EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Similar Triangles
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
JKLM is a square and △JKN is an equilateral triangle. Also, △JLO is an equilateral triangle. If area of △JKN is 'a' sq.units, then the area of △JLO is
(i)
2a sq.units
(ii)
1
2
√
3
a sq.units
(iii)
a
2
sq.units
(iv)
1
2
a sq.units
(v)
√
3
a sq.units
Question
2
2.
In the given figure, △ABC is an obtuse angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
+
BD
2
(ii)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(iii)
AC
2
=
AB
2
+
BC
2
+
2
BD
.
CD
(iv)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
(v)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
Question
3
3.
In the given figure, △ABC is an acute angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
−
AD
2
(ii)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
(iii)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(iv)
AC
2
=
AB
2
+
BC
2
−
2
AB
.
BC
(v)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
Question
4
4.
In the given figure, △EFG is a triangle with EH being the median of FG. Then
(i)
EF
2
+
EG
2
=
2
HG
2
+
2
EH
2
(ii)
EF
2
+
EG
2
=
2
FH
2
+
2
EH
2
(iii)
EF
2
+
EG
2
=
2
FH
2
+
2
HG
2
(iv)
EF
2
+
EG
2
=
FG
2
(v)
EF
2
+
EG
2
=
EH
2
Question
5
5.
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
=
IK
.
JK
(iii)
HI
2
+
HK
2
=
IJ
2
(iv)
HI
2
−
HK
2
=
HK
.
JK
(v)
HI
2
−
HK
2
=
HK
.
IK
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
=
FG
2
+
IH
2
+
HF
2
−
GK
2
−
HI
2
−
JF
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
=
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
+
OK
2
Question
7
7.
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
=
DH
2
+
FG
2
+
EI
2
(ii)
DI
2
+
EG
2
+
FH
2
=
OD
.
OE
+
OE
.
OF
+
OF
.
OD
(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
8
8.
In the given figure,
△DFE
is right-angled at
F
.
T
is the mid-point of
DF
and
U
is the mid-point of
EF
.
Which of the following cases are true?
a)
4
DU
2
=
4
DF
2
+
EF
2
b)
4 (
DU
2
+
ET
2
) =
5
DE
2
c)
4
ET
2
=
4
DF
2
+
EF
2
d)
4
DU
2
=
4
EF
2
+
DF
2
e)
4
ET
2
=
4
EF
2
+
DF
2
(i)
{c,a,b}
(ii)
{c,d,e}
(iii)
{a,b,e}
(iv)
{d,b}
(v)
{c,a}
Question
9
9.
In the given figure, △ABC is isosceles with AB = AC and BD ⟂ AC. Then
(i)
BD
2
+
AD
2
= 2
CD
.
AD
(ii)
BD
2
+
CD
2
= 2
CD
.
AD
(iii)
BD
2
−
CD
2
= 2
CD
.
AD
(iv)
BD
2
−
AD
2
= 2
CD
.
AD
Question
10
10.
In the given figure, BCDE is a rhombus. Which of the following are true?
a)
CD
2
+
DE
2
=
CE
2
b)
4
BC
2
=
BD
2
+
CE
2
c)
BC
2
+
CD
2
+
DE
2
+
BE
2
=
BD
2
+
CE
2
d)
2
BC
2
=
BD
2
+
CE
2
e)
BC
2
+
CD
2
=
BD
2
(i)
{d,c}
(ii)
{b,c}
(iii)
{e,a,b}
(iv)
{d,c,b}
(v)
{a,b}
Question
11
11.
In the given figure, △FGH, FI ⟂ GH. Which of the following are true?
a)
FG
2
+
FH
2
=
GI
2
+
HI
2
b)
FG
2
−
FH
2
=
GI
2
−
HI
2
c)
FG
2
−
GI
2
=
FH
2
−
HI
2
d)
FG
2
+
GI
2
=
FH
2
+
HI
2
e)
FI
2
=
2
GI
.
HI
(i)
{d,c,b}
(ii)
{b,c}
(iii)
{e,a,b}
(iv)
{a,b}
(v)
{d,c}
Question
12
12.
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
2
√
3
a
2
(iii)
√
3
a,
1
2
√
3
a
(iv)
1
2
√
3
a,
1
4
√
3
a
2
Question
13
13.
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
14
14.
In the given figure, △CDE , F is the mid-point of DE and CG ⟂ DE. Which of the following are true?
a)
CD
2
+
CE
2
= 2
CF
2
+
1
2
DE
2
b)
CD
2
=
CF
2
−
DE
.
FG
+
1
4
DE
2
c)
CE
2
=
CG
2
+
DE
.
FG
+
1
4
DE
2
d)
CE
2
=
CF
2
+
DE
.
FG
+
1
4
DE
2
e)
CD
2
=
CG
2
−
DE
.
FG
+
1
4
DE
2
(i)
{e,b}
(ii)
{a,b,d}
(iii)
{c,a}
(iv)
{c,a,b}
(v)
{c,e,d}
Question
15
15.
In the given figure, △BDC is right-angled at D, DE ⟂ BC.
BC
= c,
DC
= a,
BD
= b and
DE
= p.
Which of the following are true?
a)
1
a
2
+
1
b
2
=
1
p
2
b)
a
2
+
b
2
=
c
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
c
2
+
1
p
2
(i)
{a,b,c}
(ii)
{d,e,c}
(iii)
{d,a}
(iv)
{e,b}
(v)
{d,a,b}
Question
16
16.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
3 AB
2
(ii)
7 AD
2
=
9 AB
2
(iii)
9 AD
2
=
7 AB
2
(iv)
3 AD
2
=
7 AB
2
Question
17
17.
In the given figure, BCD is a triangle and 'O' is a point inside △BCD. The angular bisector of ∠COB, ∠DOC & ∠BOD meet BC, CD & DB at E, F & G respectively . Then
(i)
BE . CF . DG = OE . OF . OG
(ii)
BE . CF . DG = OB . OC . OD
(iii)
BE . CF . DG = BC . CD . DB
(iv)
BE . CF . DG = EF . FG . GE
(v)
BE . CF . DG = EC . FD . GB
Question
18
18.
A vehicle goes 14 km South and then 15 km East. How far is it from its starting point ?
(i)
21.52 km
(ii)
19.52 km
(iii)
18.52 km
(iv)
20.52 km
(v)
22.52 km
Question
19
19.
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 15 m, find the length of the ladder
(i)
18.85 m
(ii)
17.85 m
(iii)
21.85 m
(iv)
19.85 m
(v)
20.85 m
Question
20
20.
Two poles of heights 5 m and 14 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops
(i)
13.00 m
(ii)
14.00 m
(iii)
17.00 m
(iv)
15.00 m
(v)
16.00 m
Question
21
21.
A ladder reaches a window which is 8 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 19 m
(i)
26.48 m
(ii)
25.48 m
(iii)
27.48 m
(iv)
28.48 m
(v)
29.48 m
Assignment Key
1) (i)
2) (ii)
3) (v)
4) (ii)
5) (ii)
6) (iii)
7) (i)
8) (iii)
9) (iii)
10) (ii)
11) (ii)
12) (iv)
13) (ii)
14) (ii)
15) (i)
16) (iii)
17) (v)
18) (iv)
19) (iv)
20) (iv)
21) (iii)
