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
+
CE
2
(ii)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
(iii)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
(iv)
BD
2
=
BC
2
+
CD
2
−
2
CD
.
CE
(v)
BD
2
=
BC
2
+
CD
2
+
2
CE
.
DE
Question
2
2.
In the given figure, △EFG is an acute angled triangle and EH ⟂ FG. Then
(i)
EG
2
=
EF
2
+
FG
2
−
EH
2
(ii)
EG
2
=
EF
2
+
FG
2
−
2
EF
.
FG
(iii)
EG
2
=
EF
2
+
FG
2
+
2
FG
.
FH
(iv)
EG
2
=
EF
2
+
FG
2
+
2
EF
.
FG
(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
=
BC
2
(ii)
AB
2
+
AC
2
=
2
BD
2
+
2
DC
2
(iii)
AB
2
+
AC
2
=
AD
2
(iv)
AB
2
+
AC
2
=
2
BD
2
+
2
AD
2
(v)
AB
2
+
AC
2
=
2
DC
2
+
2
AD
2
Question
4
4.
In the given figure, △HIJ is a triangle in which HI = HJ and K is a point on IJ. Then
(i)
HI
2
+
HK
2
=
IK
.
JK
(ii)
HI
2
+
HK
2
=
IJ
2
(iii)
HI
2
−
HK
2
=
IK
.
JK
(iv)
HI
2
−
HK
2
=
HK
.
JK
(v)
HI
2
−
HK
2
=
HK
.
IK
Question
5
5.
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
=
OB
2
+
OC
2
+
OD
2
−
OE
2
−
OF
2
−
OG
2
(ii)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
+
OE
2
+
OF
2
+
OG
2
(iii)
BG
2
+
CE
2
+
DF
2
=
BC
2
+
ED
2
+
DB
2
−
CG
2
−
DE
2
−
FB
2
(iv)
BG
2
+
CE
2
+
DF
2
=
OG
2
+
OF
2
+
OE
2
Question
6
6.
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
.
OG
+
OG
.
OH
+
OH
.
OF
(ii)
FK
2
+
GI
2
+
HJ
2
=
OI
2
+
OJ
2
+
OK
2
(iii)
FK
2
+
GI
2
+
HJ
2
=
OK
.
OI
+
OI
.
OJ
+
OJ
.
OK
(iv)
FK
2
+
GI
2
+
HJ
2
=
FJ
2
+
HI
2
+
GK
2
Question
7
7.
In the given figure,
△ACB
is right-angled at
C
.
P
is the mid-point of
AC
and
Q
is the mid-point of
BC
.
Which of the following cases are true?
a)
4
AQ
2
=
4
BC
2
+
AC
2
b)
4
AQ
2
=
4
AC
2
+
BC
2
c)
4
BP
2
=
4
AC
2
+
BC
2
d)
4
BP
2
=
4
BC
2
+
AC
2
e)
4 (
AQ
2
+
BP
2
) =
5
AB
2
(i)
{a,b}
(ii)
{a,b,d}
(iii)
{c,d}
(iv)
{a,c,e}
(v)
{b,d,e}
Question
8
8.
In the given figure, △CDE is isosceles with CD = CE and DF ⟂ CE. Then
(i)
DF
2
+
EF
2
= 2
EF
.
CF
(ii)
DF
2
−
CF
2
= 2
EF
.
CF
(iii)
DF
2
+
CF
2
= 2
EF
.
CF
(iv)
DF
2
−
EF
2
= 2
EF
.
CF
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)
EF
2
+
FG
2
+
GH
2
+
EH
2
=
EG
2
+
FH
2
d)
2
EF
2
=
EG
2
+
FH
2
e)
EF
2
+
FG
2
=
EG
2
(i)
{b,a}
(ii)
{a,c}
(iii)
{e,b,a}
(iv)
{d,c,a}
(v)
{d,c}
Question
10
10.
In the given figure, △ABC, AD ⟂ BC. Which of the following are true?
a)
AB
2
−
BD
2
=
AC
2
−
CD
2
b)
AB
2
+
AC
2
=
BD
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)
{a,e}
(ii)
{d,b,a}
(iii)
{b,a}
(iv)
{c,e,a}
(v)
{c,e}
Question
11
11.
In the given figure, O is a point in the interior of the rectangle ABCD. Then
(i)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AB
2
+
BC
2
+
CD
2
+
DA
2
(ii)
OA
2
+
OC
2
=
OB
2
+
OD
2
(iii)
OA
2
−
OC
2
=
OB
2
−
OD
2
(iv)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AC
2
+
BD
2
Question
12
12.
In the given figure, △EFG , H is the mid-point of FG and EI ⟂ FG. Which of the following are true?
a)
EF
2
=
EH
2
−
FG
.
HI
+
1
4
FG
2
b)
EG
2
=
EH
2
+
FG
.
HI
+
1
4
FG
2
c)
EF
2
=
EI
2
−
FG
.
HI
+
1
4
FG
2
d)
EG
2
=
EI
2
+
FG
.
HI
+
1
4
FG
2
e)
EF
2
+
EG
2
= 2
EH
2
+
1
2
FG
2
(i)
{c,a}
(ii)
{d,b}
(iii)
{c,a,b}
(iv)
{a,b,e}
(v)
{c,d,e}
Question
13
13.
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)
ab
=
pc
c)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
d)
a
2
+
b
2
=
c
2
e)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
(i)
{a,b,d}
(ii)
{c,e,d}
(iii)
{c,a,b}
(iv)
{c,a}
(v)
{e,b}
Question
14
14.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
3 AD
2
=
7 AB
2
(ii)
9 AD
2
=
7 AB
2
(iii)
7 AD
2
=
9 AB
2
(iv)
7 AD
2
=
3 AB
2
Question
15
15.
A vehicle goes 15 km North and then 10 km West. How far is it from its starting point ?
(i)
19.03 km
(ii)
18.03 km
(iii)
16.03 km
(iv)
17.03 km
(v)
20.03 km
Question
16
16.
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 14 m, find the length of the ladder
(i)
17.80 m
(ii)
15.80 m
(iii)
16.80 m
(iv)
18.80 m
(v)
19.80 m
Question
17
17.
Two poles of heights 5 m and 14 m stand vertically on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
(i)
19.49 m
(ii)
18.49 m
(iii)
15.49 m
(iv)
17.49 m
(v)
16.49 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 19 m
(i)
28.58 m
(ii)
29.58 m
(iii)
27.58 m
(iv)
31.58 m
(v)
30.58 m
Assignment Key
1) (iii)
2) (v)
3) (iv)
4) (iii)
5) (i)
6) (iv)
7) (v)
8) (iv)
9) (ii)
10) (i)
11) (ii)
12) (iv)
13) (i)
14) (ii)
15) (ii)
16) (i)
17) (iv)
18) (ii)
