Lesson 2.1 Inductive Reasoning

Transcription

1 Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10, 90,, 6. 1,, 9, 7, 81,, 7. 1,, 14, 0,,, For Eerises 8 10, use inutive resoning to rw the net two shpes in eh piture pttern ( 1, ) (, 1) (, 1) For Eerises 11 1, use inutive resoning to test eh onjeture. Deie if the onjeture seems true or flse. If it seems flse, give ounteremple. 11. he squre of numer is lrger thn the numer. 1. Ever multiple of 11 is plinrome, tht is, numer tht res the sme forwr n kwr. 1. he ifferene of two onseutive squre numers is n o numer. 10 CAPER Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

2 Lesson. Fining the nth erm Nme Perio Dte For Eerises 1 4, tell whether the rule is liner funtion. 1.. f(n) h(n) g(n) j(n) For Eerises n 6, omplete eh tle.. 6. f(n) 7n 1 g(n) 8n For Eerises 7 9, fin the funtion rule for eh sequene. hen fin the 0th term in the sequene n... 0 f(n) n... 0 g(n) n... 0 h(n) Use the figures to omplete the tle.... n... 0 Numer of tringles Use the figures ove to omplete the tle. Assume tht the re of the first figure is 1 squre unit.... n... 0 Are of figure Disovering Geometr Prtie Your Skills CAPER Kenll unt Pulishing

3 Lesson. Mthemtil Moeling Nme Perio Dte 1. Drw the net figure in this pttern.. ow mn smll squres will there e in the 10th figure?. ow mn in the th figure?. Wht is the generl funtion rule for this pttern?. If ou toss oin, ou will get he or til. Cop n omplete the geometri moel to show ll possile results of three onseutive tosses.. ow mn sequenes of results re possile?. ow mn sequenes hve etl one til?. Assuming he or til is equll likel, wht is the proilit of getting etl one til in three tosses?. If there re 1 people sitting t roun tle, how mn ifferent pirs of people n hve onverstions uring inner, ssuming the n ll tlk to eh other? Wht geometri figure n ou use to moel this sitution? 4. ournment gmes n results re often isple using geometri moel. wo emples re shown elow. Sketh geometri moel for tournment involving tems n tournment involving 6 tems. Eh tem must hve the sme hne to win. r to hve s few gmes s possile in eh tournment. Show the totl numer of gmes in eh tournment. Nme the tems,,... n numer thegmes 1,, tems, gmes (roun roin) 4 tems, gmes (single elimintion) 1 CAPER Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

4 Lesson.4 Deutive Resoning Nme Perio Dte 1. ABC is equilterl. Is ABD equilterl? Eplin our nswer. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem? B C A D. A n D re omplementr. A n E re supplementr. Wht n ou onlue out D n E? Eplin our nswer. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem?. Whih figures in the lst group re whtnots? Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem?.... e. f. Whtnots Not whtnots Whih re whtnots? 4. Solve eh eqution for. Give reson for eh step in the proess. Wht tpe of resoning, inutive or eutive, o ou use when solving these prolems?. 4 ( ) ( 1). A sequene egins 4, 1, 6, Give the net two terms in the sequene. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem?. Fin rule tht genertes the sequene. hen give the 0th term in the sequene. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem? Disovering Geometr Prtie Your Skills CAPER Kenll unt Pulishing

5 Lesson. Angle Reltionships Nme Perio Dte For Eerises 1 6, fin eh lettere ngle mesure without using protrtor e e For Eerises 7 10, tell whether eh sttement is lws (A), sometimes (S), or never (N) true. 7. he sum of the mesures of two ute ngles equls the mesure of n otuse ngle. 8. If XAY n PAQ re vertil ngles, then either X, A, n P or X, A, n Q re olliner. 9. If two ngles form liner pir, then the re omplementr. 10. If sttement is true, then its onverse is true. For Eerises 11 1, fill in eh lnk to mke true sttement. 11. If one ngle of liner pir is otuse, then the other is. 1. If A B n the supplement of B hs mesure, then m A. 1. If P is right ngle n P n Q form liner pir, then m Q is. 14. If S n re omplementr n n U re supplementr, then U is (n) ngle. 1. Swithing the if n then prts of sttement hnges the sttement to its. 14 CAPER Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

6 Lesson.6 Speil Angles on Prllel Lines Nme Perio Dte For Eerises 1, use our onjetures to fin eh ngle mesure For Eerises 4 6, use our onjetures to etermine whether 1, n eplin wh. If not enough informtion is given, write nnot e etermine Fin eh ngle mesure f e Fin. 9. Fin n Disovering Geometr Prtie Your Skills CAPER Kenll unt Pulishing

7 11. Kite 4. Possile nswers: B... Q P A LESSON 1.8 Spe Geometr 1.. LESSON.1 Inutive Resoning 1. 0, , , 4. 1, 1. 7, , , 140. Retngulr prism 4. Pentgonl prism ues 8., 1 (, 1) LESSON 1.9 A Piture Is Worth housn Wors m Possile lotions A 1 m. Dor, Ellen, Chrles, Ani, Fre, Brue Gs Power (1, ) 11. Flse; Flse; , rue LESSON. Fining the nth erm 1. Liner. Liner. Not liner 4. Liner. D E C A F B f (n) ringles Aute tringles 6. g(n) Isoseles tringles Slene tringles 7. f(n) 4n ; f(0) 0 8. f(n) n 11; f(0) 9 9. f(n) 1 n 6; f(0) 1 Disovering Geometr Prtie Your Skills ANSWERS Kenll unt Pulishing

8 n... 0 Numer n of tringles n... 0 Are of figure n Answers will vr. Possile nswers: e 7 9 tems, 10 gmes 1 4 e 6 f 7 6 tems, 7 gmes LESSON. Mthemtil Moeling f e f(n) n(n ), or f(n) n 4n. 8 sequenes. sequenes hve 1 til ifferent pirs. Use oegon showing sies n igonls. 6 tems, 6 gmes LESSON.4 Deutive Resoning 1. No. Eplntions will vr. Smple eplntion: Beuse ABC is equilterl, AB BC. Beuse C lies etween B n D, BD BC, so BD is not equl to AB. hus ABD is not equilterl, eutive resoning.. Answers will vr. m E m D (m E m D 90 ); eutive., e, f; inutive 4. Deutive. 4 ( ) 8 he originl eqution Distriutive propert. 6 8 Comining like terms. 6 8 Aition propert of equlit. Sutrtion propert of equlit. Division propert of equlit. 94 ANSWERS Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

9 . 19 ( 1) he originl eqution. 19 ( 1) ( ) Multiplition propert of equlit Distriutive propert Comining like terms Aition propert of equlit Sutrtion propert of equlit. 1 Division propert of equlit... 16, 1; inutive. f(n) n 9; 41; eutive LESSON.1 Dupliting Segments n Angles 1. P. XY PQ RS X A Q. Possile nswer: Y R B B S LESSON. Angle Reltionships 1. 68, 11, , 40,, , 90, 4, 48, e 1. 0, 70, 0, 70, e ,, 7. Sometimes 8. Alws 9. Never 10. Sometimes 11. ute otuse 1. onverse LESSON.6 Speil Angles on Prllel Lines. 6. B C D C D D C D LESSON. Construting Perpeniulr Bisetors 1.. Squre 1. 4, 4, 4. 11, 6, 11, 6. 7, nnot e etermine 7. 10, 78, 8, 1, e 6, f , Disovering Geometr Prtie Your Skills ANSWERS Kenll unt Pulishing