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
CE
.
DE
(ii)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
(iii)
BD
2
=
BC
2
+
CD
2
+
CE
2
(iv)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
(v)
BD
2
=
BC
2
+
CD
2
−
2
CD
.
CE
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
EF
.
EG
(ii)
DF
2
=
DE
2
+
EF
2
−
DG
2
(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
−
2
DE
.
EF
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
=
2
HG
2
+
2
EH
2
(iii)
EF
2
+
EG
2
=
EH
2
(iv)
EF
2
+
EG
2
=
2
FH
2
+
2
EH
2
(v)
EF
2
+
EG
2
=
2
FH
2
+
2
HG
2
Question
4
4.
In the given figure, △IJK is a triangle in which IJ = IK and L is a point on JK. Then
(i)
IJ
2
+
IL
2
=
JK
2
(ii)
IJ
2
−
IL
2
=
IL
.
JL
(iii)
IJ
2
−
IL
2
=
IL
.
KL
(iv)
IJ
2
−
IL
2
=
JL
.
KL
(v)
IJ
2
+
IL
2
=
JL
.
KL
Question
5
5.
In the given figure, in △CDE, 'O' is a point inside the triangle. OF ⟂ DE, OG ⟂ CE and OH ⟂ CD. Then
(i)
CH
2
+
DF
2
+
EG
2
=
CD
2
+
FE
2
+
EC
2
−
DH
2
−
EF
2
−
GC
2
(ii)
CH
2
+
DF
2
+
EG
2
=
OH
2
+
OG
2
+
OF
2
(iii)
CH
2
+
DF
2
+
EG
2
=
OC
2
+
OD
2
+
OE
2
+
OF
2
+
OG
2
+
OH
2
(iv)
CH
2
+
DF
2
+
EG
2
=
OC
2
+
OD
2
+
OE
2
−
OF
2
−
OG
2
−
OH
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
=
AE
2
+
CD
2
+
BF
2
(ii)
AF
2
+
BD
2
+
CE
2
=
OD
2
+
OE
2
+
OF
2
(iii)
AF
2
+
BD
2
+
CE
2
=
OA
.
OB
+
OB
.
OC
+
OC
.
OA
(iv)
AF
2
+
BD
2
+
CE
2
=
OF
.
OD
+
OD
.
OE
+
OE
.
OF
Question
7
7.
In the given figure,
△ACB
is right-angled at
C
.
R
is the mid-point of
AC
and
S
is the mid-point of
BC
.
Which of the following cases are true?
a)
4 (
AS
2
+
BR
2
) =
5
AB
2
b)
4
AS
2
=
4
BC
2
+
AC
2
c)
4
AS
2
=
4
AC
2
+
BC
2
d)
4
BR
2
=
4
AC
2
+
BC
2
e)
4
BR
2
=
4
BC
2
+
AC
2
(i)
{b,a}
(ii)
{b,a,c}
(iii)
{a,c,e}
(iv)
{d,c}
(v)
{b,d,e}
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
+
EH
2
= 2
GH
.
EH
(iii)
FH
2
−
GH
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)
EF
2
+
FG
2
+
GH
2
+
EH
2
=
EG
2
+
FH
2
b)
EF
2
+
FG
2
=
EG
2
c)
4
EF
2
=
EG
2
+
FH
2
d)
FG
2
+
GH
2
=
FH
2
e)
2
EF
2
=
EG
2
+
FH
2
(i)
{a,c}
(ii)
{b,a}
(iii)
{d,c}
(iv)
{e,b,a}
(v)
{d,c,a}
Question
10
10.
In the given figure, △HIJ, HK ⟂ IJ. Which of the following are true?
a)
HI
2
+
HJ
2
=
IK
2
+
JK
2
b)
HK
2
=
2
IK
.
JK
c)
HI
2
−
HJ
2
=
IK
2
−
JK
2
d)
HI
2
−
IK
2
=
HJ
2
−
JK
2
e)
HI
2
+
IK
2
=
HJ
2
+
JK
2
(i)
{c,d}
(ii)
{a,c}
(iii)
{e,a,c}
(iv)
{b,d,c}
(v)
{b,d}
Question
11
11.
In the given figure, O is a point in the interior of the rectangle EFGH. Then
(i)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EF
2
+
FG
2
+
GH
2
+
HE
2
(ii)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EG
2
+
FH
2
(iii)
OE
2
−
OG
2
=
OF
2
−
OH
2
(iv)
OE
2
+
OG
2
=
OF
2
+
OH
2
Question
12
12.
In the given figure, △FGH , I is the mid-point of GH and FJ ⟂ GH. Which of the following are true?
a)
FG
2
=
FJ
2
−
GH
.
IJ
+
1
4
GH
2
b)
FH
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)
FG
2
=
FI
2
−
GH
.
IJ
+
1
4
GH
2
(i)
{a,b,e}
(ii)
{b,d}
(iii)
{a,c}
(iv)
{c,d,e}
(v)
{a,c,d}
Question
13
13.
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)
a
2
+
b
2
=
c
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
c
2
+
1
p
2
e)
1
a
2
+
1
b
2
=
1
p
2
(i)
{d,c}
(ii)
{b,d,e}
(iii)
{a,c,e}
(iv)
{b,a,c}
(v)
{b,a}
Question
14
14.
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)
7 AD
2
=
9 AB
2
(iv)
9 AD
2
=
7 AB
2
Question
15
15.
A vehicle goes 11 km North and then 15 km West. How far is it from its starting point ?
(i)
19.60 km
(ii)
16.60 km
(iii)
17.60 km
(iv)
18.60 km
(v)
20.60 km
Question
16
16.
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 13 m, find the length of the ladder
(i)
17.85 m
(ii)
20.85 m
(iii)
21.85 m
(iv)
19.85 m
(v)
18.85 m
Question
17
17.
Two poles of heights 5 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)
14.14 m
(ii)
16.14 m
(iii)
13.14 m
(iv)
12.14 m
(v)
15.14 m
Question
18
18.
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)
25.07 m
(ii)
26.07 m
(iii)
22.07 m
(iv)
23.07 m
(v)
24.07 m
Assignment Key
1) (ii)
2) (i)
3) (iv)
4) (iv)
5) (iv)
6) (i)
7) (iii)
8) (iii)
9) (i)
10) (i)
11) (iv)
12) (iv)
13) (iii)
14) (iv)
15) (iv)
16) (iv)
17) (i)
18) (v)
