huong dan su dung gsp 5-vi com

Bin son : H Quc Vn THPT NGUYN HU

Hng dn s dng Geometer's Sketchpad

M C L C CHNG 1. M U 1.1. Gii thiu......................................................................................................................................................... 4 1.2. Bt u Lm Quen Vi GSP. ......................................................................................................................... 5 1.2.1. Giao din ngi dng ............................................................................................................................... 5 1.2.2 Cc cng c c bn:................................................................................................................................... 5 1.2.2. Kho St Cc Menu.................................................................................................................................. 7 Menu Tp........................................................................................................................................................ 7 Menu Hiu chnh ............................................................................................................................................ 8 Menu Hin th............................................................................................................................................... 11 Menu Dng hnh........................................................................................................................................... 11 Menu Bin hnh ............................................................................................................................................ 12 Menu Php o............................................................................................................................................... 12 Menu S........................................................................................................................................................ 13 Menu th.................................................................................................................................................. 13 CHNG 2. CC I TNG HNH HC C BN CHC NNG V QUAN H GIA CHNG 2.1. Cc i Tng Hnh Hc C Bn V Chc Nng Ca Chng .................................................................... 14 2.1.1. im ....................................................................................................................................................... 14 2.1.2. ng trn ............................................................................................................................................. 15 2.1.3. on thng, ng thng v tia............................................................................................................. 15 2.1.4. Vit ch .................................................................................................................................................. 16 2.2. Quan H Gia Cc i Tng Hnh Hc ..................................................................................................... 16 2.3. i tng ng.............................................................................................................................................. 17 CHNG 3. DNG HNH V QU TCH 3.1. Cc Cng C Dng Hnh C Bn ................................................................................................................. 18 3.1.1. Dng mt im trn i tng. .............................................................................................................. 18 3.1.2. Dng trung im ca mt on thng .................................................................................................... 18 3.1.3. Dng giao im ca 2 i tng ............................................................................................................ 18 3.1.4. Dng on thng, tia, ng thng. ....................................................................................................... 18 3.1.5. Dng ng thng i qua mt im v song song vi ng thng cho trc ..................................... 18 3.1.6. Dng ng thng vung gc vi ng thng cho trc .................................................................... 18 3.1.7. Dng ng phn gic ca mt gc cho trc ...................................................................................... 18 3.1.8. Dng ng trn bit tm v mt im thuc ng trn..................................................................... 18 3.1.9. Dng ng trn khi bit bn knh v tm............................................................................................. 19 3.1.10. Dng cung trn ng trn .................................................................................................................. 19 3.1.11. Dng cung trn i qua 3 im .............................................................................................................. 19 3.1.12. Dng min trong ca mt i tng .................................................................................................... 19 3.2. Qy Tch Ca Mt im Hay i Tng .................................................................................................... 19 3.3. Bi Tp p Dng........................................................................................................................................... 21 CHNG 4. PHP BIN HNH 4.1. Cc Cng C Bin Hnh C Bn................................................................................................................... 24 4.1.1. Php tnh tin.......................................................................................................................................... 24 Tnh tin theo vector chn trc.............................................................................................................. 24 4.1.2. Php quay ............................................................................................................................................... 24 4.1.3. Php v t................................................................................................................................................ 25 T s v t uc nhp t hp thoi................................................................................................................ 25 4.1.4. Php i xng trc.................................................................................................................................. 26 4.2. Bi Tp p Dng........................................................................................................................................... 27 CHNG 5. O C V TNH TON 5.1. Cc Cng C o c C Bn ....................................................................................................................... 28 5.1.1. Tnh chiu di v khong cch ............................................................................................................... 28 Tnh chiu di (Lenght) ................................................................................................................................ 28 Tnh khong cch (Distance)........................................................................................................................ 28 5.1.2. Tnh chu vi.............................................................................................................................................. 28 Chu vi a gic (Perimeter)............................................................................................................................ 28 Chu vi ng trn (Circumference) ............................................................................................................. 28Blog: etoanhoc.blogspot.comTrang 2


5.1.3. Tnh gc v din tch .............................................................................................................................. 28 Tnh gc(Angle) ........................................................................................................................................... 28 Tnh din tch(Area) ..................................................................................................................................... 29 5.1.4. Tnh s o cung v di cung.............................................................................................................. 29 5.1.5. Tnh bn v t s ..................................................................................................................................... 29 Bn knh(Radius).......................................................................................................................................... 29 Tnh t s gia 2 on thng (Ratio)............................................................................................................. 29 5.1.6. My tnh (Calculator) ............................................................................................................................. 29 5.1.7. Ta ..................................................................................................................................................... 30 Tnh honh ca im (x).......................................................................................................................... 30 Tnh tung ca im (y) ............................................................................................................................ 30 Tnh khong cch theo ta Coordinate Distance..................................................................................... 30 5.1.8. H s gc v phng trnh ..................................................................................................................... 30 Tnh h s gc (Slope).................................................................................................................................. 30 Xem phng trnh ca i tng (Equation) ............................................................................................... 30 5.2. Bi Tp p Dng........................................................................................................................................... 31 CHNG 6. TH V H TA 6.1. Th (Graphic) ........................................................................................................................................... 32 6.1.1. Xc nh h trc ta cho h thng ..................................................................................................... 32 6.1.2. nh du h trc ta cho h thng .................................................................................................... 32 6.1.3. Cc li ta hin th .......................................................................................................................... 32 6.1.4. n hoc hin h ta v xc nh im c ta nguyn ................................................................. 33 6.1.5. Dng im khi bit ta ca n .......................................................................................................... 33 6.1.6. To ra tham s mi................................................................................................................................. 33 6.1.7. To ra mt hm s mi........................................................................................................................... 34 6.1.8. V th hm s..................................................................................................................................... 34 6.1.9. o hm v tip tuyn ng cong........................................................................................................ 35 o hm........................................................................................................................................................ 35 Tip tuyn ng cong................................................................................................................................. 35 6.1.10. Lp bng gi tr tng ng ................................................................................................................... 36 6.2. Cc H Trc Ta ...................................................................................................................................... 37 6.2.1. H ta cc.......................................................................................................................................... 37 6.2.2. Ta Descartes v ta ch nht...................................................................................................... 38 6.3. V Th Hm S Cho Bi Phng Trnh C Cha Tham S ................................................................... 38 6.3.1. ng thng ........................................................................................................................................... 38 6.3.2. ng trn: ............................................................................................................................................ 40 6.3.3. ng Elip ............................................................................................................................................. 40 6.4. Bi Tp p Dng....................................................................................................................................... 41 CHNG 7. CNG C NGI DNG V HNH HC FRACTAL 7.1. Cng C Ty Bin......................................................................................................................................... 42 7.2. Hnh Hc Fractal ........................................................................................................................................... 43 7.2.1. Thm Sierpinski...................................................................................................................................... 43 7.2.2. ng Von Koch ................................................................................................................................... 44 7.2.3. Cy Pitago .............................................................................................................................................. 45 Mt s lu khi s dng php lp trong Menu Bin hnh........................................................................... 45 CHNG 8. DNG CC NG CONIC 8.1. Parabol........................................................................................................................................................... 47 8.1.1. Parabol Cho Bi ng Chun V Tiu im...................................................................................... 47 8.1.2. Parabol Qua Hai im V Bit Tiu im ............................................................................................ 47 8.2. Elip ................................................................................................................................................................ 47 8.3. Hypebol ......................................................................................................................................................... 48 8.4. Elip Hoc Hypebol Khi C Tm Sai V Tiu im ..................................................................................... 48 8.5. Conic Qua Nm im ................................................................................................................................... 48 CHNG 9. LI KT

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CHNG 1. M U1.1. Gii thiuNgy nay tin hc c vai tr ht sc quan trng trong cuc sng, c th ni hu nh khng c bt k mt ngnh no m khng ng dng tin hc. V th, gio dc cng khng nm ngoi phm vi . ng dng tin hc vo vic hc v dy lun lun l mt trong nhng vn c nhiu ngi quan tm. c bit l cc qu thy c gio cng nh nhng sinh vin s phm ang hc chun b c lm thy, c... Phn mm hnh hc ng Geometer's Sketchpad (GSP) l mt phn mm thc s hay v b ch v ti ngh bt c mt gio vin ton no cng nn bit. V th, vi s hiu bit t i v tin hc ca mnh, ti bin son ti liu hng dn nh ny hy vng c th gip c phn no nhng ai quan tm mun hc, tm hiu GSP. Nhc n phn mm hnh hc ng chc chng ta nghe ni n nhng anh ti ni tingnh: - Cabri II Plus: l mt phn mm hnh hc ng c bn quyn ca cng ty CabriLog-Php, ni ting vi cabri 2D v 3D. Hin nay, ti Vit Nam c nh phn phi v bn ting Vit ca Cabri. Bn c th tham kho thm ti a ch www.cabri.com - Geogebra: l phn mm hnh hc ng c pht trin bi mt tin s ngi o. L phn mm min ph, m ngun m v hin ny c vit ha gn nh 100%. Bn c th tham kho thm ti a ch www.geogebra.org. - C.a.R: l mt phn mm hnh hc ng (Dynamic Geometry) c vit trn ngn ng Java m ngun m v hon ton min ph. C.a.R (Circle And Rules) nh gn, tng i d s dng. Gio s ton hc ni ting ca c,ng Rene. Grothmann l tc gi ca C.a.R. Tuy nhin c mt iu khng thun li cho Geogebra v C.a.R l chy c 2 phn mm ny th my ca bn phi ci my o Java. bit thm xin vo http://www.z-u-l.de - GSP: cng l phn mm hnh hc ng c vit bi cng ty Keypress, l mt cng ty chuyn vit cc phn mm gio dc v sch tham kho ni ting ca M. Phn mm ny c Vit ha (tnh n V5.00). GSP c nhng u im ni bt m cc phn mm khc khng c nh: + Nh gn d ci t, khng yu cu my tnh c cu hnh mnh (khi son ti liu ny ti dng PC 860 MHz nhng vn chy tt GSP). C th sao chp tp tin thc thi l chy c ngay m khng cn ci t. iu ny rt c li, bn ch cn lu n vo USB v sau c th chy trn bt c ni u. + Phn mm khng ci kha, v vy bn c th ci t v s dng n m khng cn c serial hay m kch hot. + Cc i tng hnh m GSP v rt mn v p. + Chuyn ng v to vt ca mt im khi kch hot chc nng chuyn ng rt t nhin. Ni nh th khng c ngha rng Skechpad khng c nhc im. Tuy nhin, ti ngh bn c th d dng chp nhn mt vi nhc im v vn s dng hiu qu Skechpad trong hc v dy ton. Ch : Bn c th tm hiu r v su hn v cc phn mm hnh hc ng bng cch hy truy cp vo www.google.com v dng cc t kha hnh hc ng; GSP; Cabri; Geogebra.... Bn c th ti phn mm GSP V4.07 ti a ch http://haquocvan.schools.officelive.com/Documents/GSP5.0viethoa.rar Ti liu hng dn ny chc chn cn rt nhiu iu hn ch v cn b sung cng nh sa i cho ph hp. Rt mong nhn c s gp ca cc bn v a ch email: [email protected]


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1.2. Bt u Lm Quen Vi GSP.1.2.1. Giao di n ng i dngGiao din chnh ca phn mm:

1.2.2 Cc cng c c b n:Cng c chn : Bn dng cng c ny chn mt hay nhiu i tng no trn mt phng. Nu sau khi chn cng c ny, bn click v gi chut tri (drag) vo i tung th bn c th di chuyn n trn mt phng. Bn cng c th dng cng c ny dng giao im ca 2 i tng no bng cch click vo v tr giao im . Ti v tr ca cng c chn bn click v gi chut tri mt khong thi gian bn s thy xut hin thm hai i tng xut hin bn cnh. Cng c ny dng drag mt i tng no trn mt phng quay xung quanh mt i tng khc no c chn lm tm Cng c ny cng c chc nng tng t nh cng c trn.Nhng n khng quay i tng quanh mt im, m hn ch hng ca i tng. Ch : Trong bt c trng hp no, d bn ang chn cng c no, bn ch cn n nt ESC ngay tc khc bn s tr v chn cng c chn.

Cng c im : cng c ny dng to ra mt IM trn mt phng. Sau khi click chut vo cng c ny, bn ch vic click chut vo mt phng, ch m bn mun IM xut hin.Blog: etoanhoc.blogspot.comTrang 5


Cng c ny cng c th dng giao im ca 2 i tng no trong mt phng. Bng cch bn click chut vo v tr giao im . Tt nhin l trc bn chn cng c im.

Cng c Compa : dng v ng trn trn mt phng. Bn ch cn ba ci click: ci u tin click vo biu tng ca cng c Compa; ci th hai click vo mt phng xc nh tm ca ng trn; ci th 3 click vo v tr bt k trn mt phng. Sau khi v c ng trn, bn c th iu chnh li kch thc ng trn sao cho hp yu cu ca bn bng cch dng cng c chn, click vo tm hoc im th hai xc nh c ng trn v sau ko (drag) n trn mt phng.

Cng c thc thng : dng cc i tng nh on thng, on thng i qua 2 im cho trc, ng thng, ng thng qua 2 im cho trc, tia. Cng ging nh cng c chn khi bn click chut tri v gi n mt khong thi gian, bn s thy xut hin . Tng ng vi n l dng v an thng, tia v ng thng. Cng c dng min a gic: Cng ging nh cng c chn khi bn click chut tri v gi n mt khong thi gian, bn s thy xut hin . Tng ng vi n l dng v min trong khng c ng bin, min trong c ng bin v ng bin.

Cng c vn bn : dng to nhn cho cc i tung khc hoc cc ghi ch, cc dng ch theo yu cu ca bn trn mt phng. Ch : Bn c th g ting Vit trong GSP bng bng m Unicode, VNI Windows,

Cng c vit - v t do: v du gc, nh du, k hiu v v bng tay.

Cng c thng tin: cho bit thuc tnh ca i tng v mi lin quan gia cc i tng.

Cng c ty bin : GSP ch h tr nhng cng c c bn nh im(point), ung trn (circle), on thng (segment), ng thng(line) v tia(ray). Trong qu trnh s dng GSP chc chc c nhng hnh bn thng xuyn s dng, chng hn nh tam gic, tc gic, hnh thoi, hnh vung V vy trnh lp i lp li mt cng vic nhm chn , GSP cho ra i Cng c ty bin (tng t cng c Macro trong Winword) Cng c ny s cho php bn ghi li cch dng v to nhng i tng theo yu cu ca bn. Nh cng c ny m ngui dng GSP cm thy thc s thoi mi hn v cm nhn c sc mnh ca phn mm.


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1.2.2. Kh o St Cc MenuMenu Tp

Trong cc Menu trn bn cn ch mc Ty chn ti liu, bn c th to thm trang, i tn trang hoc xa trangchn mc ny bn s thy ca s nh hnh bn.


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Menu Hiu chnh

Lm vic vi GSP bn cn ch rng khng c Menu cha lnh Insert. Nu bn mun chn mt bc nh vo th bn hy copy bc nh trong mt chng trnh x l nh no (v d nh chng trnh Paint). Ri dn (Paste) nh vo mt phng ang lm vic. Lc hnh nh s tr thnh nh nn ca mt phng lm vic. Trong menu Hiu chnh bn cn ch thm lnh Nt hnh ng, n rt hu ch cho bn sau ny.

Click chut vo s thy c menu con gm cc lnh sau: n/Hin: Lnh ny s to ra mt nt(button) mi. Khi click chut vo button ny th s n hoc hin mt i tng no trn mt phng do bn chn trc. Chuyn ng: to mt button thc thi lnh cho mt hay nhiu i tng no s chuyn ng. Chuyn ng ti ch: lnh ny di chuyn mt i tng ny n mt i tng khc. V d: bn cho im A di chuyn n im B. Nh l theo mc nh th im bn chn trc s di chuyn li im chn th hai. Trnh din: to ra mt button m khi bn click vo button ny th cc lnh trong cc button khc s c din ra hng lot hoc ng thi. Lnh ny hu hiu to ra mt lot hnh ng cng xy ra mt lc. Lin kt: to ra mt lin kt. C th l lin kt ngoi hoc lin kt trong u kh dng. Cun: cun thanh trt tri, hay phi ca mn hnh. Qua lm thay i v tr ca i tng hnh hc trong mt phng hay mn hnh.


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Hp thoi Chuyn ng ca Nt hnh ng: Khi chn mt i tng, sau bn chn lnh Chuyn ng trong Nt hnh ng bn s thy hp thoi nh sau, gm c 3 th (Tab) Th Chuyn ng

Th Tn

Th i tng


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Hp thoi Chuyn ng ti ch ca Nt hnh ng:

Trong hp thoi trn cc th i tng, Tn cng c chc nng gn ging nh trong hp thoi Chuyn ng. Tuy nhin, c 2 ty chn bn cn ch l i theo sau mc tiu chuyn ng v n v tr ban u ca mc tiu chuyn ng V d: Trong mt phng, ti mun cho im A di chuyn n im B. Nhng im B khng c nh, m im B l im chuyn ng. Lc , nu bn ch mun im A di chuyn n v tr ban u, trc khi im B di chuyn th bn hy chn n v tr ban u ca mc tiu chuyn ng, cn nu bn mun im A rt theo im B ang di chuyn th hy chn i theo sau mc tiu chuyn ng. Ch : sau khi chn xong thuc tnh cho mt i tng no ti cc hp thoi tng ng th bn phi Click vo nt Ok cc thng s c hiu lc. Gi s rng, bn v c im B trn mt phng. Bn dng lnh Chuyn ng to ra mt button m khi click vo th im B s chuyn ng trn mt phng. Sau bn v thm im A v dng lnh Chuyn ng ti ch to ra mt button m khi click vo th im A s di chuyn n im B. By gi, bn mun to ra mt button, m khi click vo th c 2 button kia u thi hnh. Tc l khi click vo button mi ny, im A th di chuyn n im B, cn im B th chuyn ng. Th lnh Trnh din s gip bn. Hp thoi Trnh din ca Nt hnh ng Bn phi chn trc cc button m bn mun a chng vo Presentation. Khi lnh ny mi c hiu lc.

Hy ch rng, khi lm vic vi cc i tng trn mt phng th chut phi rt c ch cho bn. Hy clickchut phi vo mt i tng no , v xem menu ng cnh hin ln bn s thy rt nhiu iu tin ch nm trong . Khi ang trong menu Edit bn hy n phm Shitf bn s thy c s thay i.Blog: etoanhoc.blogspot.comTrang 10


Menu Hin th

Menu Dng hnh

Xin hy ch l bn mun dng mt i tng mi, ph thuc vo cc i tng trc th bn phi chni tng ph thuc trc. Cn khng, khi bn vo menu Dng hnh th cc lnh ca n u cha hiu dng (nt m nht). Trong hnh trn cc lnh u cha hiu dng.Blog: etoanhoc.blogspot.comTrang 11


Menu Bin hnh

Menu Php o


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Menu S

Xin ch : Trong cc lnh trn bn cn lnh My tnh khi chn ln ny mt chic my tnh con s hin ln cho bn tnh ton v t bn cng c th to ra cc hm s theo yu cu ca bn. Menu th


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CHNG 2. CC I TNG HNH HC C BN CHC NNG V QUAN H GIA CHNG2.1. Cc i Tng Hnh Hc C Bn V Chc Nng Ca Chng2.1.1. i m* V mt im: Bc 1: dng chut tri click vo cng c Bc 2: tip tc dng chut tri click vo mt phng. Ti v tr no bn mun im xut hin. Bn s c c mt im th ny v ang trng thi c chn.

Theo mc nh, khi mt im mi c khi to GSP s t nhn cho im theo tn cc ch ci A, B, C. v ang trong trng thi n. Nu mun thy nhn ca im hay ca mt i tng ni chung, bn hy dng cng c chn chn im hay i tng v sau Click chut phi > Hin tn. Bn s c c Lp li cc thao tc trn nu bn mun to ra nhiu im. Khi bn Click chut phi vo mt im hay i tng bn s thy mt menu ng cnh nh sau: .

* Di chuyn im: bn c th di chuyn im mt cch d dng trn mt phng n nhng v tr bn thch bng cch dng cng c chn v di chuyn im i. * im chuyn ng: bn cng c th to ra mt im chuyn ng bng cch chn lnh Chuyn ng im trong menu ng cnh hay trong Menu Hin th. Khi mt hp thoi nh s xut hin cho php bn iu khin s chuyn ng ca im. Nu bn chn thm Vt im th im va chuyn ng va li du vt. * im A di chuyn n im B: trn mt phng bn v 2 im A v B. By gi bn mun to mt button m khi click vo button ny th im A s di chuyn n im B. Th bn lm nh sau: Bc 1: dng cng c im v im A v im B. Bc 2: dng cng c chn chn im A ri chn im B. Bc 3: thc hin lnh Hiu chnh > Nt hnh ng > Chuyn ng ti ch Bc 4: Click chut ln button mi xut hin .


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2.1.2. ng trnTrong GSP ng trn c th xc nh khi bit tm v bn knh hoc tm v mt im th hai thuc ng trn. * V ng trn : Bc 1: click chut tri vo cng c Compa Bc 2: click chut vo mt v tr no trn mt phng. Bc 3: ko chut ra xa v tr ban u.

Bn cng c th v trc hai im phn bit. Sau chn cng c Compa ri click vo im th nht, im th hai. * im trn ng trn: sau khi v xong ng trn. Nu bn mun xc nh mt im trn ng trn th bn click chut tri vo cng c im ri click chut tri ln ng trn. Lc im mi khi to s nm trn ng trn. Bn hy th dng chut drag im mi to , v s thy n khng di chuyn t do na, m di chuyn trn ng trn.

2.1.3. o n th ng, ng th ng v tia.Ba cng c v on thng, ng thng, tia c gom chung vo mt nhm l Cng c dng on thng. Bn hy n v gi chut tri ln cng c Cng c dng on thng bn s thy xut hin cc cng c cn li . * V on thng : Bc 1: click chut vo Bc 2: click chut vo 2 v tr khc nhau hoc 2 im phn bit trn mt phng. * V ng thng: Bc 1: click chut vo Bc 2: click chut vo 2 v tr khc nhau hoc 2 im phn bit trn mt phng. * V tia: Bc 1: click chut vo Bc 2: click chut vo 2 v tr khc nhau hoc 2 im phn bit ca mt phng Ch : Khi mi khi to mt i tng th mc nh GSP chn i tng cho bn. V vy nu bn khng mun chn i tng th bn n phm ESC hoc click chut tri vo mt ch trng no trn mt phng. Bn cng cn phi phn bit mt i tng no ang c chn, i tng no khng c chn.


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2.1.4. Vi t chKhi lm vic vi GSP bn c th vit ch xen k vi v hnh. Bn cng c th nhp nhng cng thc ton v cc cng thc hnh hc. Bn cng c th vit ch Vit vo bng v. * Vit ch Bc 1: click chut tri vo Bc 2: click chut tri vo mt phng v n chut xung ng thi di chuyn chut i n v tr khc ri th chut ra. Bc 3: nhp ch vo vng c hnh ch nht mi va khi to .

2.2. Quan H Gia Cc i Tng Hnh HcChng ta cn bit rng quan h gia cc i tng hnh hc l mt trong nhng iu c bn nht, ct li nht xy dng nn mt phn mm hnh hc ng. GSP cng vy, ton b cc i tng hnh hc trong phn mm u c th kt ni vi nhau theo nhng qua h ton hc cht ch. Nh s kt ni gia cc i tng theo quan h ton hc cht ch ny m cc i tng ca phn mm c th to nn mt h thng ng. chnh l cha kha to ra sc mnh cho phn mm-khi mt i tng thay i, th nhng i tng c quan h vi n t nhiu cng thay i theo. Quan h gia cc i tng hnh hc trong GSP l mt quan h cha- con (parent-children) hay cn gi l quan h ph thuc. Ni nh vy khng c ngha rng tt c cc i tng tn ti trong mt phng ca phn mm u c quan h cha-con hay con-cha vi nhau. V d: Bn v mt im A trn mt phng, sau bn v tip mt im B trn mt phng. Hai im ny bn v mt cch c lp, tc l v im B khng ph thuc vo cch v im A th c th xem rng 2 i tng im A v B chng c quan h g vi nhau c, nhng nu bn v mt on thng AB, v tip bn v mt im C nm trn an thng AB th lc ny thc s c mi quan h. on thng AB l i tng cha ca i tng im C, ta ni quan h gia an thng AB v C l quan h cha-con. Ngc li im C l i tng con ca on thng AB, ta ni quan h gia im C v AB l quan h con-cha. Bn cng thy c rng, an thng AB c c l nh vo s xc nh ca im A v im B. V th on thng AB l i tng con ca im A v im B. y im A v B l hai i tng t do trn mt phng, nn bn c th dng chut di chuyn n i n bt c mt ni no trn mt phng m bn thch. Khi di chuyn A hoc B bn s thy rng cc i tng con ca chng l on AB v im C cng s di chuyn theo. CnBlog: etoanhoc.blogspot.comTrang 16


im C, n l i tng con ca on thng AB do bn khng th di chuyn n mt cch t do na, m n ch c th di chuyn trn on thng AB. Do vy c th ni mt i tng c khi to trc l cha ca mt i tng khi to sau trn n. Quan h gia i tng cha v i tng con l quan h mt-nhiu v i tng con vi i tng cha cng l quan h mt-nhiu. iu ny c ngha rng, mt i tng trong GSP c th l cha ca nhiu i tng khc v ngc li mt i tng cng c th l con ca nhiu i tng khc nhau. chn tt c cc i tng con ca mt i tng no bn lm nh sau: Bc 1: chn i tng cha. Bc 2: dng lnh Hiu chnh > Chn tt c i tng con. Ngc li, bn mun xem nhng i tng no l cha ca mt i tng. Bn lm nh trn nhng bc 2 bn thay bng lnh Hiu chnh > Chn tt c i tng cha.

2.3. i tng ngThit ngh, s c mt thiu sot ln nu khi tm hiu phn mm hnh hc ng (Dynamic Geometry) m khng nhc n nhng i tng ng. u im, cng nh sc mnh ca phn mm GSP l n khng ch c th v c gn nh tt c nhng i tng hnh hc m bn c th v trn giy m n cn c th to ra nhng i tng m bn khng th no lm c vi mt cy bt v mt t giy. l i tng chuyn ng. Trong GSP bn c th cho mt im (point) mt ng trn (circle) mt on thng (segment), ng thng (line), mt tia (ray) chuyn ng. Bc 1: chn i tng m bn mun cho chuyn ng. Bc 2: dng lnh Hin th > Chuyn ng i tng hoc Click chut phi > Chuyn ng i tng Ty theo i tng no m bn chn trc th t i tng s thay tng ng trong cc lnh trn. Khi kch hot cho mt i tng chuyn ng, nu l i tng t do th n s chuyn ng t do trn mt phng. Nu i tng chuyn ng l con ca i tng no , th n ch c th chuyn ng trn i tng cha ca n. Ngc li, nu mt i tng cha chuyn ng th tt c cc i tng con ca n cng chuyn ng theo. Khi thm lnh Hin th > Vt i tng hoc Click chut phi > Vt i tng bn s thy qu tch ca mt i tng khi n chuyn ng.


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CHNG 3. DNG HNH V QU TCH3.1. Cc Cng C Dng Hnh C Bn3.1.1. D ng m t i m trn i t ng.Cng c ny cho php bn dng mt im mi l i tng con ca mt i tng cha no do bn chn trc. im mi khi to s khng b rng buc g thm ngoi vic n l i tng con ca i tng bn chn trc . thc hin lnh dng hnh ny bn dng lnh Dng hnh > im thuc Cn ch thm l khi bn cha chn mt i tng no dng im ln th n s b m nht i

Nhng khi bn chn th

3.1.2. D ng trung i m c a m t o n th ngLnh ny cho php bn dng mt im mi l trung im ca mt on thng m trc bn chn. Bc 1: chn on thng. Bc 2: Dng hnh > Trung im (Ctrl+M)

3.1.3. D ng giao i m c a 2 i t ngLnh ny cho php bn dng giao im ca 2 i tng hnh hc no . Bc 1: chn 2 i tng cn dng giao im. Bc 2: Dng hnh > Giao im

3.1.4. D ng o n th ng, tia, ng th ng.Bc 1: Chn 2 im. Bc 2: on thng: Dng hnh > on thng (Ctrl+L) ng thng: Dng hnh > ng thng Tia: Dng hnh > Tia

3.1.5. D ng ng th ng i qua m t i m v song song v i ng th ng cho tr cBc 1: chn ng thng hay on thng lm phng v im m ng thng cn dng i qua Bc 2: Dng hnh > ng song song

3.1.6. D ng ng th ng vung gc v i ng th ng cho tr cBc 1: chn ng thng cho trc v im m ng thng cn dng i qua. Bc 2: Dng hnh > ng vung gc

3.1.7. D ng ng phn gic c a m t gc cho tr cV d ti cn dng ng phn gic ca ABC Bc 1: chn theo th t A, B, C. Bc 2: Dng hnh > Gc v tia phn gic Khi dng ng phn gic ca mt gc. im chn th 2 c xem nh l im gc.

3.1.8. D ng ng trn bi t tm v m t i m thu c ng trnBc 1: chn tm v mt im thuc ng trn. Bc 2: Dng hnh > ng trn bit tm + imBlog: etoanhoc.blogspot.comTrang 18


3.1.9. D ng ng trn khi bi t bn knh v tm.Bc 1: chn an thng c di m bn mun lm bn knh v chn tm. Bc 2: Dng hnh > ng trn bit tm + bn knh

3.1.10. D ng cung trn ng trnBc 1: chn tm v sau chn 2 im trn ng trn m bn mun dng cung. Bc 2: Dng hnh > Cung trn ng trn Khi dng cung trn ng trn bn cn ch rng im u tin bn chn l tm ca ng trn, im th hai bn chn l im bt u ca cung v im cui cng bn chn l im kt thc ca cung (cung c v theo chiu dng)

3.1.11. D ng cung trn i qua 3 i mBc 1: Chn 3 im mun cung trn i qua. Bc 2: Dng hnh > Cung i qua 3 im

3.1.12. D ng mi n trong c a m t i t ngBc 1: chn i tng bn mun dng min trong Bc 2: Dng hnh > Min trong (Ctrl+P)

3.2. Qy Tch Ca Mt im Hay i TngMt trong nhng iu tht tuyt vi m phn mm GSP em li cho chng ta l kh nng tm qu tch ca mt i tng hnh hc. Tt nhin l GSP khng c kh nng chng minh c qu tch ca mt i tng hnh hc m n v nn qu tch. Nhng n c th gip chng ta hnh dung c qu tch ca i tng trc khi chng minh. tm qu tch ca mt i tng bn lm nh sau: Bc 1: chn i tng cha.(y l i tng c th thay i, v cc i tng khc thng ph thuc vo n). Bc 2: Chn i tng con ca i tng trn (y l i tng m bn mun tm qu tch) Bc 3: Dng hnh > Qu tch V d 1: Cho ng trn (O), AB l ng knh, mt im C thay i trn (O). Hy dng im D sao cho ABCD l hnh bnh hnh. Khi C thay i tm qu tch im D. Gii: Bc 1: Dng on thng AB. Bc 2: Dng O l trung im ca AB. Bc 3: Dng ng trn bit tm (O) v im (A). Bc 4: Dng C thuc ng trn (O) v dng an CB. Bc 5: Dng ng thng a qua C v song song vi AB, dng ng thng b qua A v song song vi CB. Bc 6: Dng D l giao im ca a v b. Bc 7: Tm qu tch ca im D khi im C thay i. Chn im C v sau chn im D. Bc 8: Dng lnh Dng hnh > Qu tch V y l kt qu m chng ta thu c khi thc hin nhng bc dng hnh trn.


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Bn hy double-click vo nhn ca i tng no m bn mun thay i tn. By gi cng bi ton dng hnh v tm qy tch trn. Nhng chng ta khng mun GSP v nn qu tch nhanh nh vy. M dng s chuyn ng ca C v im D v ln qu tch. lm c iu ny, bc 7 bn khng dng lnh Dng hnh > Qu tch tm qu tch m thay th bc 7 bng lnh sau: - nh du to vt cho im D (chn im D, dng lnh Click chut phi > Vt giao im - Kch hat cho im C chuyn ng. (chn im C, dng lnh Click chut phi > Chuyn ng im)

V d 2: Cho tam gic ABC ni tip trong ng trn (O) v c AB l ng knh. Gi H l trc tm ca tam gic OAC. Tm qu tch ca im H khi C thay i trn ng trn O. Ch : khi tn ca i tng cha xut hin th bn c th chn i tng v dng lnh Click chut phi > Hin tn V d 3: Cho ng trn (O,R) v mt im A nm ngoi ng trn (O). Mt im B thay i trn (O). Gi d l ng trung trc ca AB. Tm qu tch ca ng thng d khi B thay i.


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3.3. Bi Tp p DngBi tp 1: Hy dng cc cng c dng hnh c bn dng cc hnh sau y: - Dng trng tm G ca tam gic ABC cho trc. - Dng trc tm H ca tam gic ABC cho trc.

- Dng ng trn (I) ni tip tam gic ABC cho trc. - Dng ng trn (O) ngoi tip tam gc ABC cho trc.

- Dng tam gic cn ABC. - Dng tam gic u ABC.

- Dng hnh bnh hnh ABCD. - Dng hnh vung ABCD.


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Trong cc hnh trn, nhng ng khng lin nt l nhng ng trnh by li cch dng. Sau khi dng xong, cc bn c th cho cc i tng khng cn thit n i, cn li hnh chnh, hnh m ta cn dng. (chn i tng > Click chut phi > n) Bi tp 2: Cho tam gic ABC ni tip trong ng trn (O), M l im di ng trn cnh BC. a) Dng (O1) i qua M v tip xc vi AB ti B. b) Dng (O2) i qua M v tip xc vi AC ti C.

Xin lu thm l t cc nhn c ch s di v d nh A1, B1, O1... th khi t tn nhn bn hy thm A[1], B[1], O[1].... Bi tp 3 : Trong mt tam gic th 3 trung im ca cc cnh ca mt tam gic, 3 chn ng cao v 3 trung im ca cc on thng ni trc tm vi cc nh ca tam gic th cng nm trn mt ng trn. Ngi ta gi ng trn l ng trn Euler. Hy dng ng trn Euler.


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Bi tp 4 : Cho ung trn tm O ng knh AB. C l mt im thay i trn ng trn O. Gi m l ng phn gic ca gc BCA v D l giao im ca (O) v m. Gi M l trung im ca CD. Hy v qu tch ca M khi C thay i.

C

A

M

O

B

D

m

Bi tp 5 Cho AB l on thng c nh. Ax, By l hai tia song song vi nhau v nm cng b so vi ng thng AB. Gi Am v An ln lt l hai ng phn gic ca cc gc xAB v ABy. Hy v qu tch giao im ca hai ng phn gic . Bi 6 : Cnh ca mt hnh thoi ABCD c chiu di khng i, v tr ca AB c nh, O l trung im ca AB, CO v BD ct nhau ti P. V qu tch ca im P khi gc ca hnh thoi thay i.


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CHNG 4. PHP BIN HNH4.1. Cc Cng C Bin Hnh C Bn4.1.1. Php t nh ti nChng ta bit rng xc nh c mt php tnh tin chng ta cn c mt Vector. GSP cng vy, xc nh php tnh tin bn cng cn c mt Vector. Vector ny c th l do bn chn t mt vector no trong mt phng. Trong trng hp bn cha chn vector no lm phng v chiu tnh tin th GSP a ra mc nh l tnh tin i tng theo cc vector cho bi ta t mt hp thoi ty chn do bn nhp thng s. Hai h trc ta m GSP h tr l Ta cc v Ta ch nht. V d: Ti cn tnh tin ng trn (O). Bc 1: chn ng trn (O). Bc 2: dng lnh Bin hnh > Php tnh tin Khi mt hp thoi s hin ln cho bn chn thng s.

Tnh tin theo vector chn trc Bn cng c th chn mt vector bt k t mt phng lm vector tnh tin. lm iu ny bn tin hnh theo cc bc sau: Bc 1:chn im gc vector v sau chn im cui ca vector tnh tin. Bc 2: dng lnh Bin hnh > nh du vector nh du vector ny. Buc 3: chn i tng mun tnh tin v dng lnh Bin hnh > Php tnh tin

4.1.2. Php quayTa bit rng xc nh mt php quay chng ta cn c tm quay v gc quay. Trong GSP cng vy. quay mt i tng hnh hc, chng ta cng phi cn chn mt im lm tm quay v mt gc quay. Gc quay ny chng ta c th nh du t mt gc no c trong mt phng hoc chng ta c th chn theo thng s nhp vo t mt hp thoi. C th ta c 2 cch sau: Cch 1: Bc 1: nh du tm quay.(Bng cch chn mt im mun lm tm quay ri dng lnh Bin hnh > nh du tm quay, v t hoc n p vo tm quay) Bc 2: chn i tng cn quay ri dng lnh Bin hnh > Php quay. Khi mt hp thoi xut hin, cho php bn chn gc quay. (chiu gc quay tnh theo chiu ngc kim ng h-chiu dng)Blog: etoanhoc.blogspot.comTrang 24


By gi gi s rng trong mt phng ta c mt gc XBY no v mt ng trn (O). Ta cn thc hin php quay tm A v gc quay l XBY cho ng trng tm O. Cch 2: Bc 1: chn tm quay. (chn A, ri dng lnh Bin hnh > nh du tm quay, v t) Bc 2: chn X ri chn B ri chn Y ri dng lnh Bin hnh > nh du gc Bc 3: chn ng trn v dng lnh Bin hnh > Php quay

4.1.3. Php v tMt php v t s hon ton xc nh nu bit tm v t v t s v t. Trong GSP cng vy, bn cng cn phi bit tm v t v t s v t. Trong , t s v t c th l t s do bn nhp vo mt hp thoi hoc bn nh du t mt t s gia hai an thng no trong mt phng. T s v t uc nhp t hp thoi. Bc 1: nh du tm quay. (chn im mun lm tm quay, ri dng lnh Bin hnh > nh du tm quay, v t hoc n p vo tm v t) Bc 2: chn i tng mun v t ri dng lnh Bin hnh > Php v t. Khi mt hp thoi s xut hin nh sau:


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By gi gi s rng ta mun cn v t ng trn (O) theo php v t tm I v t s l AC/AB. Bc 1: nh du I lm tm quay. Bc 2: nh du t s AC/AB bng cch chn im A ri chn im B ri chn im C v dng lnh Bin hnh > nh du t s Bc 3: chn ng trn v dng lnh Bin hnh > Php v t

A

B

C

I

O

nh du t s theo on thng rt c li khi bn mun thay i t s v t. V nh trong trng hp trn, bn ch cn di chuyn im B l php v t s thay i theo.

4.1.4. Php i x ng tr cTrong GSP mt php i xng trc s c xc nh nu c mt ng thng hoc mt on thng lm trc i xng. thc hin php i xng trc trong GSP chng ta lm: Bc 1: chn ng thng hay on thng mun lm trc i xng ri dng lnh Bin hnh > nh du trc i xng hoc n p vo ng thng hay on thng. Bc 2: chn i tng mun cho i xng ri dng lnh Bin hnh > Php i xng trc Hnh sau y cho thy nh ca mt ng trn qua trc i xng l mt ng thng v mt on thng.

O

O1 O2

ch : trong GSP khng c php i xng tm. Nhng chng ta bit rng php i xng tm ch l trng hp c bit ca php quay khi m gc quay bng 180. V vy, nu cn thc hin php i xng tm, th chng ta dng php quay v gc quay bng 180.


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4.2. Bi Tp p DngBi 1: Cho ng trn (O) vi ng knh AB c nh, mt ng knh MN thay i. Cc ng thng AM v AN ct cc tip tuyn ti B ln lt ti P v Q. V qu tch trc tm cc tam gic MPQ v NPQ. (Hnh bn cho thy qu tch trc tm H ca tam gic MPQ khi M di chuyn trn (O)).

Bi 2: Cho tam gic ABC vi I l tm ng trn ni tip v P l mt im nm trong tam gic. Gi A, B, C l cc im i xng vi P ln lt qua cc ng thng AI, BI, CI. Hy xc nh giao im ca cc ng thng AA, BB, CC v drag im P trong tam gic ABC. C thm kt lun g v giao im ca 3 ng thng trn? Bi 3: Cho tam gic ABC. Gi A, B, C ln lt l tm cc ng trn bng tip trong gc A, gc B, v gc C. Hy xc nh giao im ca cc ng thng ia qua A vung gc vi BC, i qua B vung gc vi AC, i qua C vung gc vi AB. Xt xem chng c ng quy khng? Bi 4: Cho ng trn (O) v mt im I khng nm trn ng trn. Vi mi im A thay i trn ng trn, ta xt hnh vung ABCD c tm l I. Tm qu tch ca cc im B, C, D. Bi 5: Cho tam gic ABC vung ti A v ng cao AD. Gi V l php v t tm D t s k=DA/DB v Q l php quay tm D gc quay l gc (DB,DA), F l php hp thnh ca V v Q. Hi php F bin tam gic ABD thnh tam gic no.

B

A I O C

D


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CHNG 5. O C V TNH TON5.1. Cc Cng C o c C Bn5.1.1. Tnh chi u di v kho ng cchTnh chiu di (Lenght) Cng c ny cho php chng ta o di ca mt on thng. Bc 1: chn on thng cn o di. Bc 2: dng lnh Php o > di

Tnh khong cch (Distance) Bc 1: chn im th nht ri chn im th hai. Bc 2: dng lnh Php o > Khong cch

5.1.2. Tnh chu viChu vi a gic (Perimeter) Bc 1: chn min trong ca a gic Bc 2: chn min trong ca a gic ri dng lnh Php o > Chu vi Chu vi ng trn (Circumference) Chn ng trn ri dng lnh Php o > Chu vi ng trn

5.1.3. Tnh gc v di n tchTnh gc(Angle) Chn gc cn o ri dng ln Php o > Gc


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Tnh din tch(Area) Ta cn chn min trong ca a gic cn o din tch ri dng lnh Php o > Din tch. Ring i vi ng trn, chng ta c th khng cn chn min trong m ch ch cn chn ng trn v dng lnh l .

5.1.4. Tnh s o cung v di cungTnh s o ca mt cung : chn cung ri chn lnh Php o > Gc ca cung hoc Php o > di cung

5.1.5. Tnh bn v t sBn knh(Radius) Lnh ny php tnh di bn knh ca mt ng trn hay cung trn. Bc 1: Chn ng trn hay cung trn cn tnh bn knh. Bc 2: Dng lnh Php o > Bn knh

Tnh t s gia 2 on thng (Ratio) Gi s c 2 on thng AB v CA, chng ta cn tnh t s AB/AC Bc 1: Chn on thng AB ri chn on thng AC. Bc 2: Dng lnh Php o > T s

5.1.6. My tnh (Calculator)Trong GSP s dng lnh S > My tnh (Alt+=) mt chic my tnh nh xut hin cho php bn tnh ton, to ra cc hm s, to ra cc tham s mi hay n gin l s dng li cc hm dng sn nh sin(), cos()


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Nt gi tr: gm gi tr ca cc hng nh s e, pi hay s o ca mt i tng no Bn cng c th to ra tham s mi y Nt Hm s : bao gm cc hm lng gic sin(), cos(), tan(), arcsin(), acrcos(), arctan(), hm tnh gi tr tuyt i (abs()), hm tnh cn bc 2(sqrt()), hm tnh lgagit N-pe(ln()), hm lgarit thp phn(log()), hm lm trn(round()), hm ly phn nguyn(trunc()), hm ly du(sgn()). Nt n v : nh Pixels(im nh), centime(cm), inches, radians(ra-di-an), degrees().

5.1.7. T a tnh ta ca mt im hay nhiu im trong h ta ta thc hin Bc 1: chn mt im hay nhiu im cn tnh ta . Bc 2: dng lnh Php o > Ta Khi tnh ta ca im trong h ta , nu bn khng ch ra h ta no cn tnh th mc nh GSP tnh theo (x,y) theo ta -Cc. Bn c th chn ta cc, hay ta hnh ch nht. Tnh honh ca im (x) Chn im cn tnh ri dng lnh Php o > Honh (x) Tnh tung ca im (y) Chn im cn tnh tung ri dng lnh Php o > Tung (y) Tnh khong cch theo ta Coordinate Distance Chn 2 im cn tnh khong cch ri dng lnh Php o > Khong cch theo ta

5.1.8. H s gc v phng trnhTrong GSP bn c th tnh c h s gc ca mt ng thng, on thng, tia. Bn cng c th tnh c phng trnh ca mt s i tng khi c i tng trn mt phng chng hn nh phng trnh ng thng khi c ng thng cho trc, phng trnh ng trn khi c ng trn cho trc. Tnh h s gc (Slope) Bc 1: chn i tng cn tnh h s gc. Bc 2: dng lnh Php o > H s gc Xem phng trnh ca i tng (Equation) Bc 1: chn i tng cn xem phng trnh. Bc 2: dng lnh Php o > Phng trnh ng chn Ch : Khi bn chn i tng no trong mt phng ri bn vo Menu Php o, nu lnh no c t en, th c ngha rng lnh hiu lc i vi i tng bn ang chn. Cn ngc li th i tng khng c h tr nhng lnh b t m.Blog: etoanhoc.blogspot.comTrang 30


5.2. Bi Tp p DngBi 1: Dng GSP thc hin cc yu cu sau: 1. V 2 im trn mt phng ri tnh khong cch gia chng. 2. V on thng ri tnh di on thng . 3. V ng thng, ng trn ri xem phng trnh ca n. 4. V on thng, ng thng ri tnh h s gc. 5. V tam gic, t gic ri tnh chu vi, din tch. 6. V ng trn, cung trn ri tnh chu vi, din tch. 7. V tam gic v tnh s o ca 3 gc. 8. V cung trn ri tnh bn knh, di cung, s o cung. 9. V 2 on thng ri tnh t s gia chng. 10. V 2 im tron mt phng ri tnh ta ca chng trong h ta . Bi 2: Cho ng trn (O,R) v mt im M thay i nm trn ng trn. Mt im A nm bn trong ng trn nhng khng trng vi tm O. Gi P l giao im ca ng trung trc ca on MA v on thng MO. 1. Khi M thay i trn (O,R) hy tm qu tch ca im P. 2. Tnh tng khong t P n A v t P n O. C nhn xt g v tng ? 3. Hy gii li bi ton trong trng hp A l mt im bt k v P l giao im ca ng thng MO vi ng trung trc ca on MA. Bi 3: V ng thng a v b. 1. Xem phng trnh ca ng thng a, b. 2. Hy xem phng trnh ca a l nh ca a qua php i xng trc b. 3. Hy xem phng trnh ca a l nh ca a qua php i xng trc b v php quay tm O gc 60 . 4. Tnh h s gc ca cc ng thng trn. Bi 4: Cho Elip (E) vi 2 tiu im F1 v F2 v M l mt im thay i nm trn (E). 1. Khi M thay i hy tnh chu vi v din tch ca tam gic M F1 F2. 2. Cho 2 im P v Q cng thuc (E). Tnh din tch tam gic F1PQ ri sau cho P v Q cng chuyn ng.


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CHNG 6. TH V H TA 6.1. Th (Graphic) ha l mt trong nhng th mnh ca my tnh m khi s dng cc cng c khc c th bn s khng gii quyt c vn . Vi GSP bn c th to ra h trc ta chun do GSP nh ngha trc, hoc bn c th t nh ngha h trc to theo c nhn bn v nh du n. Bn cng c th v th ca cc hm s phc tp hoc ch n gin l xc nh ta ca mt im no . Bn cng c th to ra cc bng gi tr, thy c s lin h gia hm s v cc bin

6.1.1. Xc nh h tr c t a cho h th ngNu nh GSP hin th ch Xc nh h ta trong Menu th th khi nu bn chn lnh ny th GSP s hin th mt h ta mc nh cho bn. Nhng nu bn chn mt hay mt s i tng no xy dng h trc ta th lnh trn c GSP thay th thnh mt trong cc lnh sau: Xc nh gc: Lnh ny hin th khi bn chn mt im no trn mt phng v bn mun im lm gc cho h ta bn khi to. Khi thc hin lnh ny th > Xc nh gc th GSP s khi to h ta vung gc c im gc l im do bn chn trc , n v o mc nh l 1 cm. Xc nh ng trn n v: Nu nh bn khi to mt ng trn no vi tm v bn knh xc nh trn mt phng. Sau , bn mun khi to mt h ta vi gc ta l tm ng trn v n v l bn knh ca ng trn (hay cn gi l ng trn n v) th lnh ny s gip bn. lm iu ny trc tin bn chn ng trn, ri sau s dng lnh th > Xc nh ng trn n v. Xc nh khong cch n v : Gi s rng trn mt phng bn v 2 im l A v B (on thng AB). Sau bn cng tnh khong cch gia chng ri. By gi, bn mun dng h trc ta vi n v l khong cch gia 2 im (bng di on thng AB) th lnh ny s gip bn. Nu bn chn mt trong 2 im A hoc B lm gc ta th khi khi to h ta mi, im A hoc B tng ng s l gc ta cn ngc li th gc ta l do GSP mc nh. lm iu ny, trc tin bn phi chn mt khong cch gia 2 im no (on thng no ) ri dng lnh th > Xc nh khong cch n v Xc nh khong cch n v : cc lnh trn bn thy rng chng ta hon ton c th to ra mt h ta Descartes vung gc vi n v do bn nh trc. By gi nu bn mun khi to h ta ch nht, vi n v trn trc honh v tung do bn chn trc th lnh ny s gip bn. lm iu ny bn hy chn mt di a no lm n v cho trc honh, chn tip di b no lm n v cho trc tung. Sau thc hin lnh th > Xc nh khong cch n v th mt h ta ch nht mi s khi to c n v trc honh l a v tung l b.

6.1.2. nh d u h tr c t a cho h th ngChng ta bit rng c th khi to nhiu h trc ta khc nhau trong mt mt phng. Trong GSP cng vy, trn mt mt phng bn hon ton c th khi to nhiu h trc ta khc nhau. Nhng bn hy nh rng ti mi thi im ch c duy nht mt h trc ta c chn lm h trc ta chnh. C ngha rng cng l cc h trc ta , nhng cc i tng ca h kia s phi biu th thng qua h ny mi cho n khi bn nh du mt h ta khc lm h trc cho h thng. lm iu ny bn thc hin nh sau: chn honh hoc tung ca h trc m bn mun nh du; sau dng lnh th > nh du h ta . thay i h trc ta h thng bn lm li cc thao tc trn. C mt ch nh l nu nh bn tnh ta ca cc im v cc Tn ca n ang hin th trn mn hnh, th khi bn thay i h ta chng s cha c cp nht, v th mun cho chng hin th ng bn phi tnh li.

6.1.3. Cc l i t a hi n thGSP cung cp cho chng ta 3 dng li ta tiu biu sau: Li h ta cc :. Khi chn lnh ny th > Kiu li > Li ta cc th cc i tng s c tnh ta theo h ta cc v li hin th cng hin th theo ta cc.Blog: etoanhoc.blogspot.comTrang 32


Li vung: Li ta vung (h ta Descartes). Khi chn lnh th > Kiu li > Li vung th cc i tng c tnh v hin th theo ta Descartes. Li ch nht: Li ta ch nht (h ta ch nht). th > Kiu li > Li ch nht

6.1.4.

n ho c hi n h t a v xc nh i m c t a nguyn

Khi lm vic vi cc i tng trong mt phng ca GSP i lc nu h trc ta hin th cng cm thy phin. Nu bn mun n chng i th cc lnh sau s gip bn. Hin li: lnh ny cho php bn n hoc hin h trc ta no do bn chn trc nu cha c h no c chn th GSP s hin th hoc n h mc nh. thc hin lnh ny trc tin bn hy chn h trc ta m bn mun n/hin sau bn dng lnh th > Hin li hoc th > n li . Nu nh ang Menu th v bn n Shift th lnh ny s tr thnh Hin h ta hoc n h ta Tch im: im c ta nguyn, nu nh lnh ny c chn ( th > Tch im) th cc im trn h ta ch hin th ti cc im c gi tr nguyn. Nu chn ri, bn chn tip ln na hy lnh ny.

6.1.5. D ng i m khi bi t t a c a nLnh ny cho php bn dng mi mt im khi bn c ta ca n trong mt phng. Nu l ta Descartes hay h ta hnh ch nht th l cp (x,y) tng ng vi honh v tung . Nu l h ta cc th s tng ng vi cp (r, ) . Khi thc thi lnh ny th > V im th mt hp thoi s xut hin:

6.1.6. T o ra tham s m iBn dng lnh th > Tham s mi to ra mt tham s mi trong bn v. Mt tham s l mt s c th d dng thay i gi tr. Rt thun tin cho bn khi bn mun to ra mt s nhng gi tr ca n c th thay i. Tham s c th c s dng trong vic tnh ton, trong cc hm s, trong cc php bin hnh. Cho v d l v th ca hm s y=ax+b mt cch tng qut trn mt phng th bn phi to ra 2 tham s l a v b c th thay i gi tr trong khong cho trc no . Hoc c th to ra mt tham s nhn gi tr t 0 n 360 cho mt php quay no . Khi bn chn lnh Tham s mi trong Menu S th mt hp thoi s xut hin:

Khi khi to c mt tham s v cho n nhn gi tr ban u ri. Nu bn mun gi tr ca tham s thay i th bn c th lm theo cc cch sau: 1. Dng cng c chn , Click p vo tham s, khi mt hp thoi s xut hin v cho php bn iu chnh thng s. 2. Chn tham s ri dng lnh Hin th > Tn tham s cho gi tr tham s thay i. 3. Chn tham s ri dng lnh Hiu chnh > Nt hnh ng > Chuyn ng to mt button m khi click vo th gi tr ca tham s s thay i theo.Blog: etoanhoc.blogspot.comTrang 33


6.1.7. T o ra m t hm s m iTrong GSP bn c th s dng lnh S > Hm s mi to ra mt hm s mi. Khi thc hin lnh ny th chic my tnh con s xut hin.

Vi chic my tnh con(Calculate) ca GSP bn c th to hoc bin tp: tnh ton; hm s. y xin gii thiu cch to ra mt hm s t Calculate ny. Gi tr: ti y bn c th ly cc gi tr hng s nh e, pi hay t cc tham s, di on thng, s o gc no do bn chn trc. Hm s: ti y bn c th s dng cc hm s c bn c sn trong GSP nh ngha hm s ca bn. n v: ti y bn c th chn n v cho bin ca hm s. Phng trnh ng: ti y bn c th chn loi hm s no m bn cn to ra. C cc loi sau: * y = f(x); x = f(y); r = f(); = f(r ) Sau khi chn xong cc thng s th n ng . Nu mun thay i hay sa li hm s th n p vo hm .

6.1.8. V th hm sV th ca mt hm s bt k l cng vic khng d cht no i vi nhng ngi hc ton nu khng ni l khng th lm c bng thc v compa. Tuy nhin gi y, nu s dng GSP bn s cm thy nh nhn hn. Nu bn to ra mt hm s ri v by gi bn mun v th ca hm s th bn c th: Click chut phi vo hm s v chn V th . Hoc chn hm s cn v th ri thc hin lnh th > V th


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Cn nu nh bn cha c mt hm s no trc hay mun v th ca mt hm s mi th bn thc hin lnh th > V th mi. Khi chic my tnh con s xut hin cho bn nhp cc thng s cho mt hm s. i khi hm s ny khng nm ht trong bn v, v gi tr ca x hoc y chy trong khong kh rng. gii hn li gi tr ca x , bn hy Click chut phi vo th v chn thuc tnh khi mt hp thoi xut hin cho php iu chnh gi tr ca x. Hoc bn cng c th iu chnh n v di ca h trc ta .

6.1.9. o hm v ti p tuy n ng congo hm GSP cho php bn tnh o hm ca mt hm s mt cch tng qut (o hm tr). tnh o hm th trc bn phi chn mt hm s. Bn cng c th tnh o hm cp 2, cp 3 ca mt hm bng cch chn o hm va tnh c v thc hin tnh o hm ln 2, 3 Khi thc hin tnh o hm xong, bn c th v th ca o hm va tnh ln mt phng. tch o hm bn lm nh sau: chn hm s ri sau hoc Click chut phi > o hm ca hm s hoc S > o hm ca hm s . Hnh sau y cho thy o hm cp 2 ca hm s mc trn v th ca chng.

Tip tuyn ng cong By gi chng ta p dng o hm vo v tip tuyn ca mt ng cong no . Chng ta bit rng o hm ca ca hm s ti mt im no thuc hm s chnh l h s gc ca tip tuyn ti im . p dng u ny v dng GSP chng ta c th d dng v tip tuyn ca mt ng cong. V d : V tip tuyn ca th hm s y = x 5x 3x + 3 1. V th ca hm s y = x 5x 3x + 3 bng cch thc hin lnh th > V th mi 2. Chn hm s v tnh o hm ca hm s trn bng lnh S > o hm ca hm s.Blog: etoanhoc.blogspot.comTrang 35


3. Dng mt im A no bt k trn th bng cch dng cng c im click vo th. Dng cng c chn chn im A va xc nh v thc hin lnh Php o > Honh (x), Php o > Tung (y) 4. Tnh f (xA) : Chn gi tr xA , chn hm s f (x) trn bng v v thc hin lnh S > My tnh khi my tnh con xut hin. Ti mc Hm s ca my tnh con hy chn f (x) v k ti mc Gi tr ca my tnh con hy chn xA ri click Ok. 5. V tip tuyn ca f(x) ti im A bng cch chn xA, yA, f (xA) ri thc hin lnh th > V th mi ri nhp hm s f (xA)*(x-xA)+yA vo my tnh con. Sau khi v xong tip tuyn, bn hy di chuyn im A di chuyn trn th f(x), khi tip tuyn cng thay i theo. V hnh sau y l kt qu:

6.1.10. L p b ng gi tr tng

ng

C l nu ai tng cm mt t giy v mt cy vit v ang chm ch theo di v ghi chp thng s ca mt i lng thay i no , mt i lng ang ph thuc i lng thay i ti mi gi tr ca n. Khi bn s cm thy s nng nhc ca cng vic. Nhng gi y nh GSP bn c th lm iu mt cch d dng vi chc nng to bng gi tr tng ng ca GSP. to mt bng gi tr bng hy chn i tng mun to bng gi tr tng ng v thc hin lnh S > Lp bng. hiu r hn chc nng ny ta cng i xt mt s v d sau: V d 1: Chng ta bit rng hng s =C , trong C l chu vi ca ng trn v R l bn knh. 2R

By gi chng ta s lp bng th hin gi tr chu vi ca ng trn, bn knh v t s ca chng khi ng trn thay i bn knh. Trc tin hy v ng trn (O,OA). Chn ng trn ri tnh bn knh bng lnh Php o > Bn knh, tnh chu vi bng lnh Php o > Chu ci ng trn. Chn gi tr bn knh, chu vi va tnh (xut hin trn bng v) ri tnh t sC bng lnh S > My tnh. By gi bn hy cho ng trn (O,OA) thay i bng cch di 2R

chuyn im A hoc im O. Khi bn thy R, C u thay i nhng t s th vn l hng. thy r hn chng ta i lp bng gi tr tng ng cho tng i lng bng cch: chn gi tr bn knh trn bng v v thc hin lnh S > Lp bng. Tng t cho chu vi v t s C/2R.


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By gi bn s c 3 bng mi bng u c 2 dng v dng u tin mi bng th hin tn ca i tng v dng th 2 th hin gi tr ca i tng . Gi chng ta thm d liu cho cc bng bng cch chn bng ri hoc Click chut phi > Thm bng d liu hoc S > Thm bng d liu. Lm cng vic ny cho ba bng trn. Ch rng khi thc hin lnh mt hp thoi s xut hin.

Cng vic cn li by gi l hy kch hot cho im A chuyn ng thay i cc gi tr ca ng trn (O,OA) v quan st cc bng. Chng ta s thy c rng GSP s thm 10 dng vo mi bng. C th chng ta c hnh sau y:

Nhn vo bng trn ta thy khi R v C u thay i nhng t s vn l 3.14. Ch : bn c th thm dng d liu vo bng th bn cng c th loi dng d liu hin c ra khi bng. loi mt dng d liu ra khi bng, bn hy chn bng ri hoc Click chut phi > Xa bng d liu hoc S > Xa bng d liu. Bn cng c th n p vo bng thm dng d liu mi v Shitf+Double-Click loi dng d liu.

6.2. Cc H Trc Ta GSP h tr hin th v v th theo 3 h ta l: H ta cc (Polar Grid); h ta Descartes (Square Grid); h ta ch nht (Rectangular Grid)

6.2.1. H t a c c mt phng lm vic ca GSP hin th li ta cc v cc i tng trn cng c tnh theo ta cc bn lm nh sau: Hoc l Click chut phi > Li ta cc hoc l th > Kiu li > Li ta cc. Khi thc hin lnh trn th mt phng s hin th li ta cc v cc i tng cng c GSP tnh theo ta dng (r,) . V d: V th ca ng trn c phng trnh l 4 sin() .


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6.2.2. T a Descartes v t a ch

nh t.

chn ta Descartes thc hin: hoc l Click chut phi > Li vung hoc l th > Kiu li > Li vung. hin th theo h ta ch nht ta thc hin: hoc l Click chut phi > Li ch nht hoc l th > Kiu li > Li ch nht Khi lm vic vi 2 h ta trn cc i tng c tnh ta theo dng (x,y) trong x l honh , y l tung . Theo mc nh th GSP chn h ta Descartes vi chiu di n v l 1cm. Nu thay i di ca n v th di chuyn im n v ( im trn trc honh v gn gc ta nht)

6.3. V Th Hm S Cho Bi Phng Trnh C Cha Tham S6.3.1. ng th ngng thng cho bi phng trnh tham s: (d) : x = x 0 + at vi t l tham s y = y0 + bt

Trong (x0;y0) l ta im trn (d), (a;b) l ta vector ch phng ca (d) Bc 1: Xc nh mt h trc ta . (C th chn h ta c sn bng lnh Click chut phi > Li vung) Bc 2: Xc nh tham s a v b bng lnh S > Tham s mi

Bc 3: Chn im A, tnh gi tr honh ca A bng lnh Php o > Honh (x) v tnh gi tr tung ca A bng lnh Php o > Tung (y) Bc 4: Chn gi tr xA v a , thc hin lnh: S > Hm s mi. Bn nhp hm s f(x) = xA + ax


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Bc 5: Chn gi tr yA v b , thc hin lnh: S > Hm s mi. Bn nhp hm s g(x) = yA + bx Bc 6: Chn hm s f(x) = xA + ax v g(x) = yA + bx , thc hin lnh th > V ng cong tham s

Thc hin 6 bc trn bn s c c th ca ng thng trn trn mt phng.


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6.3.2. ng trn:ng trn cho bi phng trnh tham s (C): x = a + R cos t vi R l bn knh v (a,b) l ta ca tm. y = b + R sin t

6.3.3. ng Elipng elip cho bi phng trnh b. x = x 0 + a cos t vi (x0;) l tm elip v 2a, 2b ln lt l di trc ln v trc y = y0 + bsin t


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6.4. Bi T p p D ngBi 1: Hy v th trong h ta cc ca cc ng cong c phng trnh sau: a. ng cong r = sin(3). b. ng xon c Archimede r = . c. ng cong c cho bi phng trnh r = 1 cos d. ng xon c logarit cho b phng trnh r = a.eb Bi 2: V th ca hm s y = sin x + cos2x . Mt im A di ng trn th , hy v tip tuyn ti A. Bi 3: V th ca ng Hypebol (H): trong p l mt s cho trc Bi 4: V th ca cc ng cong c cho bi phng trnh sau: a. ng Cycloid b. ng Astroid x = a(t sin t) y = a(t cos t) x2 a2

y2 b2

= 1 trong a, b l s cho trc v Parabol (P): y = 2px2

x = a.cos3 t

3 y = a sin t 3at x = 1 + t3 c. L Descartes 2 y = 3at 1 + t3


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CHNG 7. CNG C NGI DNG V HNH HC FRACTAL7.1. Cng C Ty BinKhi lm vic vi GSP i lc chng ta cm thy bt tin v c nhng cng vic chng ta phi lm i lm li kh nhiu ln. V d v mt tam gic, mt t gic hay mt lc gic iu ny l do GSP ch cung cp nhng cng c c bn nh im, thc k, compass. T nhng cng c ny chng ta c th dng nn nhng i tng hnh hc khc. Tuy nhin c mt iu rt hay, l GSP cho php ngi s dng to ra nhng cng c ring cho mnh l Cng c ty bin V d 1: Dng tam gic. Bc 1: dng 3 im bt k, dng 3 on thng qua 3 im c mt tam gic. Bc 2: chn tam gic va mi dng ri click v gi chut ln nt Cng c ty bin v chn To cng c mi

Bc 3: t tn cho Tn cng c ti hp thoi Cng c mi l Tam giac ri Click OK.

dng mt tam gic ngoi cch dng truyn thng ra bn cn mt cch nhanh hn l Click v gi chut ti nt Cng c ty bin v chn Tam giac.

Sau khi chn cng c Tam giac m bn va to, bn ch cn Click ti 3 im trn mt phng l bn dng c mt tam gic. Thc cht ca vic lm trn l bn bt GSP ghi nh li cch dng mt tam gic, v sau mun dng li mt tam gic bn ch cn gi lnh m bn va cho GSP nh. thy r hn bn hy chn cng c Tam giac ri chn lnh Hin kch bn Menu ca Cng c ty bin bn s thy cc bc dng nn tam gic. V d 2: dng mt lc gic u. Bc 1: V on thng AB bt kBlog: etoanhoc.blogspot.comTrang 42


Bc 2: Chn A lm tm v thc hin php quay 120 i vi B thu c C. Bc 3: Chn C lm tm v thc hin php quay 120 i vi A thu c D. Bc 4: Chn D lm tm v thc hin php quay 120 i vi C thu c E. Bc 5: Chn E lm tm v thc hin php quay 120 i vi D thu c F. Bc 6: Ni cc im Khi chng ta s thu c mt lc gic u. Bc 7: Chn lc gic u va mi dng ri chn nt Cng c ty bin v chn To cng c mi, t tn cho Tn cng c ti hp thoi Cng c mi l Luc gia deu ri Click OK

Nu chu b ra t thi gian, ngi dng nhng hnh cn thit ri thm n vo thanh cng c ty bin th sau mt thi gian, bn s cm thy thoi mi hn khi s dng GSP.

7.2. Hnh Hc FractalHnh hc Fractal l hnh hc nghin cu v cc hnh t ng dng. Mt hnh c gi l t ng dng nu nh mi mu nh ca n u cha mt b phn ng dng vi hnh , tc l khi phng to mt b phn no ca hnh theo mt t l thch hp ta s thu c mt hnh c th t chng kht ln hnh cho. Mi hnh t ng dng th c gi l mt Fractal, cc fractal lun lun l mt tc phm p i vi nhng ngi hc ton v to ra n cng l mt th thch c v s hiu bit v tnh nhn ni v n tn kh nhiu thi gian cho vic tnh ton, o c v v hnh Nhng gi y vi lnh Bin hnh > Php lp ca GSP th bn c th to ra mt fractal mt cch d dng v nhanh chng hn bao gi ht min l bn bit lm cch no to ra fractal . By gi hiu r hn v chc nng ny ca GSP chng ta hy i to ra mt vi Fractal no .

7.2.1. Th m SierpinskiBc 1: V tam gic ABC v dng 3 ng trung bnh ca chng: Bc 2: Chn 3 im A, B, C v thc hin lnh Bin hnh > Php lp khi mt hp thoi s xut hin nh hnh sau:

Bc 3: Cho im A bin thnh B (AD) bng cch Click vo im D (lu l im A phi ang c chn, nu im A khng c chn, khi bn click vo im D th im no bin thnh D ch khng phi A bin thnh D. Trong hnh trn im A ang c chn), B bin thnh chnh n (BB), C bin thnh E (CE) Bc 4: Nhn Ctrl+A hoc chn lnh Thm nh x mi t Cu trc to ra s bin i mi v cho AF, BE, CC. Bc 5: Tip tc nhn Ctrl+A v cho AA, BD, CF. Khi ta c nh hnh sau:Blog: etoanhoc.blogspot.comTrang 43


Bc 6: Click vo nt ng s thu c thm Sierpinski cho tam gic nh sau:

By gi bn hy chn dng chut qut chn thm bn va to v sau nhn phm + hai ln bn s thu c chic thm nh hnh k bn. hnh th nht, trong hp thoi Interate bn chn Number of interations: l 3. hnh th 2 do bn chn hnh u tin v nhn phm + hai ln nn s ln lp l 5. Nu mun gim s ln lp bn hy nhn phm

7.2.2. ng Von KochBc 1: V on thng AB. Bc 2: Dng B l nh ca B qua php v t tm A t s 2/3 v A l nh ca A qua php v t tm B t s 2/3 Bc 3: Dng B l nh ca B qua php quay tm A v gc quay l 60 . Bc 4: Dng cc on thng AA, AB, BB, BB v du i on AB. Bc 5: Chn A chn B v thc hin lnh Bin hnh > Php lp Cho AA, BA Ctrl+A: AA,BB Ctrl+A: AB, BB Ctrl+A: AB, BB Bc 6: Hin th > Ch lp ln cui Bc 7: Du i cc on thng AA, AB, BB, BB ta s thu c ng Von Koch nh sau:


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7.2.3. Cy PitagoBc 1: Dng on thng CD. Bc 2: Dng hnh vung ABCD nhn CD l mt cnh. Bc 3: Dng M l trung im ca AB. Bc 4: Thc hin php quay tm M mt gc ty chn trong khong 0 n 180 i vi im B thu c im C. Bc 5: Dng tam gic ABC. Bc 6: Dng hnh vung cnh AC, CB hng ra min ngoi tam gic. Bc 7: Chn D chn C v thc hin lnh Bin hnh > Php lp Cho DA, CC; Ctrl+A: DC, CB. Thc hin theo cc bc trn chng ta s thu c mt Fractal v n c gi l cy Pitago.

Mt s lu khi s dng php lp trong Menu Bin hnh Php lp ch c hiu lc khi bn chn cc i tng thc hin php lp l cc i tng t do. V trn cc i tng t do bn phi to ra mt vi i tng khc, nhng i tng ny c quan h con-cha vi cc i tng t do trc . Hay ni mt cch khc l bn phi thc hin mt vi php bin hnh t i tng t do ban u.


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Ti hp thoi Php lp Pre-Image: y l cc im to nh ca php lp. T cc im to nh-im ban u bn cho php n bin thnh cc im mi. First Images: y l cc im nh ca cc im bn nhm to nh.

Mc du s dng php lp khng kh, nhng nu mi ln u bn s dng s thy nhiu ch bi ri. V th hiu r n khng cn cch no khc l bn i thc hnh vi n.


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CHNG 8. DNG CC NG CONIC8.1. Parabol8.1.1. Parabol Cho B i ng Chu n V Tiu i m. dng Parabol khi bit tiu im v ng chun chng ta lm nh sau: 1. Dng ng thng d lm ng chun ca Parabol 2. Dng tiu im F (tt nhin l nm ngoi ng chun). 3. Dng mt im D trn ng thng d. 4. Dng ng trung trc ca on FD. 5. Dng ng vung gc vi d ti D. 6. Dng M l giao im ca 2 ng thng va to trn. 7. Chn im D ri tip tc chn M v thc hin lnh Dng hnh > Qu tch. 8. n i tt c cc i tng ngoi tr ng chun, tiu im v qu tch. 9. n Ctrl+A (chn tt c cc i tng cn li) v chn Cng c ty bin > To cng c mi. V t tn l Parabol. Sau khi tin hnh thc hin nhng bc nh trn bn dng c Parabol v t nay tr v sau bn c cng c dng Parabol khi bit tiu im v ng chun.

8.1.2. Parabol Qua Hai i m V Bi t Tiu i m1. Dng ba im A, F, B ln mt phng trong sketchpad. 2. Dng ng trn (A,AF) v (B,BF). 3. Dng tip tuyn chung ca 2 ng trn trn: a. Dng ng thng AB. b. Dng bn knh AM ca (A,AF). c. Dng bn knh BN ca (B,BF) sao cho AM//BN. d. Xc nh O l giao im ca ng thng MN v AB. e. Dng ng trn ng knh OA. f. Dng C l giao im ca ng trn va dng v (A,AM). g. Dng ng thng OC. h. Dng E l giao im ca OC v (B,BF). 4. Khi ta thy CE l tip tuyn chung ca 2 ng trn (A,AF) v (B,BF). 5. Dng im D trn tip tuyn chung CE. 6. Dng trung trc ca DF v ng thng qua D v vung gc vi CE. 7. Dng K l giao im ca 2 ng thng va dng. 8. Chn D ri chn K v thc hin lnh Dng hnh > Qu tch. 9. n i tt c cc i tng v ch li 3 im A, F, B v qu tch. 10. Chn lnh Cng c ty bin > To cng c mi v t tn l Parabol_2

8.2. ElipC rt nhiu cch khc nhau dng mt ng Elip nhng y ch xin gii thiu cch dng Elip khi bit 2 tiu im v mt im th 3 m Elip i qua. 1. 2. 3. 4. 5. 6. 7. 8. 9. Dng F1, F2, P. Dng on F1F2 v trung im D ca n. Dng on F2P v tia F1P. Dng ng trn (P, PF2) Dng E l giao im ca ng trn (P,PF2) vi tia F1P. Dng on F1E v F l trung im ca n. Dng on FF1v ng trn tm D c bn knh bng on FF1. Dng ng trung trc ca F1F2. Dng ng trn tm F2 v c bn knh bng FF1.Trang 47



10. Dng G, H l giao im ca ng trn va dng v ng trung trc ca F1F2. 11. Dng ng trn ng knh GH. 12. Dng mt im I thuc ng trn va dng. 13. Qua I dng ng thng song song vi F1F2. 14. Dng tia DI v J l giao im ca n vi ng trn tm D bn knh FF1. 15. Qua J dng ng vung gc vi F1F2 v K l giao im ca ng thng va dng vi ng thng qua I v song song vi F1F2. 16. Chn I ri chn K v thc hin lnh Dng hnh > Qu tch. 17. n i tt c cc i tng ngai tr F1, F2, P v qu tch. Ta thu c Elip.

8.3. HypebolDng mt hypebol khi bit hai tiu im v mt im m n i qua. 1. Dng tiu 2 tiu im A, B v mt im C m n i qua. 2. Dng ng thng AC. 3. Dng (C,CB). 4. Dng D l giao im ca on AC v (C,CB). 5. Dng (A,AD). 6. Dng mt im E trn (A,AD). 7. Dng on EB v F l trung im ca chng. 8. Dng ng trung trc ca EB 9. Dng ng trn (E, ED). 10. Dng ng thng EA. 11. Gi G l giao im ca EA v ng trung trc ca on EB. 12. Chn E ri chn G v thc hin lnh Dng hnh > Qu tch. 13. n tt c cc i tng ngoi tr A,B,C v qu tch ta thu c Hypebol 14. Chn tt c cc i tng v chn lnh Cng c ty bin > To cng c mi v t tn l Hypebol.

8.4. Elip Hoc Hypebol Khi C Tm Sai V Tiu imPhn ny chng ta s cng i dng mt ng Elip hay Hypebol khi bit tiu im v tm sai. 1. To ra mt tham s c tn l e v cho gi tr ban u l 0.75. 2. Tnh t s 1/e. 3. Dng 2 tiu im A, B. 4. Dng B l nh ca B qua php v t tm A, t s 1/e. 5. Dng (A,AB). 6. Dng mt im C trn ng trn (A,AB). 7. Dng on thng CB v ng trung trc ca n. 8. Dng ng thng CA. 9. Dng E l giao im ca 2 ng thng trn. 10. Chn C ri chn E v thc hin lnh Dng hnh > Qu tch. 11. n i tt c cc i tng ngoi tr tham s, 2 tiu im v qu tch.

8.5. Conic Qua Nm im1. 2. 3. 4. 5. 6. 7. 8. Dng nm im A, B, C, D, E. Dng ng thng AB, BC, CD, EA. Dng F l giao im ca DC v AE. Dng E ty , dng E l nh ca E qua php i xng tm E. Dng na ng trn c tm l E v qua EE.(chn E,E,E v Dng hnh > Cung trn ng trn ) Dng im G thuc na ng trn . Dng ng thng EG. Dng H l giao im ca EG v AB.Trang 48



9. Dng I l giao im ca EG v BC. 10. Dng ng thng FI. 11. Dng J l giao im ca FI v AB. 12. Dng ng thng DJ. 13. Dng im K l giao ca JD v EG 14. Chn G ri chn K v thc hin lnh Dng hnh > Qu tch. 15. n i tt c cc i tng ngoi tr qu tch v nm im ban u. 16. Chn tt c cc i tng cn li v thc hin lnh Cng c ty bin > To cng c mi lu cch dng li cho tin dng sau ny.


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CHNG 9. LI KTBit s dng cc tnh nng c bn ca mt phn mm l mt vn hu nh khng bao gi kh. Tuy nhin tn dng v khai thc ht cc tnh nng ca phn mm th hu nh lun lun li l mt iu khng d. Rt kt kinh nghim t chnh mnh, mt ngi cha tng s dng Geometer's Sketchpad trc . Qua thi gian t tm hiu v hc hi (ch yu t nhng ti liu trn Internet) ti cn thn ghi nhn li nhng kh khn m mnh gp phi khi tip cn vi phn mm. T ch cha bit g, n ch s dng tng i ti cng phi mt mt khong thi gian nht nh. Vi mong mun gip nhng ngi cha tng s dng GSP trc kia. Ti son ti liu hng dn ny, n c thit k cho nhng ngi mi u lm quen vi GSP. Tuy nhin cng c th l ti liu tham kho, cng nh ni trn, GSP cng l mt phn mm v th bit s dng n cng l mt iu khng kh, nhng lm sao khai thc ht tnh nng ca phn mm l iu khng d. Nu bn thc s mun lm ch phn mm, th li khuyn tt nht l bn hy ng dng n vo vic gii cc bi ton bn ang dy hay ang hc hng ngyqua qu trnh bn lm vic vi phn mm, bn s khm ph ra rt nhiu iu b ch. GSP l mt phn mm 2D (hnh hc 2 chiu) tuy nhin bn cng c th ng dng n vo gii mt s bi ton hnh hc khng gian nht nh. Do c th ch thit k cho 2D nn bn s mt thi gian khi ng dng vo th gii 3D. Mt li khuyn thc sc l nu dng trong mi trng 3D th tt nht l bn nn s dng Cabri 3D, n s d dnh hn cho cc thao tc dng hnh ca bn. GSP l mt phn mm thin nhiu v ng dng cho ton, tuy nhin bn cng c th ng dng vo to cc m hnh cho vt l hay ha hc. Cui cng, mc du ti c rt c gng nhng chc chn khng th khng mc nhng thiu st nht nh. Mong rng ti s nhn c kin gp ca cc bn khi tham kho ti liu ny.


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