EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Similar Triangles
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
KLMN is a square and △KLO is an equilateral triangle. Also, △KMP is an equilateral triangle. If area of △KLO is 'a' sq.units, then the area of △KMP is
(i)
1
2
√
3
a sq.units
(ii)
a
2
sq.units
(iii)
1
2
a sq.units
(iv)
2a sq.units
(v)
√
3
a sq.units
Question
2
2.
In the given figure, △DEF is an obtuse angled triangle and DG ⟂ EF. Then
(i)
DF
2
=
DE
2
+
EF
2
+
2
DE
.
EF
(ii)
DF
2
=
DE
2
+
EF
2
−
2
EF
.
EG
(iii)
DF
2
=
DE
2
+
EF
2
+
EG
2
(iv)
DF
2
=
DE
2
+
EF
2
+
2
EF
.
EG
(v)
DF
2
=
DE
2
+
EF
2
+
2
EG
.
FG
Question
3
3.
In the given figure, △CDE is an acute angled triangle and CF ⟂ DE. Then
(i)
CE
2
=
CD
2
+
DE
2
+
2
CD
.
DE
(ii)
CE
2
=
CD
2
+
DE
2
−
2
DE
.
DF
(iii)
CE
2
=
CD
2
+
DE
2
+
2
DE
.
DF
(iv)
CE
2
=
CD
2
+
DE
2
−
2
CD
.
DE
(v)
CE
2
=
CD
2
+
DE
2
−
CF
2
Question
4
4.
In the given figure, △DEF is a triangle with DG being the median of EF. Then
(i)
DE
2
+
DF
2
=
2
EG
2
+
2
DG
2
(ii)
DE
2
+
DF
2
=
2
EG
2
+
2
GF
2
(iii)
DE
2
+
DF
2
=
EF
2
(iv)
DE
2
+
DF
2
=
DG
2
(v)
DE
2
+
DF
2
=
2
GF
2
+
2
DG
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
=
FH
.
GH
(iii)
EF
2
−
EH
2
=
EH
.
FH
(iv)
EF
2
−
EH
2
=
EH
.
GH
(v)
EF
2
+
EH
2
=
FG
2
Question
6
6.
In the given figure, in △GHI, 'O' is a point inside the triangle. OJ ⟂ HI, OK ⟂ GI and OL ⟂ GH. Then
(i)
GL
2
+
HJ
2
+
IK
2
=
OG
2
+
OH
2
+
OI
2
+
OJ
2
+
OK
2
+
OL
2
(ii)
GL
2
+
HJ
2
+
IK
2
=
GH
2
+
JI
2
+
IG
2
−
HL
2
−
IJ
2
−
KG
2
(iii)
GL
2
+
HJ
2
+
IK
2
=
OL
2
+
OK
2
+
OJ
2
(iv)
GL
2
+
HJ
2
+
IK
2
=
OG
2
+
OH
2
+
OI
2
−
OJ
2
−
OK
2
−
OL
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
=
OH
2
+
OI
2
+
OJ
2
(iv)
EJ
2
+
FH
2
+
GI
2
=
OJ
.
OH
+
OH
.
OI
+
OI
.
OJ
Question
8
8.
In the given figure,
△GIH
is right-angled at
I
.
P
is the mid-point of
GI
and
Q
is the mid-point of
HI
.
Which of the following cases are true?
a)
4
HP
2
=
4
HI
2
+
GI
2
b)
4
HP
2
=
4
GI
2
+
HI
2
c)
4
GQ
2
=
4
HI
2
+
GI
2
d)
4 (
GQ
2
+
HP
2
) =
5
GH
2
e)
4
GQ
2
=
4
GI
2
+
HI
2
(i)
{b,c,e}
(ii)
{c,d}
(iii)
{b,a}
(iv)
{a,d,e}
(v)
{b,a,d}
Question
9
9.
In the given figure, △DEF is isosceles with DE = DF and EG ⟂ DF. Then
(i)
EG
2
+
FG
2
= 2
FG
.
DG
(ii)
EG
2
−
FG
2
= 2
FG
.
DG
(iii)
EG
2
−
DG
2
= 2
FG
.
DG
(iv)
EG
2
+
DG
2
= 2
FG
.
DG
Question
10
10.
In the given figure, ABCD is a rhombus. Which of the following are true?
a)
4
AB
2
=
AC
2
+
BD
2
b)
AB
2
+
BC
2
=
AC
2
c)
AB
2
+
BC
2
+
CD
2
+
AD
2
=
AC
2
+
BD
2
d)
2
AB
2
=
AC
2
+
BD
2
e)
BC
2
+
CD
2
=
BD
2
(i)
{a,c}
(ii)
{d,c}
(iii)
{d,c,a}
(iv)
{b,a}
(v)
{e,b,a}
Question
11
11.
In the given figure, △CDE, CF ⟂ DE. Which of the following are true?
a)
CD
2
+
CE
2
=
DF
2
+
EF
2
b)
CD
2
+
DF
2
=
CE
2
+
EF
2
c)
CD
2
−
DF
2
=
CE
2
−
EF
2
d)
CD
2
−
CE
2
=
DF
2
−
EF
2
e)
CF
2
=
2
DF
.
EF
(i)
{c,d}
(ii)
{b,d,c}
(iii)
{b,d}
(iv)
{a,c}
(v)
{e,a,c}
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)
1
2
√
3
a,
1
2
√
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 EFGH. Then
(i)
OE
2
+
OG
2
=
OF
2
+
OH
2
(ii)
OE
2
−
OG
2
=
OF
2
−
OH
2
(iii)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EF
2
+
FG
2
+
GH
2
+
HE
2
(iv)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EG
2
+
FH
2
Question
14
14.
In the given figure, △FGH , I is the mid-point of GH and FJ ⟂ GH. Which of the following are true?
a)
FH
2
=
FI
2
+
GH
.
IJ
+
1
4
GH
2
b)
FH
2
=
FJ
2
+
GH
.
IJ
+
1
4
GH
2
c)
FG
2
=
FI
2
−
GH
.
IJ
+
1
4
GH
2
d)
FG
2
+
FH
2
= 2
FI
2
+
1
2
GH
2
e)
FG
2
=
FJ
2
−
GH
.
IJ
+
1
4
GH
2
(i)
{b,e,d}
(ii)
{a,c,d}
(iii)
{e,c}
(iv)
{b,a,c}
(v)
{b,a}
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
c
2
+
1
p
2
b)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
c)
ab
=
pc
d)
a
2
+
b
2
=
c
2
e)
1
a
2
+
1
b
2
=
1
p
2
(i)
{a,b,e}
(ii)
{a,c,d}
(iii)
{b,d}
(iv)
{a,c}
(v)
{c,d,e}
Question
16
16.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
3 AB
2
(ii)
9 AD
2
=
7 AB
2
(iii)
3 AD
2
=
7 AB
2
(iv)
7 AD
2
=
9 AB
2
Question
17
17.
In the given figure, CDE is a triangle and 'O' is a point inside △CDE. The angular bisector of ∠DOC, ∠EOD & ∠COE meet CD, DE & EC at F, G & H respectively . Then
(i)
CF . DG . EH = FG . GH . HF
(ii)
CF . DG . EH = FD . GE . HC
(iii)
CF . DG . EH = CD . DE . EC
(iv)
CF . DG . EH = OC . OD . OE
(v)
CF . DG . EH = OF . OG . OH
Question
18
18.
A vehicle goes 13 km North and then 14 km West. How far is it from its starting point ?
(i)
17.10 km
(ii)
19.10 km
(iii)
21.10 km
(iv)
18.10 km
(v)
20.10 km
Question
19
19.
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 12 m, find the length of the ladder
(i)
19.21 m
(ii)
18.21 m
(iii)
17.21 m
(iv)
21.21 m
(v)
20.21 m
Question
20
20.
Two poles of heights 5 m and 15 m stand vertically on a plane ground. If the distance between their feet is 11 m, find the distance between their tops
(i)
13.87 m
(ii)
15.87 m
(iii)
12.87 m
(iv)
14.87 m
(v)
16.87 m
Question
21
21.
A ladder reaches a window which is 10 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 20 m
(i)
32.60 m
(ii)
33.60 m
(iii)
30.60 m
(iv)
29.60 m
(v)
31.60 m
Assignment Key
1) (iv)
2) (iv)
3) (ii)
4) (i)
5) (i)
6) (iv)
7) (ii)
8) (iv)
9) (ii)
10) (i)
11) (i)
12) (i)
13) (i)
14) (ii)
15) (v)
16) (ii)
17) (ii)
18) (ii)
19) (i)
20) (iv)
21) (v)
