Lines and Angles Notes.pdf class 9th Lines and Angles Notes

class 9th Lines and Angles Notes

1. CHAPTER-6
LINES &ANGLES MIND MAP
Intersecting Lines
Line
Parallel or
Pair of Lines
Intersecting Lines
Line Segment
Complementary
O gles
Supplementary
Ray
Adjacent
Linear Pair
Vertically Opposite
Types ofAngles
Acute
Angle
Obtuse
Angle
Right
Angle
Altermate
Corresponding
Angles
Angles
Co-interior Angles

2. Date
Page No.
LINES & ANGLES
has
Point A point is hart whíchfno_camponent length, uidth)
A is epresenrted by a dot
Line Line is a collecthion_of points uwhích has only
lergth neitbex breadtHh noy thickness A Line haa
no endpoints t_can be extended infinitely.
I Line &gment Apast on pontion of a line with tuwo
pointg end
Ray 8 A pant of line uith only one end point and
Cther síde Can be extended ininitely
1 Collinear Points; Poits lie on the eSane Line are called
Collinea points
Non-collirearPoints Poiris thatdontLie on the Samelire
ae Called non collinec points
e
D

3. Page No.
Angles An ange is omed when uo nys oniginate
omSame end poi The rays maKin an angle
ae
called Axms anc end point 1s calledVexkx
Tes of Angles
Acute angle Angle wbich is betwen
and go
Right angle
Angle which is exac+I
equal to 9o.
Ang
le whic h is between
Jo and 180
e Obtuse angle
,
Ange whicb is between
80 and 360.
Reflex angle
SHoaig ht argle
Ang le whichís exac+ ly
eua to l80
CombleHe angle
Angle which is exact1
equa to 360.
Supple menrtar Angleg Compliímentar Angles
A pair f anglex
uhose
Sum is 90
Apa ot anges wbose sum
is 180
x A+ C8 = 9o Ea A+<8 = 180

4. Date
Page No.
Adjacent Angles Tuoo angles ae adjacert i
Theu have a Common Vertex
acommon am
QIiL) Non-common ayms Qxe on opposite Sides ot Common am
Iinear paîr ot angle8 A pair of adjacert angles whase Sum
is 180
A O
LAoB k 2co8 are ming inear pair
Vextically Dpposite angles g T two Lines_intersectt each othe
at d point then the oposite angles ame
Vortically oppste angles
Here IELZ
W
TntersectinqLines g The lies which cross each other
oam a parliculaa poirnt is called intersecliq
Lines
I Non-Iex sectingPearalel_ lines lhe lines which neu cross each
other at an Poirt are called non intersectinq
These Lines ae Calkd Parallel lines
DELTA Notebook

5. Date
Page No.
lans versal line Ifa Line passes though tuo lines
and intersects henm at a
paicular poiks -then his
ine iscalled txansuersal line
1
34
a) Verically oppasite angles L1=43
L5=21
L26=28
6) Coespondinq angles Ll=45
L= L6
3=
Lz=28
(c) AHernate Interíor Apgle 8 3-L5
L3+46= 180 Agles onthe Same Sides of a
ansuersal ae upplenentay
ZY+CS= l80
DELTA Notebcok

6. Date
Page No.
IGnes paallel to the Same lLine
wo Lines are paallel uth a Common Line then hese
wo lines uwill also be panalte to each atbey
D
As in above igure it AB LCD
and CD IL EF then
AB I eF
LAngle Sum p0perty o a tiangle
1. he Sum ot dhe angles ot a miangle is 180
ZA t< Btc = l80
A
9. Exterior Andle is equal to Sum othe tudo interior of
OpostO aglesS
L8cD=LBACtLABC
A D
DELTA Notebook

7. LINES&ANGLES
Part-A
1. An angle which is greater than 180°& less than 360 is-
b) Straight Angle a) Obtuse Angle
c) Reflex Angle d) Complete Angle
2. If three or more points does not lie on the same straight line the
points are called
a) Concurent points b) Collinear Points
c)Non Collinear Points
Reflex angle of 110° is
d) Adjacent Point
3
90
190
a) 70° )
C) 250° d)
4. Ifan angle is equal its complement, then the angle is -
a) 90° b) 0
c) 48° d) 45
5. If the figure POQ is a straight line. The three adjacent angles are
consecutive numbers, the measure of these angles is-
a) 50,60°, 70
c)58°,60°,62
b) 59,60,61
d) All are correct
*2
6. In the figure, twice of x is 30 less than y, then the values of x & y are
respectively, given OB& OAare
opposite rays
a) 130, 50° ) 50.130
c) 100. 80° d) 75.105

8. 7. One of the angles of a pair of supplementary angles is 2° more than
its supplement, the angles are:
a) 90° 90
c) 89,91
b) 88 92
d) All are correct
oR40
D
8. In the figure AB & CD are two straight lines intersecting at 0, OP is a
ray.Whatis the measure of ZAOD.
100
128
9. If the difference between two supplementary angles is 40 then the
a) 40° )
c) 140° d)
angles are
a) 40°,140° b) 80,100°
65,115 c)110,70
10. Theangles which is four times more than its complement is
a) 120
c)150
11. An exterior angle of a triangle is 100° & its two interior opposite
angles are equal. Measure of there equal angles are-
a) 40
80
12. The value of x in the figureis
a) 230
c) 120
d)
144
100
b)
d)
b)
0°
c) d) 90
100
115
)
d)
120
x
x*10

9. 13. Which ofthe following options is correct
Apair of adjacent angles have.
i) Common vertex
(i) Common Arm.
(ii) Non Common arms are an opposite sides of common arms
(iv) Non Common arms are on the same side of common arms.
a) (i)& (i) are sufficient
b)(.i)& (i) are sufficient
c)). (i)&(v) are sufficient
d
All are sufficient
14. Anglesx&yforms a linear pair and x+2y= 30°, the value ofy is
a) 70 ) 110
c) 210
15. The degree measure of x &y respectively in the figure are
a) 80,100
c) 80, 80
d) 60
b) 100. 80
d) 100. 100
80°
16. In the figure AB, CD& EF are three Straight lines intersecting at O.
The measure of LAOFis-
a) 98
c)54
152
82
b)
d)
17. If LABC+4DEF=180, name the pair of anglesLABC & DEF
a) Adjacent Angles
c)Supplementary Angle
d) vO.A
18. In the figure, AB|| CD, What is x*y
a) 40
c)100
b) Complementary Angles
D
60
80
b)
d) A40 601

10. 19. Fromthe Figure, choose the
corect option.
(21828are allemate angles
(i) 41&L7
are alternate angles
(i) 23& 45 are altemate angles
(v) 24&8
are corresponding angles
(v) 2& 26 are not corresponding angles.
(vi) 3& L8 are interior angles on the same side of the transversal.
m
a) ). (). (iv). (v) are correct b)). (i). (iü) are correct
c)(i), (i). (iv), (vi) are correct d) (i), (i), (iv), (v)are correct.
20. If two parallel lines are intersected by a transversal, then the interior
angles
on the same side of the transversal are-
a) equal b) adjacent
c)Supplementary d) Complementary
21. In the figure, measure of x is-
a) 65
c)100
b) 55
d) 80
22. In the figure, I|| m &|| n then x is
45
60
a) 90° b)
c) 30 d)
23. Inthe figure, if/|| mwhat is x.
a) 30
) 70°
c) 43 d) 37
6 3x-20

11. 24. In the figure, AB || CD, EG & FG are Bi Sectors of ZBEF & 2DFE
respectively,the m LFGE is-
a) 45
c)60
b) 90
d) 100
25. Inthe figure, /|| m such that LA =110°& LB= 130° then m LACBis
60 a) 50 b)
130
m
C) 70 d) 120
26. The ratio of two interior angles on the same side of the transversal is
2:3, the measure of diference of both the angles is-
a) 36
c)72
180
108
b)
d)
27. In the figure, /|| m|| n and AB|| CD, then BCD is-
a) 120
c) 85
145
d) 60
b)
28. In
the figure
/|| m, then y=-
a) 145
60
25
120
35
b)
d)
60
29. An exterior angle is drawn to a triangle, which is acute, then on the
basis of angles what type of triangle is this-
a) Acuteangled b) Obtuse angled
c) Rightangled d) Scalene

12. 30. In the figure what iste m ZA=
a) 80 60
140
b)
c)40° d)
100 120
31. In the figure, if AB=AC the m LA is
55
70
a)
b) 75
C) d) 110
32. In the figure, measure of x is
DO
a) 100 b) 140
) 60 d) 20°
33. In thefigure, measure of ZB iss
a) 90
110
b)
20°
) d) 70
TO
34. Ifone of the angles of a triangles is 120°, then the angle between the
interior bisectors of the other two angles is
90
150
30
60
b)
) d)
35. If one of the angles of a triangle is 62, then the angle between the
exterior bisectors of the other two angles is
a) 31 b) 59
c)121 d) 118°
36. Ifa&bforms a pair of adjacent angles then which figures proves it.
b)
d)