EduSahara™ Assignment
Name : Pythagoras Theorem
Chapter : Similar Triangles
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
GHIJ is a square and △GHK is an equilateral triangle. Also, △GIL is an equilateral triangle. If area of △GHK is 'a' sq.units, then the area of △GIL 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, △CDE is an obtuse angled triangle and CF ⟂ DE. Then
(i)
CE
2
=
CD
2
+
DE
2
+
2
DF
.
EF
(ii)
CE
2
=
CD
2
+
DE
2
+
2
CD
.
DE
(iii)
CE
2
=
CD
2
+
DE
2
−
2
DE
.
DF
(iv)
CE
2
=
CD
2
+
DE
2
+
DF
2
(v)
CE
2
=
CD
2
+
DE
2
+
2
DE
.
DF
Question
3
3.
In the given figure, △BCD is an acute angled triangle and BE ⟂ CD. Then
(i)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
(ii)
BD
2
=
BC
2
+
CD
2
−
2
CD
.
CE
(iii)
BD
2
=
BC
2
+
CD
2
−
2
BC
.
CD
(iv)
BD
2
=
BC
2
+
CD
2
−
BE
2
(v)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
Question
4
4.
In the given figure, △CDE is a triangle with CF being the median of DE. Then
(i)
CD
2
+
CE
2
=
CF
2
(ii)
CD
2
+
CE
2
=
2
FE
2
+
2
CF
2
(iii)
CD
2
+
CE
2
=
2
DF
2
+
2
CF
2
(iv)
CD
2
+
CE
2
=
2
DF
2
+
2
FE
2
(v)
CD
2
+
CE
2
=
DE
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
=
IJ
2
(ii)
HI
2
−
HK
2
=
HK
.
IK
(iii)
HI
2
−
HK
2
=
HK
.
JK
(iv)
HI
2
+
HK
2
=
IK
.
JK
(v)
HI
2
−
HK
2
=
IK
.
JK
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
=
OG
2
+
OH
2
+
OI
2
−
OJ
2
−
OK
2
−
OL
2
(iii)
GL
2
+
HJ
2
+
IK
2
=
GH
2
+
JI
2
+
IG
2
−
HL
2
−
IJ
2
−
KG
2
(iv)
GL
2
+
HJ
2
+
IK
2
=
OL
2
+
OK
2
+
OJ
2
Question
7
7.
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
.
OC
+
OC
.
OD
+
OD
.
OB
(ii)
BG
2
+
CE
2
+
DF
2
=
BF
2
+
DE
2
+
CG
2
(iii)
BG
2
+
CE
2
+
DF
2
=
OG
.
OE
+
OE
.
OF
+
OF
.
OG
(iv)
BG
2
+
CE
2
+
DF
2
=
OE
2
+
OF
2
+
OG
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
DF
2
+
EF
2
b)
4
ER
2
=
4
DF
2
+
EF
2
c)
4
DS
2
=
4
EF
2
+
DF
2
d)
4
ER
2
=
4
EF
2
+
DF
2
e)
4 (
DS
2
+
ER
2
) =
5
DE
2
(i)
{a,d,e}
(ii)
{b,a}
(iii)
{b,c,e}
(iv)
{c,d}
(v)
{b,a,d}
Question
9
9.
In the given figure, △ABC is isosceles with AB = AC and BD ⟂ AC. Then
(i)
BD
2
+
CD
2
= 2
CD
.
AD
(ii)
BD
2
−
AD
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, HIJK is a rhombus. Which of the following are true?
a)
HI
2
+
IJ
2
+
JK
2
+
HK
2
=
HJ
2
+
IK
2
b)
IJ
2
+
JK
2
=
IK
2
c)
2
HI
2
=
HJ
2
+
IK
2
d)
4
HI
2
=
HJ
2
+
IK
2
e)
HI
2
+
IJ
2
=
HJ
2
(i)
{c,d,a}
(ii)
{c,d}
(iii)
{a,d}
(iv)
{e,b,a}
(v)
{b,a}
Question
11
11.
In the given figure, △IJK, IL ⟂ JK. Which of the following are true?
a)
IJ
2
−
IK
2
=
JL
2
−
KL
2
b)
IL
2
=
2
JL
.
KL
c)
IJ
2
−
JL
2
=
IK
2
−
KL
2
d)
IJ
2
+
IK
2
=
JL
2
+
KL
2
e)
IJ
2
+
JL
2
=
IK
2
+
KL
2
(i)
{d,c,a}
(ii)
{d,c}
(iii)
{b,a}
(iv)
{e,b,a}
(v)
{a,c}
Question
12
12.
The altitude and area of an equilateral triangle of side 'a' is
(i)
√
3
a,
1
2
√
3
a
(ii)
1
2
√
3
a,
1
4
√
3
a
2
(iii)
√
3
a,
1
2
√
3
a
2
(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 ABCD. Then
(i)
OA
2
+
OC
2
=
OB
2
+
OD
2
(ii)
OA
2
−
OC
2
=
OB
2
−
OD
2
(iii)
OA
2
+
OB
2
+
OC
2
+
OD
2
=
AB
2
+
BC
2
+
CD
2
+
DA
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)
CE
2
=
CF
2
+
DE
.
FG
+
1
4
DE
2
c)
CD
2
=
CG
2
−
DE
.
FG
+
1
4
DE
2
d)
CE
2
=
CG
2
+
DE
.
FG
+
1
4
DE
2
e)
CD
2
=
CF
2
−
DE
.
FG
+
1
4
DE
2
(i)
{d,b}
(ii)
{c,d,e}
(iii)
{c,a}
(iv)
{c,a,b}
(v)
{a,b,e}
Question
15
15.
In the given figure, △EGF is right-angled at G, GH ⟂ EF.
EF
= c,
GF
= a,
EG
= b and
GH
= 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)
a
2
+
b
2
=
c
2
d)
ab
=
pc
e)
1
a
2
+
1
b
2
=
1
p
2
(i)
{a,c}
(ii)
{a,c,d}
(iii)
{c,d,e}
(iv)
{a,b,e}
(v)
{b,d}
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)
7 AD
2
=
3 AB
2
(iv)
9 AD
2
=
7 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 = OH . OI . OJ
(iii)
EH . FI . GJ = EF . FG . GE
(iv)
EH . FI . GJ = HI . IJ . JH
(v)
EH . FI . GJ = HF . IG . JE
Question
18
18.
A vehicle goes 11 km North and then 15 km West. How far is it from its starting point ?
(i)
18.60 km
(ii)
20.60 km
(iii)
17.60 km
(iv)
16.60 km
(v)
19.60 km
Question
19
19.
The foot of a ladder resting on a wall from the foot of the wall is 12 m. If the height of the top of the ladder from ground is 14 m, find the length of the ladder
(i)
16.44 m
(ii)
18.44 m
(iii)
20.44 m
(iv)
17.44 m
(v)
19.44 m
Question
20
20.
Two poles of heights 5 m and 18 m stand vertically on a plane ground. If the distance between their feet is 14 m, find the distance between their tops
(i)
17.10 m
(ii)
19.10 m
(iii)
21.10 m
(iv)
20.10 m
(v)
18.10 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 17 m high. Find the width of the street if the length of the ladder is 19 m
(i)
25.72 m
(ii)
26.72 m
(iii)
27.72 m
(iv)
23.72 m
(v)
24.72 m
Assignment Key
1) (iii)
2) (v)
3) (ii)
4) (iii)
5) (v)
6) (ii)
7) (ii)
8) (i)
9) (iii)
10) (iii)
11) (v)
12) (ii)
13) (i)
14) (v)
15) (iii)
16) (iv)
17) (v)
18) (i)
19) (ii)
20) (ii)
21) (i)
