Prllel Lines nd Trnsversls How cn you descrie ngles formed y rllel lines nd rnsversls? Trnsverse When n ojec is rnsverse, i is lying or exending cross somehing ACTIVITY: A Proery of Prllel Lines Work wih rner 0 9 0 9 0 9 0 In his lesson, you will idenify he ngles formed when rllel lines re cu y rnsversl find he mesures of ngles formed when rllel lines re cu y rnsversl Geomery Drw hird line h inersecs he wo rllel lines This line is clled rnsversl in 9 Discuss wh i mens for wo lines o e rllel Decide on sregy for drwing wo rllel lines Then drw he wo rllel lines cm rllel lines rnsversl How mny ngles re formed y he rllel lines nd he rnsversl? Lel he ngles Which of hese ngles hve eul mesures? Exlin your resoning 0 Cher ms_lue e_00indd 0 Angles nd Tringles // :: PM
ACTIVITY: Creing Prllel Lines Mh Prcice Use Cler Definiions Wh do he words rllel nd rnsversl men? How does his hel you nswer he uesion in r ()? Work wih rner If you were uilding he house in he hoogrh, how could you mke sure h he suds re rllel o ech oher? Idenify ses of rllel lines nd rnsversls in he hoogrh Suds ACTIVITY: Using Technology Work wih rner Use geomery sofwre o drw wo rllel lines inerseced y rnsversl Find ll he ngle mesures Adjus he figure y moving he rllel lines or he rnsversl o differen osiion Descrie how he ngle mesures nd relionshis chnge G A F D C E B H IN YOUR OWN WORDS How cn you descrie ngles formed y rllel lines nd rnsversls? Give n exmle Use geomery sofwre o drw rnsversl h is erendiculr o wo rllel lines Wh do you noice ou he ngles formed y he rllel lines nd he rnsversl? Use wh you lerned ou rllel lines nd rnsversls o comlee Exercises on ge 0 Secion Prllel Lines nd Trnsversls 0
Lesson Lesson Tuorils Key Voculry rnsversl, 0 inerior ngles, 0 exerior ngles, 0 Lines in he sme lne h do no inersec re clled rllel lines Lines h inersec righ ngles re clled erendiculr lines Indices lines nd m re erendiculr m Indices lines nd re rllel A line h inersecs wo or more lines is clled rnsversl When rllel lines re cu y rnsversl, severl irs of congruen ngles re formed Sudy Ti Corresonding ngles lie on he sme side of he rnsversl in corresonding osiions Corresonding Angles When rnsversl inersecs rllel lines, corresonding ngles re congruen Corresonding ngles EXAMPLE Finding Angle Mesures Use he figure o find he mesures of () nd () nd he 0 ngle re corresonding ngles They re congruen So, he mesure of is 0 0 nd re sulemenry + = 0 Definiion of sulemenry ngles 0 + = 0 Susiue 0 for = 0 Surc 0 from ech side So, he mesure of is 0 Exercises 9 Use he figure o find he mesure of he ngle Exlin your resoning m 0 Cher Angles nd Tringles
EXAMPLE Using Corresonding Angles Use he figure o find he mesures of he numered ngles : nd he ngle re vericl ngles They re congruen So, he mesure of is nd : The ngle is sulemenry o oh nd + = 0 Definiion of sulemenry ngles = 0 Surc from ech side So, he mesures of nd re 0,,, nd : Using corresonding ngles, he mesures of nd re, nd he mesures of nd re 0 Exercises Use he figure o find he mesures of he numered ngles m 9 When wo rllel lines re cu y rnsversl, four inerior ngles re formed on he inside of he rllel lines nd four exerior ngles re formed on he ouside of he rllel lines,,, nd re inerior ngles,,, nd re exerior ngles EXAMPLE Clernce 0 Sle Using Corresonding Angles A sore owner uses ieces of e o in window dverisemen The leers re slned n 0 ngle Wh is he mesure of? A 0 B 00 C 0 D 0 Becuse ll he leers re slned n 0 ngle, he dshed lines re rllel The iece of e is he rnsversl Using corresonding ngles, he 0 ngle is congruen o he ngle h is sulemenry o, s shown 0 The mesure of is 0 0 = 00 The correc nswer is B Secion Prllel Lines nd Trnsversls 0
WHAT IF? In Exmle, he leers re slned ngle Wh is he mesure of? Exercises nd 9 Alerne Inerior Angles nd Alerne Exerior Angles When rnsversl inersecs rllel lines, lerne inerior ngles re congruen nd lerne exerior ngles re congruen Sudy Ti Alerne inerior ngles nd lerne exerior ngles lie on oosie sides of he rnsversl Alerne inerior ngles EXAMPLE Alerne exerior ngles Idenifying Alerne Inerior nd Alerne Exerior Angles The hoo shows orion of n iror Descrie he relionshi eween ech ir of ngles nd nd re lerne exerior ngles So, is congruen o nd nd re lerne inerior ngles So, is congruen o Exercises 0 nd 0 Cher ms_lue e_00indd 0 In Exmle, he mesure of is Find he mesure of he ngle Exlin your resoning Angles nd Tringles // ::0 PM
Exercises Hel wih Homework VOCABULARY Drw wo rllel lines nd rnsversl Lel ir of corresonding ngles WHICH ONE DOESN T BELONG? Which semen does no elong wih he oher hree? Exlin your resoning Refer o he figure for Exercises The mesure of The mesure of The mesure of The mesure of 9+(-)= +(-)= +(-9)= 9+(-)= In Exercises, use he figure Idenify he rllel lines Idenify he rnsversl How mny ngles re formed y he rnsversl? m n Which of he ngles re congruen? Use he figure o find he mesures of he numered ngles 9 0 9 9 0 ERROR ANALYSIS Descrie nd correc he error in descriing he relionshi eween he ngles PARKING The ined lines h sere rking sces re rllel The mesure of is 0 Wh is he mesure of? Exlin is congruen o OPEN-ENDED Descrie wo rel-life siuions h use rllel lines Secion Prllel Lines nd Trnsversls 0
PROJECT Trce line nd line on iece of er Lel Move he er so h ligns wih Descrie he rnsformions h you used o show h is congruen o REASONING Two horizonl lines re cu y rnsversl Wh is he les numer of ngle mesures you need o know in order o find he mesure of every ngle? Exlin your resoning Use he figure o find he mesures of he numered ngles Exlin your resoning í 99í Comlee he semen Exlin your resoning If he mesure of =, hen he mesure of = 9 If he mesure of =, hen he mesure of = 0 If he mesure of =, hen he mesure of = If he mesure of = 0, hen he mesure of = If he mesure of = 0, hen he mesure of = If he mesure of =, hen he mesure of = c RAINBOW A rinow forms when sunligh reflecs off rindros differen ngles For lue ligh, he mesure of is 0 Wh is he mesure of? REASONING When rnsversl is erendiculr o wo rllel lines, ll he ngles formed mesure 90 Exlin why LOGIC Descrie wo wys you cn show h is congruen o 0 Cher ms_lue e_00indd 0 Angles nd Tringles // :: PM
CRITICAL THINKING Find he vlue of x c d c 0 d x x 9 OPTICAL ILLUSION Refer o he figure Do he horizonl lines er o e rllel? Exlin Drw your own oicl illusion using rllel lines m m 0 The figure shows he ngles used o mke doule nk sho in n ir hockey gme Gol x Gol Find he vlue of x Cn you sill ge he red uck in he gol when x is incresed y lile? y lo? Exlin Evlue he exression (Skills Review Hndook) + () + ( ) 9 + MULTIPLE CHOICE The ringles re similr Wh lengh does x reresen? (Secion ) A f B f f x f C f D f f Secion Prllel Lines nd Trnsversls 09