Lesson 2.1 Inductive Reasoning

Transcription

1 Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, , 200, 100, 50, 25,, , 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, 14, 30, 55,, For Eerises 8 10, use inutive resoning to rw the net two shpes in eh piture pttern y y y ( 1, 3) (3, 1) ( 3, 1) For Eerises 11 13, use inutive resoning to test eh onjeture. Deie if the onjeture seems true or flse. If it seems flse, give ounteremple. 11. The squre of numer is lrger thn the numer. 12. Every multiple of 11 is plinrome, tht is, numer tht res the sme forwr n kwr. 13. The ifferene of two onseutive squre numers is n o numer. 10 CHAPTER 2 Disovering Geometry Prtie Your Skills

2 Lesson 2.2 Fining the nth Term Nme Perio Dte For Eerises 1 4, tell whether the rule is liner funtion f(n) h(n) g(n) j(n) For Eerises 5 n 6, omplete eh tle f(n) 7n 12 g(n) 8n 2 For Eerises 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) Use the figures to omplete the tle.... n Numer of tringles Disovering Geometry Prtie Your Skills CHAPTER 2 11

3 Lesson 2.3 Mthemtil Moeling Nme Perio Dte 1. Drw the net figure in this pttern.. How mny smll squres will there e in the 10th figure?. How mny in the 25th figure?. Wht is the generl funtion rule for this pttern? 2. If there re 12 people sitting t 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? 12 CHAPTER 2 Disovering Geometry Prtie Your Skills

4 Lesson 2.4 Deutive Resoning Nme Perio Dte 1. ABC is equilterl. Is ABD equilterl? Eplin your nswer. Wht type of resoning, inutive or eutive, o you use when solving this prolem? B C A D 2. A n D re omplementry. A n E re supplementry. Wht n you onlue out D n E? Eplin your nswer. Wht type of resoning, inutive or eutive, o you use when solving this prolem? 3. Whih figures in the lst group re whtnots? Wht type of resoning, inutive or eutive, o you 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 type of resoning, inutive or eutive, o you use when solving these prolems?. 4 3(2 ) ( 3 1) A sequene egins 4, 1, 6, Give the net 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? Disovering Geometry Prtie Your Skills CHAPTER 2 13

5 Lesson 2.5 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 lwys (A), sometimes (S), or never (N) true. 7. The 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 they re omplementry. 10. If sttement is true, then its onverse is true. For Eerises 11 15, fill in eh lnk to mke true sttement. 11. If one ngle of liner pir is otuse, then the other is. 12. If A B n the supplement of B hs mesure 22, then m A. 13. If P is right ngle n P n Q form liner pir, then m Q is. 14. If S n T re omplementry n T n U re supplementry, then U is (n) ngle. 15. Swithing the if n then prts of sttement hnges the sttement to its. 14 CHAPTER 2 Disovering Geometry Prtie Your Skills

6 Lesson 2.6 Speil Angles on Prllel Lines Nme Perio Dte For Eerises 1 3, use your onjetures to fin eh ngle mesure For Eerises 4 6, use your onjetures to etermine whether 1 2, n eplin why. If not enough informtion is given, write nnot e etermine Fin eh ngle mesure f e Fin. 9. Fin n y y Disovering Geometry Prtie Your Skills CHAPTER 2 15