm and 8 cm, find the hypotenuse
(i)
10.00 cm
(ii)
11.00 cm
(iii)
12.00 cm
(iv)
9.00 cm
(v)
8.00 cm
Question
23
23.
In a right angled triangle, if one of the angles is 36.25°, find the third angle
(i)
63.75°
(ii)
83.75°
(iii)
68.75°
(iv)
58.75°
(v)
53.75°
Question
24
24.
In a right angled triangle, if one of the angles is 42.27°, find the third angle
(i)
47.73°
(ii)
77.73°
(iii)
52.73°
(iv)
62.73°
(v)
57.73°
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (i)
5) (iii)
6) (ii)
7) (v)
8) (i)
9) (ii)
10) (i)
11) (iv)
12) (ii)
13) (v)
14) (ii)
15) (iv)
16) (v)
17) (ii)
18) (i)
19) (ii)
20) (i)
21) (iv)
22) (i)
23) (v)
24) (i)
