Lesson 2.1 Inductive Reasoning
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1 Lesson 2.1 Inutive Resoning Nme Perio Dte For Exerises 1 8, use inutive resoning to fin the next two terms in eh sequene. 1. 4, 8, 12, 16,, , 200, 100, 50, 25,, 3. 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2, 1, 1, 0,, , 180, 120, 90,, 6. 1, 3, 9, 27, 81,, 7. 1, 5, 17, 53, 161,, 8. 1, 5, 14, 30, 55,, For Exerises 9 12, use inutive resoning to rw the next two shpes in eh piture pttern y y y ( 1, 3) (3, 1) x x x ( 3, 1) For Exerises 13 15, use inutive resoning to test eh onjeture. Deie if the onjeture seems true or flse. If it seems flse, give ounterexmple. 13. Every o whole numer n e written s the ifferene of two squres. 14. Every whole numer greter thn 1 n e written s the sum of two prime numers. 15. The squre of numer is lrger thn the numer. Disovering Geometry Prtie Your Skills CHAPTER Key Curriulum Press
2 Lesson 2.2 Deutive Resoning Nme Perio Dte 1. ABC is equilterl. Is ABD equilterl? Wht type of resoning, inutive or eutive, o you use when solving this prolem? B 2. If 6 # 8 7, 10 # 3 6, 2 n 3 # 2 2.5, then 4 # 8 5 # 0 2 # 2 Wht type of resoning, inutive or eutive, o you use when solving this prolem? A C D 3. A n D re omplementry. A n E re supplementry. Wht n you onlue out D n E? Wht type of resoning, inutive or eutive, o you use when solving this prolem? 4... g.. e. Whtnots Not whtnots. f. Wht type of resoning, inutive or eutive, o you use when solving this prolem? 5. Solve eh eqution for x. Give reson for eh step in the proess.. 4x 3(2 x) 8 2x. 9 2( 3x ) 5 x 2 Wht type of resoning, inutive or eutive, o you use when solving these prolems? 6. A sequene is generte y the funtion f(n) 5 n 2. Give the first five terms in the sequene. Wht type of resoning, inutive or eutive, o you use when solving this prolem? 7. A sequene egins 4, 1, 6, Give the next two terms in the sequene. Wht type of resoning, inutive or eutive, o you use when solving this prolem?. Fin rule tht genertes the sequene. Then give the 50th term in the sequene. Wht type of resoning, inutive or eutive, o you use when solving this prolem? 8. Choose ny 3-igit numer. Multiply it y 7. Multiply the result y 11. Then multiply the result y 13. Do you notie nything? Try few other 3-igit numers n mke onjeture. Use eutive resoning to explin why your onjeture is true. Whih re whtnots? 10 CHAPTER 2 Disovering Geometry Prtie Your Skills 2003 Key Curriulum Press
3 Lesson 2.3 Fining the nth Term Nme Perio Dte For Exerises 1 4, tell whether or not the rule is liner funtion f(n) h(n) g(n) j(n) For Exerises 5 n 6, omplete eh tle f(n) 7n 2 6 g(n) 8n 2 For Exerises 7 9, fin the funtion rule for eh sequene. Then fin the 50th term in the sequene n f(n) n g(n) n h(n) Fin the rule for the numer of tiles in the nth figure. Then fin the numer of tiles in the 200th figure.... n Numer of tiles Sketh the next figure in the sequene. Then omplete the tle. Disovering Geometry Prtie Your Skills CHAPTER Key Curriulum Press n n Numer of segments 2 6 n lines Numer of regions of 4 the plne
4 Lesson 2.4 Mthemtil Moeling Nme Perio Dte 1. If you toss oin, you will get he or til. Copy n omplete the geometri moel to show ll possile results of four onseutive tosses. H H T How mny sequenes of results re possile? How mny sequenes hve extly one til? Assuming he or til is eqully likely, wht is the proility of getting extly one he in four tosses? 2. If there re 12 people sitting roun tle, how mny ifferent pirs of people n hve onverstions uring inner, ssuming they n ll tlk to eh other? Wht geometri figure n you use to moel this sitution? 3. Tournment gmes n results re often isplye using geometri moel. Two exmples re shown elow. Sketh geometri moel for tournment involving 4 tems n tournment involving 6 tems. Eh tem must hve the sme hne to win. Try to hve s few gmes s possile in eh tournment. Show the totl numer of gmes in eh tournment. Nme the tems,,... n numer the gmes 1, 2, tems, 3 gmes (roun roin) 4 tems, 3 gmes (single elimintion) 12 CHAPTER 2 Disovering Geometry Prtie Your Skills 2003 Key Curriulum Press
5 Lesson 2.5 Angle Reltionships Nme Perio Dte For Exerises 1 8, fin eh lettere ngle mesure without using protrtor e e 138 For Exerises 9 14, tell whether eh sttement is lwys (A), sometimes (S), or never (N) true. 9. The sum of the mesures of two ute ngles equls the mesure of n otuse ngle. 10. If XAY n PAQ re vertil ngles, then either X, A, n P or X, A, n Q re olliner. 11. The sum of the mesures of two otuse ngles equls the mesure of n otuse ngle. 12. The ifferene etween the mesures of the supplement n the omplement of n ngle is If two ngles form liner pir, then they re omplementry. 14. If sttement is true, then its onverse is true. For Exerises 15 19, fill in eh lnk to mke true sttement. 15. If one ngle of liner pir is otuse, then the other is. 16. If A B n the supplement of B hs mesure 22, then m A. 17. If P is right ngle n P n Q form liner pir, then m Q is. 18. If S n T re omplementry n T n U re supplementry, then U is (n) ngle. 19. Swithing the if n then prts of sttement hnges the sttement to its. 25 Disovering Geometry Prtie Your Skills CHAPTER Key Curriulum Press
6 Lesson 2.6 Speil Angles on Prllel Lines Nme Perio Dte For Exerises 1 11, use the figure t right. For Exerises 1 5, fin n exmple of eh term. 1. Corresponing ngles 2. Alternte interior ngles 3. Alternte exterior ngles 4. Vertil ngles 5. Liner pir of ngles For Exerises 6 11, tell whether eh sttement is lwys (A), sometimes (S), or never (N) true n 6 re supplementry n 8 re supplementry. 10. m 1 m m 5 m 4 For Exerises 12 14, use your onjetures to fin eh ngle mesure For Exerises 15 17, use your onjetures to etermine whether or not 2, n explin why. If not enough informtion is given, write nnot e etermine Fin eh ngle mesure f e CHAPTER 2 Disovering Geometry Prtie Your Skills 2003 Key Curriulum Press
Lesson 2.1 Inductive Reasoning
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,
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