Lines and Angles Notes.pdf class 9th Lines and Angles Notes
1 like4,001 views
The document covers concepts related to lines and angles, including definitions of points, lines, segments, rays, and various types of angles such as acute, obtuse, right, and supplementary angles. It explains the relationships between intersecting and parallel lines, specifically the properties of adjacent angles, vertically opposite angles, and linear pairs. Additionally, it includes several example problems and their solutions related to these concepts.
Lines and Angles Notes.pdf class 9th Lines and Angles Notes
- 1. CHAPTER-6 LINES &ANGLES MIND MAP Intersecting Lines Line Parallel or Pair ofLines Intersecting Lines Line Segment Complementary O gles Supplementary Ray Adjacent Linear Pair Vertically Opposite Types of Angles 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_canbe extendedinfinitely. I Line &gment Apaston pontion of a line with tuwo pointg end Ray 8 A pantof line uith only oneendpoint and CthersídeCanbe extended ininitely 1 CollinearPoints; PoitslieontheeSane Line arecalled Collinea points Non-collirear Points Poiris that dont Lie on the Same lire ae Called non collinec points e D
- 3. Page No. Angles Anange is omed whenuo nys oniginate omSame end poi The rays maKin an angle ae called Axms anc end point 1s calledVexkx Tesof Angles Acute angle Anglewbichis betwen and go Right angle Angle which is exac+I equal to 9o. Angle which is between Jo and 180 e Obtuse angle , Ange whicb is between 80 and 360. Reflex angle SHoaight argle Angle which ís exac+ly eua to l80 CombleHe angle Angle which is exact1 equa to 360. Supplemenrtar Angleg Compliímentar Angles A pairf anglexuhose Sum is 90 Apa ot anges wbosesum is 180 x A+ C8 = 9o Ea A+<8 = 180
- 4. Date Page No. Adjacent Angles Tuoo angles ae adjacert i Theu havea Common Vertex acommon am QIiL) Non-common ayms Qxe o n opposite Sides ot Common am Iinear paîr ot angle8 Apairof adjacert angles whaseSum is 180 A O LAoB k 2co8 are ming inear pair Vextically Dpposite anglesg T twoLines_intersectteach othe at d point then the oposite angles ame Vortically oppste angles HereIELZ W Tntersectinq Linesg The lies which cross each other oam a parliculaa poirnt is called intersecliq Lines I Non-IexsectingPearalel_lines lhe lines whichneu cross each other at an Poirt are called nonintersectinq These Linesae Calkd Parallellines DELTA Notebook
- 5. Date Page No. lansversal line Ifa Linepasses though tuo lines and intersects henm at a paicular poiks -then his ine iscalled txansuersal line 1 34 a) Verically oppasiteangles L1=43 L5=21 L26=28 6) Coespondinq angles Ll=45 L=L6 3= Lz=28 (c) AHernate InteríorApgle 8 3-L5 L3+46= 180 Agles onthe SameSidesofa ansuersal ae upplenentay ZY+CS= l80 DELTA Notebcok
- 6. Date Page No. IGnespaallelto the SamelLine 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 Sump0perty o a tiangle 1. he Sum ot dheanglesot a miangle is 180 ZA t<Btc =l80 A 9. Exterior Andle is equal to Sumothe tudo interior of OpostO aglesS L8cD=LBACtLABC A D DELTA Notebook
- 7. LINES&ANGLES Part-A 1. An angle which is greaterthan 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)NonCollinearPoints 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 ofthese angles is- a) 50,60°,70 c)58°,60°,62 b) 59,60,61 d) All are correct * 2 6. In the figure, twice ofx is 30 less than y, then the values of x &yare respectively, given OB& OAare oppositerays 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 isfourtimesmore 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 ofthereequal angles are- a) 40 80 12. The valueof x in the figure is 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 ofadjacentangles have. i) Common vertex (i) Common Arm. (ii) Non Common arms are an opposite sides ofcommon arms (iv) Non Common arms are on the same side ofcommon arms. a) (i)& (i) are sufficient b)(.i)&(i)aresufficient c)).(i)&(v)aresufficient d All are sufficient 14. Anglesx&yforms a linearpairand x+2y= 30°, the value ofy is a) 70 ) 110 c) 210 15. The degree measure ofx&yrespectively 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& EFare three Straight lines intersecting at O. The measure of LAOFis- a) 98 c)54 152 82 b) d) 17. If LABC+4DEF=180, name thepairofangles LABC&DEF a) AdjacentAngles c)SupplementaryAngle d) vO.A 18. Inthefigure,AB|| CD, What is x*y a) 40 c)100 b) ComplementaryAngles D 60 80 b) d) A40 601
- 10. 19. From the Figure, choose thecorectoption. (21828are allemateangles (i) 41&L7 arealternateangles (i) 23& 45 arealtemateangles (v) 24&8 arecorrespondingangles (v) 2& 26 are notcorresponding angles. (vi) 3& L8 are interior angles on the same side ofthe 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 angleson the same side ofthe transversal are- a) equal b) adjacent c)Supplementary d) Complementary 21. In the figure, measure ofxis- a) 65 c)100 b) 55 d) 80 22. Inthefigure,I|| m&|| nthen xis 45 60 a) 90° b) c) 30 d) 23. Inthefigure, 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 LFGEis- a) 45 c)60 b) 90 d) 100 25. Inthefigure, /|| msuch 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 ofthe transversal is 2:3, the measure ofdiference ofboth 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 thefigure/|| 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 ofangleswhat type oftriangle isthis- a) Acuteangled b) Obtuse angled c) Rightangled d) Scalene
- 12. 30. In thefigure whatiste m ZA= a) 80 60 140 b) c)40° d) 100 120 31. In the figure,ifAB=ACthe m LA is 55 70 a) b) 75 C) d) 110 32. In thefigure, measure ofx 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 ofthe anglesofa triangles is 120°, then the angle between the interior bisectors ofthe 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 ofthe othertwo angles is a) 31 b) 59 c)121 d) 118° 36. Ifa&bforms a pair of adjacentangles then which figures proves it. b) d)