EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Similar Triangles
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
CDEF is a square and △CDG is an equilateral triangle. Also, △CEH is an equilateral triangle. If area of △CDG is 'a' sq.units, then the area of △CEH is
(i)
a
2
sq.units
(ii)
1
2
a sq.units
(iii)
2a sq.units
(iv)
1
2
√
3
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
AB
.
BC
(iv)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(v)
AC
2
=
AB
2
+
BC
2
+
2
BD
.
CD
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
AB
.
BC
(iv)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(v)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
Question
4
4.
In the given figure, △ABC is a triangle with AD being the median of BC. Then
(i)
AB
2
+
AC
2
=
AD
2
(ii)
AB
2
+
AC
2
=
2
DC
2
+
2
AD
2
(iii)
AB
2
+
AC
2
=
BC
2
(iv)
AB
2
+
AC
2
=
2
BD
2
+
2
DC
2
(v)
AB
2
+
AC
2
=
2
BD
2
+
2
AD
2
Question
5
5.
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
=
FH
.
GH
(ii)
EF
2
−
EH
2
=
EH
.
GH
(iii)
EF
2
−
EH
2
=
EH
.
FH
(iv)
EF
2
+
EH
2
=
FG
2
(v)
EF
2
+
EH
2
=
FH
.
GH
Question
6
6.
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
=
OG
2
+
OF
2
+
OE
2
(iii)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
−
OE
2
−
OF
2
−
OG
2
(iv)
BG
2
+
CE
2
+
DF
2
=
BC
2
+
ED
2
+
DB
2
−
CG
2
−
DE
2
−
FB
2
Question
7
7.
In the given figure, in △EFG, 'O' is a point inside the triangle. OH ⟂ FG, OI ⟂ EG and OJ ⟂ EF. Then
(i)
EJ
2
+
FH
2
+
GI
2
=
OE
.
OF
+
OF
.
OG
+
OG
.
OE
(ii)
EJ
2
+
FH
2
+
GI
2
=
EI
2
+
GH
2
+
FJ
2
(iii)
EJ
2
+
FH
2
+
GI
2
=
OJ
.
OH
+
OH
.
OI
+
OI
.
OJ
(iv)
EJ
2
+
FH
2
+
GI
2
=
OH
2
+
OI
2
+
OJ
2
Question
8
8.
In the given figure,
△BDC
is right-angled at
D
.
P
is the mid-point of
BD
and
Q
is the mid-point of
CD
.
Which of the following cases are true?
a)
4 (
BQ
2
+
CP
2
) =
5
BC
2
b)
4
CP
2
=
4
CD
2
+
BD
2
c)
4
BQ
2
=
4
CD
2
+
BD
2
d)
4
CP
2
=
4
BD
2
+
CD
2
e)
4
BQ
2
=
4
BD
2
+
CD
2
(i)
{d,b}
(ii)
{c,a}
(iii)
{c,a,b}
(iv)
{c,d,e}
(v)
{a,b,e}
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
−
AD
2
= 2
CD
.
AD
(iv)
BD
2
−
CD
2
= 2
CD
.
AD
Question
10
10.
In the given figure, DEFG is a rhombus. Which of the following are true?
a)
EF
2
+
FG
2
=
EG
2
b)
DE
2
+
EF
2
+
FG
2
+
DG
2
=
DF
2
+
EG
2
c)
DE
2
+
EF
2
=
DF
2
d)
2
DE
2
=
DF
2
+
EG
2
e)
4
DE
2
=
DF
2
+
EG
2
(i)
{c,e}
(ii)
{d,a,b}
(iii)
{a,b}
(iv)
{c,e,b}
(v)
{b,e}
Question
11
11.
In the given figure, △DEF, DG ⟂ EF. Which of the following are true?
a)
DE
2
+
EG
2
=
DF
2
+
FG
2
b)
DE
2
−
DF
2
=
EG
2
−
FG
2
c)
DE
2
−
EG
2
=
DF
2
−
FG
2
d)
DG
2
=
2
EG
.
FG
e)
DE
2
+
DF
2
=
EG
2
+
FG
2
(i)
{a,b}
(ii)
{d,c}
(iii)
{e,a,b}
(iv)
{b,c}
(v)
{d,c,b}
Question
12
12.
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
2
(iii)
1
2
√
3
a,
1
4
√
3
a
2
(iv)
√
3
a,
1
2
√
3
a
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, △EFG , H is the mid-point of FG and EI ⟂ FG. Which of the following are true?
a)
EF
2
+
EG
2
= 2
EH
2
+
1
2
FG
2
b)
EG
2
=
EI
2
+
FG
.
HI
+
1
4
FG
2
c)
EG
2
=
EH
2
+
FG
.
HI
+
1
4
FG
2
d)
EF
2
=
EI
2
−
FG
.
HI
+
1
4
FG
2
e)
EF
2
=
EH
2
−
FG
.
HI
+
1
4
FG
2
(i)
{b,d,e}
(ii)
{a,c,e}
(iii)
{b,a,c}
(iv)
{d,c}
(v)
{b,a}
Question
15
15.
In the given figure, △CED is right-angled at E, EF ⟂ CD.
CD
= c,
ED
= a,
CE
= b and
EF
= p.
Which of the following are true?
a)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
b)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
c)
1
a
2
+
1
b
2
=
1
p
2
d)
ab
=
pc
e)
a
2
+
b
2
=
c
2
(i)
{a,c,d}
(ii)
{a,b,e}
(iii)
{c,d,e}
(iv)
{a,c}
(v)
{b,d}
Question
16
16.
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
=
3 AB
2
(iv)
7 AD
2
=
9 AB
2
Question
17
17.
In the given figure, ABC is a triangle and 'O' is a point inside △ABC. The angular bisector of ∠BOA, ∠COB & ∠AOC meet AB, BC & CA at D, E & F respectively . Then
(i)
AD . BE . CF = OD . OE . OF
(ii)
AD . BE . CF = DE . EF . FD
(iii)
AD . BE . CF = OA . OB . OC
(iv)
AD . BE . CF = AB . BC . CA
(v)
AD . BE . CF = DB . EC . FA
Question
18
18.
A vehicle goes 14 km South and then 13 km East. How far is it from its starting point ?
(i)
21.10 km
(ii)
17.10 km
(iii)
20.10 km
(iv)
18.10 km
(v)
19.10 km
Question
19
19.
The foot of a ladder resting on a wall from the foot of the wall is 14 m. If the height of the top of the ladder from ground is 15 m, find the length of the ladder
(i)
21.52 m
(ii)
20.52 m
(iii)
19.52 m
(iv)
18.52 m
(v)
22.52 m
Question
20
20.
Two poles of heights 5 m and 17 m stand vertically on a plane ground. If the distance between their feet is 14 m, find the distance between their tops
(i)
18.44 m
(ii)
20.44 m
(iii)
17.44 m
(iv)
19.44 m
(v)
16.44 m
Question
21
21.
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 15 m high. Find the width of the street if the length of the ladder is 21 m
(i)
35.67 m
(ii)
31.67 m
(iii)
34.67 m
(iv)
32.67 m
(v)
33.67 m
Assignment Key
1) (iii)
2) (ii)
3) (iv)
4) (v)
5) (i)
6) (iii)
7) (ii)
8) (v)
9) (iv)
10) (v)
11) (iv)
12) (iii)
13) (iii)
14) (ii)
15) (iii)
16) (ii)
17) (v)
18) (v)
19) (ii)
20) (i)
21) (v)
