CHAPTER 11. Think & Discuss (p. 659) Lesson A 1 2 bh in. 8 in.

Transcription

1 CHAPTER Thik & Discuss (p. 65). 6. The bse gles of equilterl trigle mesure 60 ech. 60 0, Skill Review (p. 660). A bh i.8 i. 8 i.. ma mb mc mb 7 80 mb mb Eterior gle to A is Eterior gle to B is Eterior gle to C is XY 3.. DE 8 3 Perimeter of DEF b. Perimeter of XYZ 8 3. Smple swer: ma si mc si 6. Developig Cocepts Activity (p. 66) Sum of Number Number of mesures of Polygo of sides trigles iterior gles Trigle Qudrilterl Petgo Hego go 80 The sum of the mesures of the iterior gles of y cove -go is 80. C 0 B A Lesso.. Guided Prctice (p. 665). Iterior gles re A, B, D, BCD, d AED. Eterior gles re AEF, BCG, d DCH.. There re eterior gles. No; the Polygo Eterior Agles Theorem specifies oly gle t ech verte. 3. The sum of the mesures of the iterior gles of petgo is Sum of mesures of iterior gles Mesure of eterior gle. Prctice d Applictios (p ) , Copyright McDougl Littell Ic. Geometry 3 Chpter Worked-out Solutio Key

2 Chpter cotiued eterior gle 3. eterior gle eterior gle eterior gle 3. eterior gle The iterior gles of the regulr hegos re 0. Two of the iterior gles of the red trigles form lier pir with the iterior gles of the regulr polygos. Therefore, ech iterior gle of the trigles is 60. The iterior gles of the yellow hegos re 0. Two of the iterior gles of the yellow petgos form lier pir with the red trigles, so, they re 0. A third gle of the yellow petgos is Regulr petgos hve iterior gles mesurig 08. The iterior gles of the red qudrilterls which form lier pirs with the iterior gles of the petgos mesure 7. The gle i the red qudrilterl formed by the joiig of two petgos is. The th gle of the red qudrilterl is For the yellow petgos, two of the gles form lier pirs with 7 gle, so they re 08. The fifth gle is Ech gle of the yellow decgo is Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

3 Chpter cotiued. m d m0 re 70 becuse they form lier pirs with d m5, respectively. m3 is 0 becuse it forms lier pir with 8. m7 is 80 becuse it forms lier pir with. m is 80 becuse the sum of the mesures of the iterior gles of petgo must equl m6 is 00 becuse forms lier pir with.. Ay -go c be divided ito trigles. The sum So, 0. mb mc md of the mesures of the iterior gles will be equl to 80. The -gos do ot eed to be regulr or similr becuse the sum of the gles of y trigle will lwys be 80. Wht mtters is tht is the sme Give petgo ABCDE, where 5 drw two digols 80 from oe verte to divide the petgo ito three trigles. The sum of the mesures of the gles of trigle is Therefore, the sum of the mesures of the gles of So, mp mv, d ms. the three trigles must be 380 or ( ABCDE is petgo. Drw digols from A to C d A to D, dividig ABCDE ito three trigles. The sum of the mesures of the iterior trigles is 380 or 80. The iterior gles of regulr polygo re cogruet to ech other. Therefore, you eed to divide the sum of the mesures of the iterior gles by the umber Yes. The polygo would Yes. The polygo of the iterior gles (which equls the umber of sides), be dodecgo. would be squre. to get the mesure of ech gle. So, ech gle hs the mesure I cove -go, eted ech side to mke eterior gle with the -go. The iterior gle d its djcet eterior gle t y verte form lier pir, whose sum is 80. Sice the -go hs sides, there will be lier pirs composed of iterior d eterior gle, so multiply by 80. The subtrct the sum of the mesures of the iterior gles, which is 80 to get the totl of the eterior gles. So, the sum of the mesures of the eterior gles of cove -go is The mesure of ech iterior gle of -go is Ech eterior gle of regulr -go is 80 mesure of iterior gle. Therefore, the mesure of eterior gle by substitutio is Smple swer: If regulr hego were costructed, ech eterior gle would mesure 60 d the sum of the eterior gles would be 360. Aswers will vry. 8. The eterior gles will vry iversely with the chge i the iterior gle. The sum of the mesures of the eterior gles will still be m m 0, No. Becuse must be iteger, regulr poygo c t hve gles of The fuctio is showig the reltioship betwee the umber of sides,, d the mesure of ech iterior gle for regulr -go. As gets lrger d lrger, f pproches f represets the mesure of the eterior gle of regulr polygo. As gets lrger d lrger, f decreses. 57. The eterior gles mesure 55 d , so B. Colum A 0. Colum B C. Both colums equl A. Colum A 7. Colum B D. If these were regulr polygos, the qutities could be determied. 6. Ech iterior gle hs S T R mesure of Z U 35 Ech eterior gle is Sice Y V the sum of the gles of is 80, R must be X W No. Becuse must be iteger, regulr poygo c t hve gles of 8. Copyright McDougl Littell Ic. Geometry 5 Chpter Worked-out Solutio Key

4 Chpter cotiued. Mied Review (p. 668) 63. A bh i. 65. bse 5 height 5 A bh 6. A bh m 66. bse 6 height 8 A bh A bh s 3 s 3 s Are hego 6 Are oe trigle 6 3 s 3 3 s 67. 3? 6 8 6? Not right ? 7 5? Not right squre uits m DH m ED 80 mfh mfe mdh m EH 65 mfh mfe m EHG m GD mde mgd mfh mfe mdh squre uits 7? 75 58? 565 Is right Guided Prctice (p. 67). J. JB or JC 3. Smple swers: BJA, AJE, BJC, EJD, or DJC. KJ 5. Divide 360 by the umber of sides Ech side would be 80 iches 8 or 0 iches. The pothem would be hlf the height of the sig or iches. The pothem cretes trigle, so the rdius of the octgo would be equl to the hypoteuse which is 3 iches.. Prctice d Applictios (pp ). A 3 s i. A P i. A 3 s A 3 s Lesso. Activity i Lesso (p. 670). Si equilterl trigles. To fid the re of oe trigle, oe must drw ltitude from oe side of the hego to the ceter formig two right trigles. If the side of the hego is s, the height of the trigle would be 3 s uits A 3 s uits uits 6 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

5 Chpter cotiued Oe side P s. 360 s s s P s uits A P uits 6 uits A P 6 3 uits A s 8 8 uits A s uits A s uits The pothem bisects the cetrl gle. If rdius is drw, trigle will be formed. 0. Use trigoometry rtios to fid the legth of the rdius r 5cos 36 d side. The side of the petgo would be equl to: 5 t t P s 530 t t uits The pothem bisects the cetrl gle. So, trigle is formed by the pothem d the rdius of the hego. cos cos uits s uits P s uits A P uits The pothem bisects the cetrl gle. So, si.5. si.5 Oe side of the octgo si.5. cos.5 P s cos.5 P 8 si.5 76 si uits A P A P 550 t 36 5 t uits si si uits cos.576 si.5 3. uits Copyright McDougl Littell Ic. Geometry 7 Chpter Worked-out Solutio Key

6 Chpter cotiued. The cetrl gle of dodecgo is 30. The cetrl gle is bisected by the pothem formig trigle. 5. A bh True. The pothem d rdius re the leg d hypoteuse of right respectively. The hypoteuse is lwys loger th the legs so the pothem will lwys be less th the rdius. cos 5 cos 5 s si 5 8 si 5 P s 8 si 5 6 si uits i The pothem bisects the cetrl gle formig trigle. t 75, t si 5 si 5 A P cos 56 si 5 7si 5cos 5 3 uits Flse. It depeds o the polygo. They re the sme for regulr hego. 30. A A t A t cetrl gle uits 6. uits The rdius bisects ech iterior gle, d with the pothem forms equilterl. The re of equilterl is A Sice 3 s. 60 regulr hego c be divided ito si equilterl s, the re of hego is si 60 si i. 0 iterior gle A 6 3 s. 35. A B t uits i. 60 A B P s 8 i. 7. True. Let be the cetrl gle d r the rdius. The side legth s would be r si r cos The. P d the pothem would be Both icrese s r icreses. icreses s r icreses. A P t t i. 38. A 6 3 s 0. Smple swer:. Smple swer: A i. C Q B A 3. Do the sme costructio but coect every other compss mrk. C Q D B 8 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

7 Chpter cotiued. Smple swer: 3. Smple swer: C C D D A B A E Q E Q. Smple swer: C A D E Q B B. 6 ft 7 i., 8 ft 6 i. A 76 6 i. umber tiles tiles of ech color 7 tiles for the floor totl 50. B. Colum A 5. Colum B A. Colum A 0.. Colum B A. Colum A 6.. Colum B A P Smple swer: cetrl gle. The pothem bisects the cetrl gle so with the rdius, it forms trigle. The pothem c be foud by usig trigoometry r i. cos i. s.8 i. P s i. 5. The rdius side 0.5 m. The pothem bisects side. So, the bse of the right trigle m. The trigle formed by the pothem d rdius is trigle with the 0.5 side beig opposite the 30 gle. The pothem m. 6. P s m A P 0.33 si i. A P 0.65 m Note: See problem 5 for epltio colors 8. The pothem will be 33 i. or 5. i. log bsed o trigle. P s i. A P i i.5. i.. i. 3. Are totl uits Aswers should be the sme. Differeces my rise due to roudig.. Mied Review (p. 675) t uits.5 Are trigle 5 si 55 cos 5 Are trpezoid b b h uits 5 5 si 55 cos P True. Correspodig sides of similr trigles re proportiol. 5. True. The perimeters of similr trigles re proportiol. 60. True. The correspodig gles of similr trigles re cogruet Copyright McDougl Littell Ic. Geometry Chpter Worked-out Solutio Key

8 Chpter cotiued 6. Flse. Correspodig sides of similr trigles re proportiol, ot ecessrily cogruet Eplorig the Cocept Activity (p. 676) For emple o p. 676-Smple Aswer: Note: The res for similr polygos should be times the re of the origil polygos. Drwig Coclusios. The rtio of the re of the similr polygos to the re of the origil polygos.. The rtio of the res of two similr polygos is the squre of the scle fctor. Lesso.3.3 Guided Prctice (p. 67). : b, : b. Flse. I order to be similr, the the legths of the correspodig sides must be proportiol d ll correspodig gles must be cogruet. 3. Flse. The scle fctor is :, so the rtio of the res is : d the re is qudrupled P red P blue Origil Similr Polygo Are Polygo Are Rectgle 5 sq uits Rectgle 0 sq uits Rectgle 8 sq uits Rectgle 3 sq uits Rectgle 3 6 sq uits Rectgle 3 sq uits.... Totl sq uits Totl sq uits P red 8 P blue 5 3 The rtios of the res is equl to the squre of the rtio of the perimeters so A red 6 5 A red 30 A blue 0 3 P red P blue 6. The rtio of the legths of the pieces of pper is :, so the rtio of the res of the piece of pper is :. The cost of the smller piece should be s much s the lrger sheet or $0...3 Prctice d Applictios (p ) 7. The rtio of the perimeters is :. The rtio of the res is :. 8. The rtio of the perimeter is 5:7. The rtio of the res is 5:.. The rtio of the perimeter is 5:6. The rtio of the res is 5: The rtio of the perimeter is 5:3. The rtio of the res is 5:.. sometimes. sometimes 3. lwys. : The scle fctor of the hypoteuses is 8:0 or :5. The rtio of the res is the squre of the scle fctor, or : iches 7. Smple swer: AB DC, so AEB DEC becuse verticl gles re. BAE ECD becuse lterte iterior gles re. CDE ~ ABE by the AA Similrity Postulte. Are of DC 3 8 DC ABE 3 sq 8 uits DC A blue Are of CDE 87 8 sq uits. 30 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

9 Chpter cotiued 8. DC AB d LK AB, so DC LK becuse lies to the sme lie re prllel. The k C d A J, d ll correspodig s re. Rtio of sides is 3:, so the rtio of the res is 3. The re of ABCD is times the re of JBKL sq i.. Perimeter of ABCDE 305. Perimeter of QRSTU 0. Rtio of perimeters 305: 0 or 35:. 0. Perimeter of smll squre 6. Rtio of perimeters 36:6 :. Rtio of res : 8:6.. The rtio of res is 0:5. The rtio of perimeters is 0:5 30:5.. Smple swer: Give two rectgles which re similr with the legths of correspodig sides i the rtio :b. If the legth of rectgle is L d the width of the rectgle is W the the legth of rectgle b L d the width would be The re of rectgle b W. LW d the re of rectgle is Therefore, b LW. (Are rectgle /Are rectgle ) b. 3. Are smll rug i. 7 i. 363 sq i. Are lrge rug 58 i. i. 55 sq i. Are smll 363 or : Are lrge 55 $7. Smll rug: $.06 sq i. 363 sq i. $ Lrge rug: $.05 sq i. 55 sq i. The lrge rug is good buy becuse it costs slightly less per squre ich th smll rug. 5. A bh 0 80 ft 7. Are ABC.3 80 ft ft Are wlkwy Are of ABC Are of DEF ft 6. AB.3 0 ft 5 ft 8... b. c. 5: d. e. Becuse AB d DE re correspodig sides of ~, the rtio of their legths is the scle fctor. You c.5 5 solve the proportio to fid z. 3z 0 z 30. Smple swer: 3. Are outer 66,70.0 Are ier 6,00 Rtio of perimeters y 5 3y 8 y 53y 6 y 5y 85 PVQ ~ RVT RVQ ~ PVU TQR ~ TUS 3 VQ 5 VT 3 VQ VQ VQ Are of ABC Are of DEF VQ 5 VT 67 ft 30 3y 7 y CONTINUED PV RV PV 5 0 PV Smple swer: Are PVQ Are RVT 5 Are RVQ 5 5 Are PVU 6. Are TQR 0 5 Are TUS. Copyright McDougl Littell Ic. Geometry 3 Chpter Worked-out Solutio Key

10 Chpter cotiued 3. CONTINUED.3 Mied Review (p. 68) m 60. Quiz (p. 68) VU VQ 3 5 VU 3 5 5VU 7 VU 7 5 UT y y 80 R 00, S 85, T 80, U 5 m 6 0 A 3 s i.. The cetrl gle of ogo is 0. The pothem bisects the cetrl gle. cm AB AB.58 cm A AP y 80 y 5 86 cos 0 AC t t 0 AC 3.8 m A 0 B cm C The scle fctor is 3:7; therefore the rtios of the re is..3 Mth & History (p. 68). Ech side of the iscribed hego will be equl to (dimeter). So, the perimeter of the iscribed hego is equl to 3 dimeter or 3 uits. If the pothem is uit, the the legth of oe side of the hego is 3 3 t 30 or The 3 3. perimeter of the circumscribed hego is so 3 < < 3.6. Lesso.. Guided Prctice (p. 686). Arc mesure is the umber of degrees of the gle whose edpoits re the eds of the rc. Arc legth the mesure of portio of the circumferece.. Arc legth AB m rc legth CD 360 r m 360 r. 3. F. D 5. C 6. B 7. A 8. E. Flse. Arc legth depeds o the rdius of the circle. So if the rdii re differet, the rc legth will be differet. 0. Flse. The circumferece is proportiol to the rdius. If the rdius doubles, the circumferece doubles.. Flse. Arc legth is determied by the mesure of the rc d the rdius of the circle. If you solve for the mesure of the rc, the it is depedet upo both the rc legth d the rdius of the circle.. P red P blue 8 6 A red 6 A blue 80 3,50 $63 3 Legth AB m AB 360 r cm or 7. cm P red P blue 5 0 A red 6 A blue cm 3 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

11 Chpter cotiued 3... Prctice d Applictios (pp ) 5. C r 7. C d. 0.. Legth CD m CD 360 Legth EF m EF cm m EF cm m EF 8 5. m C r 3 r 3 r i. 5. yd r 55 m EF Legth AB m AB cm Legth AB m AB cm or 8.0 cm i. r. r r r 6. r C r r 7.0 ft r 8. C r 5 30 i.. i Legth AB m AB ft Legth of XY m XY 360 Legth of AB m AB r r 36 uits r Legth of CD m CD r 7.7 uits r Legth of AB m AB 360 Legth of ST m ST r uits r Legth of LM m LM r r 0.6 uits r r Rdius m AB Legth of m AB uits 0 0. r r r 0 60 r 360 r uits r r Copyright McDougl Littell Ic. Geometry 33 Chpter Worked-out Solutio Key

12 Chpter cotiued P l r3. Tire A 5 i..6 i..6 i uits P uits P uits 5 35 Legth of rc m rc 360 5y Legth of rc m rc Legth of rc m rc 360 y r 3 y C r C y 3 6 y 5y 300 y y 3.75 y.75 r r r y 0.3 uits 37. r C r C 7 r C r C 0.. The sidewll width must be dded twice to the rim dimeter to get the tire dimeter Tire A: Tire B: Tire C:. i. Tire B 6 i..3 i..7 i. L strightwys curves L m 60 m 3..8 lps 63 mlp. Arc., rdius 000 mi Legth of rc m Arc 360 Legth of rc 6 rer sprocket Legth of rc 6 frot sprocket 360 Legth of chi umber of teeth 7.6 i. 0.5 i.tooth P 3 r.86 i. Tire A 7 i..33 i..33 i i. 500 ft 6000 i i. 7 rev. i i. 77 rev.86 i i. 7 rev 5.66 i miles 3.6 i..8 i. r 7.6 i. 5 teeth ft 3 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

13 Chpter cotiued 8. B.. B. 50. The four semicircles form complete circles so tht the legth would be r r segmets 8r 6 segmets 6r segemets r No. The umber of segmets does t mtter.. Mied Review (p. 68) y 8 Techology Activity. (p. 60). The perimeter icreses s icreses, gettig closer d closer to.. Legth of XZ m XZ r y A r 5.7 ft A r cm y m b b 3 6 b 8 b y y 36 y 360 r 360 r 6; p 6 si 80 6 si uits y 360 r Copyright McDougl Littell Ic. r A r i. A 55. m go: Lesso.5.5 Guided Prctice (p. 65). A sector of circle is bouded by two rdii of the circle d their itercepted rc.. The rdius is oe hlf of the dimeter or. The re is 3. A r 5. A r Prctice d Applictios (p ) go: P 6. uits 8-go: P 6.5 uits -go: P 6.7 uits r. 5.7 i ft A m AB 360 r m A Are of circle Are of sector i. A i. A ft A 50.7 m A ft P 6. uits A cm. A r cm A m AB 360 r ft A cm A i. A i. A m Geometry 35 Chpter Worked-out Solutio Key

14 Chpter cotiued A A 0 Mesure of rc, 3.63 i. 3.6 ft Are of 50 r correspodig sector y 5. r 3. m r A m AB 360 r r r 6.0 r 3 i. r A m rc 360 d d d 763. d m d A Are lrge circle Are smll circle m A Are lrge semicircle Are smll semicircle cm A Are of circle Are of petgo 30. y 3. Yes it ppers to be lier. The equtio would be 3. With 5-ich rdius, the re of the sectors would be Mesure of rc, Are of correspodig sector y 30 lrger. Howerver the reltioship would still be lier. y 5 7. A mi light house y miles 6. si 55 cos 5. ft Are A Are of sector Are of trigle ft 3.6 cm A Are squre Are circles i. A Are semicircle Are trigle cm A Are of sector Are of trigle m A Are of sector Are of trigle cm 36 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

15 Chpter cotiued To fid the re of the sector, you would eed to either kow the rc legth or the mesure of the cetrl gle, d the rdius. To fid the re of the kite you would hve to kow the legths of the digols or be give sufficiet iformtio to determie the legth of the digols, such s side with gle or two sides. 0. A Totl re Are of lrger sector 5. A Are of trigle 3 Are of sector ft Are ABCD Are of sector formed by APB ft Are of sector formed by DPC. If you double the rdius, the re is qudrupled becuse it is proportiol to the squre of the rdius. If you double the rdius, the circumferece doubles lso becuse the circumferece is directly proportiol to the rdius.. As gets lrger, the re of the polygo pproches, the re of the circle. Smple spredsheet: -go Dt A B # of sides Are.5*cos(80/)***si(80/) Mied Review (p. 68) uits y y y y 5. C cm DB 8 si 68. cm 5. DC 8 cm 53. mdbc 68 BC 8 t cm 78.5 i. Legth of AB r r.0 r.03 ft 3. C A D A Copyright McDougl Littell Ic. Geometry 37 Chpter Worked-out Solutio Key

16 Chpter cotiued.6 Guided Prctice. A geometric probbility ivolves geometric mesures such s legth d re isted of coutig evets or outcomes.. Are method should be used becuse you re lookig for somethig withi regio of spce. 3. Legth method should be used becuse time c be relted to lie.. P AB AF 8 % 5. P BD AF 8 50% 6. P BF 6 AF 8 8 8% 7. AF AB BF. Therefore y poit ot o AB must be o BF. So the sum of the probbilities is 8. P.6 Prctice d Applictios (p ) P JL GN % 7 P JN GN 8 57% 7 P GJ GN 6 3 3% 7 P PS 8 PU % P SU 0 PU 8 5 % P PU 00% PU 7. P % P GH GN % 7 P PQ PU 8 5% Are shded Are totl Are squre Are circle Are squre 3..5% Sice the probbility is betwee l d %, to drts would probbly hit the bulls-eye.. J M K Let L be the midpoit of JM d N be the midpoit of MK. The LN is the prt of the lie closer to M th to J or K, so P 50%. 5. P P P % % Are of squre Are of circle 6.8 Are shded uits P Are circle Are squre Are circle % Are trigle P Are rectgle % Are of semicircle Are of trigle 5 00 Are of circle Are of hego Are shded % Are of circle P % P % 38 Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

17 Chpter cotiued 5 7. P 8. P 3 0% 60.7%. P 50 0.% 5 50,000. A ,000,000 yd If the re is doubled, the probbility is doubled Are of circle ,66. yd P 87, % 0,000,000 Are Totl Are of 0 poit regio. 8. P 8. % Are yellow regio P 7.38 % Are white regio Totl re Are regios 3 0 P % Are regios Are regios Are regios Are regio P.05 % Smple swer: It would ot hold becuse epert rcher is more likely to hit the bull s eye, so it is o loger true tht every poit o the trget hs equl probbility of beig hit. 36. y Totl Are y y P 50% P 00.8% 50,000 The probbility is four times s much. P.63 % b. 5 cois c. 50 prizes 5 d. Yes, the probbility will chge becuse ow peies just hve to touch the circle, ot be iside it so the trget re is lrger d the probbility icreses..6 Mied Review (p.705) 5. AB is ot tget to C becuse ABC is ot right s follows AB is tget to C. ABC is right s follows AB is tget to C. ABC is right s follows sect. tget Are of jr cm Are of dish.5.63 cm y y y 3 P.5 6 8% 3 y y 0 y P % , tget 5. sect y y 6 y Copyright McDougl Littell Ic. Geometry 3 Chpter Worked-out Solutio Key

18 Chpter cotiued 5. The locus of poits distce of from, is circle. The locus of ll poits equidistt from 3, d, is the bisector. The bisector d circle itersect t poits,, 0 d,. The locus is ll poits, y where < y < 0..6 Quiz (p.705) m r Legth of AB.6 ft r A r r mi A ft ft Are of trigle Are of squre 0 00 P % y i..6 ft 38 r ft r.6 Techology Activity (p.706) 5. A cm. This is the equtio for the regio iside the circle cetered t the origi with rdius 5.. Aswers my vry. Smple swer: Eperimetl probbility is pproimtely 7.5% with the grphig clcultor progrm d theoreticl probbility is.6%. 3. Aswers my vry.. The more trils there re, the closer the theoreticl d eperimetl probbilities will be to ech other. Chpter Review (p ) 80. mesure of iterior 0 mesure of eterior mesure of iterior mesure of eterior mesure of iterior mesure of eterior mesure of iterior mesure of eterior A 3s.. 3. sometimes. sometimes 5. lwys cm A m Mesure of iterior gle 0.75 t 7 A P 0.75 t ft Perimeter CDE Perimeter BDF 3 3 Are CDE Are BDF S 6 t 60 3 A 3s 0.78 i Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

19 Chpter cotiued Perimeter ADG 5 Perimeter BDF 5 3 Are ADG Are BDF C r 5.3 cm Legth of AB C r m Legth of AB C r 75. ft Legth of AB r C. i. d C 5 5 m A r i A ft A cm A cm A ft. cm. m.7 ft Rdius of circle P P P P P or 6.% Are shded 33. P Are of semicircle r r 6 5% Legth of KM Legth of JN Are of rectgle Are of circle 5 Are shded Totl re 50% A r A r 0 r 3.57 i. r Legth of LM Legth of JN Legth of JL 0 Legth of JN Copyright McDougl Littell Ic. Geometry Chpter Worked-out Solutio Key

20 Chpter cotiued Chpter Test (p. 7) mesure of iterior A r 5.6 cm Are sector ARB marb r cm. eterior A 3s ft Are of sector i Mesure of iterior gle A 6 3 A P t 5 3. i ft Are of sectors P Are of circle Are of squre or 78.5% 5.3 m 8. Are of trigle P Are of squre or.5% cm Mesure of iterior gle A P 80 0 cos 70 si bot ft skiier ft P ft 0 mi 0 mi 6.67% 6.. Perimeter ABCD Perimeter EFGH Are of ABCD Are of EFGH C r 5 3. cm A r cm. Legth of AB 6 3 m AB 360 r m cm Chpter Stdrdized Test (p. 7 73). C. A A Polygo : 5 cos 36. Polygo b: cos 30. Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.

21 Chpter cotiued J 80.5 m. A Polygo : P 55 si uits 7. Smple swer: Oe method is to fid the re of the Polygo b: P 66 si 30 8 uits circle d from tht subtrct the re of the octgo. A secod method is to fid the re of sector. From tht, 5. A Polygo : A uits subtrct the re of trigle. The multiply by 8. Polygo b: A uits From problems 6, Are d 6. A Are of smller octgo Are of lrger octgo 8 3 re octgo 7.08 m Shded re m 7. B Legth of AB Are sector m 8. E Are shded. C Are shded 0. C. A P. C m A m P 86 si m A 6 cos.586 si m 6. Legth of Are P Are Q Are P % 6.7 ft 67.0 cm P AB m.6 ft Are trigle 6 si.5 6 cos.5 Shded Are m Ech method yields the sme result. r 3 i. C i. A i. P P P Are of circle Are of drt bord 3 3.7% 36 Are of blue regio Are of drt bord re gree re red re blue re drt bord % P 7.8% 0.5 m 5.73% 36 00% 8.6% swer from questio ) Copyright McDougl Littell Ic. Geometry 3 Chpter Worked-out Solutio Key

22 Chpter cotiued Chpter Project (p. 7). yes. yes 3. No; y two gret circles must itersect.. Smple swer: No. There re o prllel lies i geometry o sphere. 5. yes 6. Aswers my vry. Smple swer: 0, 0, 0 7. Aswers my vry. The sum should be lrger th 80. Smple swer: Aswers my vry. Smple swer: 0, 0, 0. o; yes; yes 0. Aswers my vry. The sum of the gles is betwee 80 d 50. Geometry Chpter Worked-out Solutio Key Copyright McDougl Littell Ic.