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Transcript
Section9-1 lntroductionto Geometry:Points, Lines,and Planes Notes Basic Geometric Fiqures Vocabularv Copythe tableon page436 IJ 7', Example1: Nameeachfigurein the diagram. a . t h r e e p o i ntsHf , W,K b. twosegments !q . nT *--+ , c. tworays -rK 1-+{ ,/ ,/ rrTr- r Twolinesintersect onepointin common. if theyhaveexactly Two linesthat lie in the same planeand do not intersectare parallel. "isparallel to." You usethe symbotll to indicate o Skew linesare linesthat do not lie in the same plane.They are Skewsegmentsmustbe partsof not parallel,andtheydo not intersect. skew lines. Example2: Usethe diagramon top of page438. Nameeachof the following. ectnr thatinters a.foursegments re , W .W "W M"w-ft b. threesegmentsparallelto nP skewb tr c. foursegments Summary: t[ ,m .-{ b .G Section9-l lntroductionto Geometry:Points, Lines,and Planes Notes Example3: Drawthe figuresindicated. a. threeparallelsegments A9 C- *- P --a eF of part(a) the parallelsegments b. a raythatintersects -+ - /c c. a segment ,q,A f Summary: F e. aline LM d. a ray QR a at # Section 9-2 Angle Relationships and ParallelLines Notes Adjacentanglessharea vertexand a sidebut no pointsin theirinteriors. B1 x. A / zAXB and zBXC are adiacent angles c x< linesandare oppositeeach Verticalanglesareformedby two intersecting other.Verticalangleshavethe samemeasure. T\ 2 / 1Xg 4 tL andL3 are verticalsngles -t----- z2 and L4 are verttcal angles -/ angleshavethe samemeasure. Congruent Lt = z3 are congruent angles Youcanwritethe measureof zl asmz1 Since 21, = 23, mz'l- : mL3 An acuteanglemeasureslessthan90 -L , 90 A rightanglemeasures t morethan90 butlessthan180. Anobtuseanglemeasures T\ Summary: Section9-2 AngleRelationships Notes and ParallelLines lf the sum of the measuresof two anglesis 90, the anglesare complementary" Pt zPQRand zRQSare complementary l/zo o -{' , S lf the sum of the measuresof two anglesis 180,the anglesare supplementary, c/ zABC and zCBD are supplementary 120/ A B D twootherlinesin differentpointsis a transversal. A linethatintersects andtwo lineshavespecial Somepairsof anglesformedby transversals a names. 1-\ ,/ Z<________ 2 Correspondinq anqles lie on the same side of the transversaland in positions. corresponding Alternateinterioranqlesare in the interiorof a pairof linesandon oppositesidesof the transversal. t< / -:4 "--z# > alternateinteriorangles. anglesandtwo pairsof congruent corresponding 4-/ ol4trfit tfilfrnvl L4 anl/.lt A i l d/ 5 Summary: (Lnalt Corw,rrnndno \ L l h ^ trl { r L{ / 4'r,sA 1 7 5*il Llr I z ^ri,L1 Section9-3 Ctassifying Potygons Notes A potygonis a ctosedfigure with at leastthree sides. The sidesmeet only at their endpoints. A triangleis a potygonwith three sides. Youcan classifytrianglesby angte and sidetength. Tick marksare usedto indicatecongruentsidesof measures a figure. ClassifvinqTrianeles lsoscetes triangte Equitate'rat triangte triangle Scalene i- ul-' \ Obtusetriangle Righttriangte Acutetriangte eachtriangteby its sidesandangtes. Example1: Ctassify O. a. l\- "/ I\./Y \| / frn-rvt i rade d r ..\\ \ '\ lsosrt,l,er WUNa Aufu, lytznnq! obtwEt I.rwnqV U \) Classifvine Quadrilaterals Rectangle Square four 90 degree angtes four 90 degree angtesandfour congrtrentsides Trapezoid exactlyone pair of parattelsides Rhombus four congruent sides Parallelograrn both pairsof opposite - - :l - --- - - - tl - l par-alrel 5toe5 are that havefour right angles Example2: Namethe typesof quadritaterals A regularpotygonhasall sidescongruentandalt anglescongruent. Example3: a. Write a formulato fi4d the perimeterof a regutarhexagon. b. Usethe formutato find the perimeterif onesideis 16cm. t! l(l 4le-an Section 9-6 Circles Notes A circteis the set of pointsin a planethat are the samedistancefrom a given point, cattedthe centerof the circte. The ratio of everycircte'scircumferenceC to its diameterd is the same. lt has "pie." Both3.14and lare good a specialsymbol,a, whichis pronounced for this ratio. approximations invotvefractions,anduse3.14whenthey do Use22forzr whencalculations not. re-ns-e-sf eire-umfr a.qlrcle The circumferenceof a circteis z timesthe diameter. o r C= 2 n r C= nd of eachcircte. Example1: Findthe circumference b.r=200mi a.d=30mm 5l4 -..---.-ai I|4Q,r0 wrn r x ho tr IJOD -------$- -- 4ro h,H A(iiaa) x 4ln LS lo.b0 wLt qrp0 4.?.n Mwl qt 4 c. d = zlir. l= = l4 A x5 5 h,l4 ry t4'' Y ^A,\1s s TTt 8,8 ' Summary: w1L +01 +g iltn-l -4{ x- l25b wr" '{ d.r=6cm 2llg)= l'e 6,1+ xla lr 7& Ttrt0 qllo 9, hln bl,lutz.r':t A centralangteis an angtewhosevertexis the centerof a circle. A circteis360'. Example2: Makea circtegraphfor the data provided. Section9-7 Constructions Ex"r"p[" fi Drawisegment. Constructa segmentbisectorto the segmentYoudrew. E "rpte to the tine segment a perpendicutar 2: Diiw i tine. Construct an angtebisectorto the E arpte 3 Drawanobtuseangte.Construct angteyou drew.