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)
1
2
a sq.units
(ii)
a
2
sq.units
(iii)
1
2
√
3
a sq.units
(iv)
2a sq.units
(v)
√
3
a sq.units
Question
2
2.
In the given figure, △EFG is an obtuse angled triangle and EH ⟂ FG. Then
(i)
EG
2
=
EF
2
+
FG
2
+
2
FG
.
FH
(ii)
EG
2
=
EF
2
+
FG
2
+
2
FH
.
GH
(iii)
EG
2
=
EF
2
+
FG
2
+
FH
2
(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, △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
+
2
EF
.
EG
(iii)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(iv)
DF
2
=
DE
2
+
EF
2
−
DG
2
(v)
DF
2
=
DE
2
+
EF
2
−
2
DE
.
EF
Question
4
4.
In the given figure, △ABC is a triangle with AD being the median of BC. Then
(i)
AB
2
+
AC
2
=
2
DC
2
+
2
AD
2
(ii)
AB
2
+
AC
2
=
2
BD
2
+
2
AD
2
(iii)
AB
2
+
AC
2
=
AD
2
(iv)
AB
2
+
AC
2
=
BC
2
(v)
AB
2
+
AC
2
=
2
BD
2
+
2
DC
2
Question
5
5.
In the given figure, △ABC is a triangle in which AB = AC and D is a point on BC. Then
(i)
AB
2
+
AD
2
=
BD
.
CD
(ii)
AB
2
+
AD
2
=
BC
2
(iii)
AB
2
−
AD
2
=
AD
.
BD
(iv)
AB
2
−
AD
2
=
AD
.
CD
(v)
AB
2
−
AD
2
=
BD
.
CD
Question
6
6.
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
2
+
OF
2
+
OG
2
−
OH
2
−
OI
2
−
OJ
2
(ii)
EJ
2
+
FH
2
+
GI
2
=
EF
2
+
HG
2
+
GE
2
−
FJ
2
−
GH
2
−
IE
2
(iii)
EJ
2
+
FH
2
+
GI
2
=
OJ
2
+
OI
2
+
OH
2
(iv)
EJ
2
+
FH
2
+
GI
2
=
OE
2
+
OF
2
+
OG
2
+
OH
2
+
OI
2
+
OJ
2
Question
7
7.
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
=
OF
.
OD
+
OD
.
OE
+
OE
.
OF
(iii)
AF
2
+
BD
2
+
CE
2
=
OA
.
OB
+
OB
.
OC
+
OC
.
OA
(iv)
AF
2
+
BD
2
+
CE
2
=
OD
2
+
OE
2
+
OF
2
Question
8
8.
In the given figure,
△DFE
is right-angled at
F
.
R
is the mid-point of
DF
and
S
is the mid-point of
EF
.
Which of the following cases are true?
a)
4
DS
2
=
4
EF
2
+
DF
2
b)
4 (
DS
2
+
ER
2
) =
5
DE
2
c)
4
ER
2
=
4
EF
2
+
DF
2
d)
4
DS
2
=
4
DF
2
+
EF
2
e)
4
ER
2
=
4
DF
2
+
EF
2
(i)
{a,e,d}
(ii)
{a,b,c}
(iii)
{e,c}
(iv)
{a,b}
(v)
{b,c,d}
Question
9
9.
In the given figure, △EFG is isosceles with EF = EG and FH ⟂ EG. Then
(i)
FH
2
−
EH
2
= 2
GH
.
EH
(ii)
FH
2
+
GH
2
= 2
GH
.
EH
(iii)
FH
2
+
EH
2
= 2
GH
.
EH
(iv)
FH
2
−
GH
2
= 2
GH
.
EH
Question
10
10.
In the given figure, HIJK is a rhombus. Which of the following are true?
a)
4
HI
2
=
HJ
2
+
IK
2
b)
HI
2
+
IJ
2
+
JK
2
+
HK
2
=
HJ
2
+
IK
2
c)
HI
2
+
IJ
2
=
HJ
2
d)
2
HI
2
=
HJ
2
+
IK
2
e)
IJ
2
+
JK
2
=
IK
2
(i)
{d,b}
(ii)
{c,a}
(iii)
{d,b,a}
(iv)
{e,c,a}
(v)
{a,b}
Question
11
11.
In the given figure, △DEF, DG ⟂ EF. Which of the following are true?
a)
DE
2
−
DF
2
=
EG
2
−
FG
2
b)
DE
2
+
EG
2
=
DF
2
+
FG
2
c)
DE
2
+
DF
2
=
EG
2
+
FG
2
d)
DG
2
=
2
EG
.
FG
e)
DE
2
−
EG
2
=
DF
2
−
FG
2
(i)
{c,e}
(ii)
{d,b,a}
(iii)
{a,e}
(iv)
{c,e,a}
(v)
{b,a}
Question
12
12.
The altitude and area of an equilateral triangle of side 'a' is
(i)
1
2
√
3
a,
1
4
√
3
a
2
(ii)
√
3
a,
1
2
√
3
a
2
(iii)
√
3
a,
1
2
√
3
a
(iv)
1
2
√
3
a,
1
2
√
3
a
2
Question
13
13.
In the given figure, O is a point in the interior of the rectangle DEFG. Then
(i)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DF
2
+
EG
2
(ii)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DE
2
+
EF
2
+
FG
2
+
GD
2
(iii)
OD
2
−
OF
2
=
OE
2
−
OG
2
(iv)
OD
2
+
OF
2
=
OE
2
+
OG
2
Question
14
14.
In the given figure, △ABC , D is the mid-point of BC and AE ⟂ BC. Which of the following are true?
a)
AC
2
=
AE
2
+
BC
.
DE
+
1
4
BC
2
b)
AB
2
+
AC
2
= 2
AD
2
+
1
2
BC
2
c)
AB
2
=
AE
2
−
BC
.
DE
+
1
4
BC
2
d)
AB
2
=
AD
2
−
BC
.
DE
+
1
4
BC
2
e)
AC
2
=
AD
2
+
BC
.
DE
+
1
4
BC
2
(i)
{a,c,e}
(ii)
{b,d,e}
(iii)
{a,b,d}
(iv)
{c,d}
(v)
{a,b}
Question
15
15.
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)
a
2
+
b
2
=
c
2
b)
1
a
2
+
1
b
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
c
2
=
1
p
2
(i)
{d,e,c}
(ii)
{d,a,b}
(iii)
{e,b}
(iv)
{d,a}
(v)
{a,b,c}
Question
16
16.
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
17
17.
In the given figure, EFG is a triangle and 'O' is a point inside △EFG. The angular bisector of ∠FOE, ∠GOF & ∠EOG meet EF, FG & GE at H, I & J respectively . Then
(i)
EH . FI . GJ = OE . OF . OG
(ii)
EH . FI . GJ = HI . IJ . JH
(iii)
EH . FI . GJ = HF . IG . JE
(iv)
EH . FI . GJ = OH . OI . OJ
(v)
EH . FI . GJ = EF . FG . GE
Question
18
18.
A vehicle goes 12 km South and then 14 km East. How far is it from its starting point ?
(i)
16.44 km
(ii)
17.44 km
(iii)
20.44 km
(iv)
19.44 km
(v)
18.44 km
Question
19
19.
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 10 m, find the length of the ladder
(i)
13.87 m
(ii)
16.87 m
(iii)
15.87 m
(iv)
12.87 m
(v)
14.87 m
Question
20
20.
Two poles of heights 8 m and 17 m stand vertically on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
(i)
18.49 m
(ii)
19.49 m
(iii)
15.49 m
(iv)
16.49 m
(v)
17.49 m
Question
21
21.
A ladder reaches a window which is 11 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)
25.74 m
(ii)
26.74 m
(iii)
23.74 m
(iv)
24.74 m
(v)
27.74 m
Assignment Key
1) (iv)
2) (i)
3) (i)
4) (ii)
5) (v)
6) (i)
7) (i)
8) (v)
9) (iv)
10) (v)
11) (iii)
12) (i)
13) (iv)
14) (ii)
15) (v)
16) (iii)
17) (iii)
18) (v)
19) (v)
20) (v)
21) (i)
