EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Triangles
Grade : ICSE Grade VIII
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
CD
.
CE
(iii)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
(iv)
BD
2
=
BC
2
+
CD
2
+
CE
2
(v)
BD
2
=
BC
2
+
CD
2
+
2
CE
.
DE
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
EF
.
EG
(iii)
DF
2
=
DE
2
+
EF
2
+
2
EF
.
EG
(iv)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(v)
DF
2
=
DE
2
+
EF
2
−
DG
2
Question
3
3.
In the given figure, △DEF is a triangle with DG being the median of EF. Then
(i)
DE
2
+
DF
2
=
2
EG
2
+
2
GF
2
(ii)
DE
2
+
DF
2
=
DG
2
(iii)
DE
2
+
DF
2
=
EF
2
(iv)
DE
2
+
DF
2
=
2
EG
2
+
2
DG
2
(v)
DE
2
+
DF
2
=
2
GF
2
+
2
DG
2
Question
4
4.
In the given figure, △EFG is a triangle in which EF = EG and H is a point on FG. Then
(i)
EF
2
−
EH
2
=
EH
.
FH
(ii)
EF
2
+
EH
2
=
FG
2
(iii)
EF
2
−
EH
2
=
FH
.
GH
(iv)
EF
2
−
EH
2
=
EH
.
GH
(v)
EF
2
+
EH
2
=
FH
.
GH
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
=
OK
2
+
OJ
2
+
OI
2
(ii)
FK
2
+
GI
2
+
HJ
2
=
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
+
OK
2
(iii)
FK
2
+
GI
2
+
HJ
2
=
FG
2
+
IH
2
+
HF
2
−
GK
2
−
HI
2
−
JF
2
(iv)
FK
2
+
GI
2
+
HJ
2
=
OF
2
+
OG
2
+
OH
2
−
OI
2
−
OJ
2
−
OK
2
Question
6
6.
In the given figure, in △ABC, 'O' is a point inside the triangle. OD ⟂ BC, OE ⟂ AC and OF ⟂ AB. Then
(i)
AF
2
+
BD
2
+
CE
2
=
OA
.
OB
+
OB
.
OC
+
OC
.
OA
(ii)
AF
2
+
BD
2
+
CE
2
=
OF
.
OD
+
OD
.
OE
+
OE
.
OF
(iii)
AF
2
+
BD
2
+
CE
2
=
AE
2
+
CD
2
+
BF
2
(iv)
AF
2
+
BD
2
+
CE
2
=
OD
2
+
OE
2
+
OF
2
Question
7
7.
In the given figure,
△FHG
is right-angled at
H
.
Q
is the mid-point of
FH
and
R
is the mid-point of
GH
.
Which of the following cases are true?
a)
4
GQ
2
=
4
FH
2
+
GH
2
b)
4
GQ
2
=
4
GH
2
+
FH
2
c)
4 (
FR
2
+
GQ
2
) =
5
FG
2
d)
4
FR
2
=
4
GH
2
+
FH
2
e)
4
FR
2
=
4
FH
2
+
GH
2
(i)
{a,d,e}
(ii)
{a,b,c}
(iii)
{a,b}
(iv)
{d,c}
(v)
{b,c,e}
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, DEFG is a rhombus. Which of the following are true?
a)
4
DE
2
=
DF
2
+
EG
2
b)
EF
2
+
FG
2
=
EG
2
c)
DE
2
+
EF
2
=
DF
2
d)
DE
2
+
EF
2
+
FG
2
+
DG
2
=
DF
2
+
EG
2
e)
2
DE
2
=
DF
2
+
EG
2
(i)
{b,a}
(ii)
{e,b,a}
(iii)
{c,d}
(iv)
{a,d}
(v)
{c,d,a}
Question
10
10.
In the given figure, △FGH, FI ⟂ GH. Which of the following are true?
a)
FG
2
+
GI
2
=
FH
2
+
HI
2
b)
FG
2
+
FH
2
=
GI
2
+
HI
2
c)
FG
2
−
FH
2
=
GI
2
−
HI
2
d)
FI
2
=
2
GI
.
HI
e)
FG
2
−
GI
2
=
FH
2
−
HI
2
(i)
{b,e,c}
(ii)
{b,e}
(iii)
{a,c}
(iv)
{c,e}
(v)
{d,a,c}
Question
11
11.
In the given figure, O is a point in the interior of the rectangle CDEF. Then
(i)
OC
2
+
OE
2
=
OD
2
+
OF
2
(ii)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CE
2
+
DF
2
(iii)
OC
2
+
OD
2
+
OE
2
+
OF
2
=
CD
2
+
DE
2
+
EF
2
+
FC
2
(iv)
OC
2
−
OE
2
=
OD
2
−
OF
2
Question
12
12.
In the given figure, △ABC , D is the mid-point of BC and AE ⟂ BC. Which of the following are true?
a)
AB
2
=
AE
2
−
BC
.
DE
+
1
4
BC
2
b)
AC
2
=
AD
2
+
BC
.
DE
+
1
4
BC
2
c)
AC
2
=
AE
2
+
BC
.
DE
+
1
4
BC
2
d)
AB
2
=
AD
2
−
BC
.
DE
+
1
4
BC
2
e)
AB
2
+
AC
2
= 2
AD
2
+
1
2
BC
2
(i)
{a,b,d}
(ii)
{b,d,e}
(iii)
{a,b}
(iv)
{c,d}
(v)
{a,c,e}
Question
13
13.
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)
ab
=
pc
b)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
c)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
d)
1
a
2
+
1
b
2
=
1
p
2
e)
a
2
+
b
2
=
c
2
(i)
{a,d,e}
(ii)
{b,c,e}
(iii)
{b,a}
(iv)
{b,a,d}
(v)
{c,d}
Question
14
14.
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)
9 AD
2
=
7 AB
2
(iv)
7 AD
2
=
3 AB
2
Question
15
15.
A vehicle goes 15 km North and then 14 km West. How far is it from its starting point ?
(i)
18.52 km
(ii)
19.52 km
(iii)
22.52 km
(iv)
20.52 km
(v)
21.52 km
Question
16
16.
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)
15.62 m
(ii)
16.62 m
(iii)
14.62 m
(iv)
17.62 m
(v)
13.62 m
Question
17
17.
Two poles of heights 8 m and 16 m stand vertically on a plane ground. If the distance between their feet is 10 m, find the distance between their tops
(i)
10.81 m
(ii)
11.81 m
(iii)
14.81 m
(iv)
13.81 m
(v)
12.81 m
Question
18
18.
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 16 m high. Find the width of the street if the length of the ladder is 21 m
(i)
29.84 m
(ii)
28.84 m
(iii)
30.84 m
(iv)
32.84 m
(v)
31.84 m
Assignment Key
1) (i)
2) (ii)
3) (iv)
4) (iii)
5) (iv)
6) (iii)
7) (v)
8) (i)
9) (iv)
10) (iv)
11) (i)
12) (ii)
13) (i)
14) (iii)
15) (iv)
16) (i)
17) (v)
18) (iii)
