huong dan su dung gspvit5.0

8/7/2019 Huong Dan Su Dung GspVit5.0

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Bin son : H Quc VnTHPT NGUYN HU


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Hng dn s dng Geometer's Sketchpad

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CHNG 1. MU1.1. Gii thiu......................................................................................................................................................... 41.2. Bt u Lm Quen Vi GSP. ......................................................................................................................... 5

1.2.1. Giao din ngi dng ............................................................................................................................... 51.2.2 Cc cng c cbn:................................................................................................................................... 51.2.2. Kho St Cc Menu.................................................................................................................................. 7

Menu Tp........................................................................................................................................................ 7

Menu Hiu chnh ............................................................................................................................................ 8Menu Hin th............................................................................................................................................... 11Menu Dng hnh........................................................................................................................................... 11Menu Bin hnh ............................................................................................................................................ 12Menu Php o............................................................................................................................................... 12Menu S........................................................................................................................................................ 13Menu th.................................................................................................................................................. 13

CHNG 2. CC I TNG HNH HC C BN CHC NNG V QUAN H GIA CHNG2.1. Cc i Tng Hnh Hc CBn V Chc Nng Ca Chng .................................................................... 14

2.1.1. im ....................................................................................................................................................... 142.1.2. ng trn ............................................................................................................................................. 15

2.1.3. on thng, ng thng v tia............................................................................................................. 152.1.4. Vit ch .................................................................................................................................................. 16

2.2. Quan H Gia Cc i Tng Hnh Hc ..................................................................................................... 162.3. i tng ng.............................................................................................................................................. 17CHNG 3. DNG HNH V QU TCH3.1. Cc Cng C Dng Hnh CBn ................................................................................................................. 18

3.1.1. Dng mt im trn i tng. .............................................................................................................. 183.1.2. Dng trung im ca mt on thng .................................................................................................... 183.1.3. Dng giao im ca 2 i tng ............................................................................................................ 183.1.4. Dng on thng, tia, ng thng. ....................................................................................................... 183.1.5. Dng ng thng i qua mt im v song song vi ng thng cho trc ..................................... 183.1.6. Dng ng thng vung gc vi ng thng cho trc .................................................................... 183.1.7. Dng ng phn gic ca mt gc cho trc ...................................................................................... 183.1.8. Dng ng trn bit tm v mt im thuc ng trn..................................................................... 183.1.9. Dng ng trn khi bit bn knh v tm............................................................................................. 193.1.10. Dng cung trn ng trn .................................................................................................................. 193.1.11. Dng cung trn i qua 3 im.............................................................................................................. 193.1.12. Dng min trong ca mt i tng .................................................................................................... 19

3.2. Qy Tch Ca Mt im Hay i Tng .................................................................................................... 193.3. Bi Tp p Dng........................................................................................................................................... 21CHNG 4. PHP BIN HNH4.1. Cc Cng C Bin Hnh CBn................................................................................................................... 24

4.1.1. Php tnh tin.......................................................................................................................................... 24Tnh tin theo vector chn trc.............................................................................................................. 24

4.1.2. Php quay ............................................................................................................................................... 244.1.3. Php v t................................................................................................................................................ 25

T s v tuc nhp t hp thoi................................................................................................................ 254.1.4. Php i xng trc.................................................................................................................................. 26

4.2. Bi Tp p Dng........................................................................................................................................... 27CHNG 5. O C V TNH TON5.1. Cc Cng Co c CBn ....................................................................................................................... 28

5.1.1. Tnh chiu di v khong cch ............................................................................................................... 28

Tnh chiu di (Lenght)................................................................................................................................ 28Tnh khong cch (Distance)........................................................................................................................ 285.1.2. Tnh chu vi.............................................................................................................................................. 28

Chu vi a gic (Perimeter)............................................................................................................................ 28Chu vi ng trn (Circumference) ............................................................................................................. 28

MC LC


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5.1.3. Tnh gc v din tch .............................................................................................................................. 28Tnh gc(Angle) ........................................................................................................................................... 28Tnh din tch(Area) ..................................................................................................................................... 29

5.1.4. Tnh so cung v di cung.............................................................................................................. 295.1.5. Tnh bn v t s ..................................................................................................................................... 29

Bn knh(Radius).......................................................................................................................................... 29Tnh t s gia 2 on thng (Ratio)............................................................................................................. 29

5.1.6. My tnh (Calculator) ............................................................................................................................. 295.1.7. Ta ..................................................................................................................................................... 30Tnh honh ca im (x).......................................................................................................................... 30Tnh tung ca im (y) ............................................................................................................................ 30Tnh khong cch theo ta Coordinate Distance..................................................................................... 30

5.1.8. H s gc v phng trnh ..................................................................................................................... 30Tnh h s gc (Slope).................................................................................................................................. 30Xem phng trnh ca i tng (Equation) ............................................................................................... 30

5.2. Bi Tp p Dng........................................................................................................................................... 31CHNG 6. TH V H TA 6.1. Th (Graphic) ........................................................................................................................................... 32

6.1.1. Xc nh h trc ta cho h thng ..................................................................................................... 326.1.2. nh du h trc ta cho h thng .................................................................................................... 326.1.3. Cc li ta hin th .......................................................................................................................... 326.1.4. n hoc hin h ta v xc nh im c ta nguyn ................................................................. 336.1.5. Dng im khi bit ta ca n .......................................................................................................... 336.1.6. To ra tham s mi ................................................................................................................................. 336.1.7. To ra mt hm s mi........................................................................................................................... 346.1.8. V th hm s..................................................................................................................................... 346.1.9. o hm v tip tuyn ng cong........................................................................................................ 35

o hm........................................................................................................................................................ 35Tip tuyn ng cong................................................................................................................................. 35

6.1.10. Lp bng gi tr tng ng ................................................................................................................... 366.2. Cc H Trc Ta ...................................................................................................................................... 37

6.2.1. H ta cc.......................................................................................................................................... 376.2.2. Ta Descartes v ta ch nht. ..................................................................................................... 38

6.3. V Th Hm S Cho Bi Phng Trnh C Cha Tham S ................................................................... 386.3.1. ng thng ........................................................................................................................................... 386.3.2. ng trn: ............................................................................................................................................ 406.3.3. ng Elip ............................................................................................................................................. 406.4. Bi Tp p Dng....................................................................................................................................... 41

CHNG 7. CNG C NGI DNG V HNH HC FRACTAL7.1. Cng C Ty Bin......................................................................................................................................... 427.2. Hnh Hc Fractal ........................................................................................................................................... 43

7.2.1. Thm Sierpinski...................................................................................................................................... 437.2.2. ng Von Koch ................................................................................................................................... 447.2.3. Cy Pitago .............................................................................................................................................. 45

Mt s lu khi s dng php lp trong Menu Bin hnh........................................................................... 45CHNG 8. DNG CC NG CONIC8.1. Parabol........................................................................................................................................................... 47

8.1.1. Parabol Cho Bi ng Chun V Tiu im...................................................................................... 478.1.2. Parabol Qua Hai im V Bit Tiu im............................................................................................ 47

8.2. Elip ................................................................................................................................................................ 47

8.3. Hypebol ......................................................................................................................................................... 488.4. Elip Hoc Hypebol Khi C Tm Sai V Tiu im ..................................................................................... 488.5. Conic Qua Nm im ................................................................................................................................... 48CHNG 9. LI KT


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CCHHNNGG 11.. MMUU

1.1. Gii thiu

Ngy nay tin hc c vai tr ht sc quan trng trong cuc sng, c th ni hu nh khng c bt kmt ngnh no m khng ng dng tin hc. V th, gio dc cng khng nm ngoi phm vi . ng dng tinhc vo vic hc v dy lun lun l mt trong nhng vn c nhiu ngi quan tm. c bit l cc quthy c gio cng nh nhng sinh vin s phm ang hc chun bc lm thy, c...

Phn mm hnh hc ng Geometer's Sketchpad (GSP) l mt phn mm thc s hay v b ch v tinghbt c mt gio vin ton no cng nn bit. V th, vi s hiu bit t i v tin hc ca mnh, ti bin sonti 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 cabri2D v 3D. Hin nay, ti Vit Nam c nh phn phi v bn ting Vit ca Cabri. Bn c th tham kho thmti a chwww.cabri.com

- Geogebra: l phn mm hnh hc ng c pht trin bi mt tin sngi o. L phn mm min ph, mngun mv hin ny c vit ha gn nh 100%. Bn c th tham kho thm ti a chwww.geogebra.org.

- C.a.R: l mt phn mm hnh hc ng (Dynamic Geometry) c vit trn ngn ng Java m ngun mvhon ton min ph. C.a.R (Circle And Rules) nh gn, tng i d s dng. Gio s ton hc ni ting cac,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 cabn 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 phnmm gio dc v sch tham kho ni ting ca M. Phn mm ny c Vit ha (tnh n V5.00). GSP cnhng 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 MHznhng vn chy tt GSP). C th sao chp tp tin thc thi l chy c ngay m khng cn ci t. iu ny rtc 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 khngc ngha rng Skechpad khng c nhc im. Tuy nhin, ti nghbn c th d dng chp nhn mt vi nhcim 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 vowww.google.com v dng cc t kha hnh hc ng; GSP; Cabri; Geogebra.... Bn c th ti phn mmGSP 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. Rtmong nhn c s gp ca cc bn va ch email: [email protected]


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1.2. Bt u Lm Quen Vi GSP.

1.2.1. Giao din ngi dng

Giao din chnh ca phn mm:

1.2.2 Cc cng c cbn:

Cng c chn : Bn dng cng c ny chn mt hay nhiu i tng no trn mt phng. Nu saukhi chn cng c ny, bn click v gi chut tri (drag) vo i tung th bn c th di chuyn n trn mtphng.Bn cng c th dng cng c ny dng giao im ca 2 i tng no bng cch click vo v tr giaoim .

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 mti 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 tngquanh 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 trv chn cng c chn.

Cng cim : cng c ny dng to ra mt IM trn mt phng. Sau khi click chut vo cng cny, bn ch vic click chut vo mt phng, ch m bn mun IM xut hin.


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

Cng cCompa : dng vng trn trn mt phng. Bn ch cn ba ci click: ci u tin click vobiu tng ca cng c Compa; ci th hai click vo mt phng xc nh tm ca ng trn; ci th 3 clickvo v tr bt k trn mt phng.

Sau khi vc ng trn, bn c thiu chnh li kch thc ng trn sao cho hp yu cu ca bn bngcch dng cng c chn, click vo tm hoc im th hai xc nh c ng trn v sau ko (drag) ntrn mt phng.

Cng c thc thng : dng cc i tng nhon thng, on thng i qua 2 im cho trc,ng thng, ng thng qua 2 im cho trc, tia.Cng ging nhcng 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 van thng, tia v ng thng.

Cng c dng min a gic:Cng ging nhcng 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 ngbin v ng bin.

Cng c vn bn : dng to nhn cho cc i tung khc hoc cc ghi ch, cc dng ch theo yu cuca bn trn mt phng.

Ch : Bn c th g ting Vit trong GSP bng bng m Unicode, VNI Windows,

Cng c vit - v tdo: 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 trnhng cng c cbn nhim(point), ung trn (circle), onthng (segment), ng thng(line) v tia(ray). Trong qu trnh s dng GSP chc chc c nhng hnh bnthng xuyn s dng, chng hn nh tam gic, tc gic, hnh thoi, hnh vung V vy trnh lp i lp limt 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. Nhcng c nym 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. Kho St Cc Menu

Menu Tp

Trong cc Menu trn bn cn ch mc Ty chn ti liu, bn c th to thm trang, i tn trang hocxa 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 voth bn hy copy bc nh trong mt chng trnh xlnh no (v d nhchng trnh Paint). Ri dn(Paste) nh vo mt phng ang lm vic. Lc hnh nh strthnh 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 sn hoc hin mt itng 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 imA di chuyn n im B. Nhl 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 sc din rahng 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 mtphng 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 nhsau, gm c 3 th (Tab)

ThChuyn ng

ThTn

Thi tng


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Hp thoi Chuyn ng ti ch ca Nt hnh ng:

Trong hp thoi trn cc thi tng, Tn cng c chc nng gn ging nh trong hp thoi Chuyn ng.

Tuy nhin, c 2 ty chn bn cn ch li theo sau mc tiu chuyn ng

vn v tr ban u ca mc

tiu chuyn ngV d: Trong mt phng, ti mun cho im A di chuyn n im B. Nhng im B khng cnh, m imB l im chuyn ng. Lc , nu bn ch mun im A di chuyn n v tr ban u, trc khi im B dichuyn th bn hy chn n v tr ban u ca mc tiu chuyn ng, cn nu bn mun im A rt theoim 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 Clickvo nt Ok cc thng s c hiu lc.

Gi s rng, bn vc 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 lnhChuyn 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 buttonmi 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 r ng, khi lm vic vi cc i tng trn mt phng th chut phi rt c ch cho bn. Hy clickchut phi vo mti tng no , v xem menu ngcnh hin ln bn sthy rt nhiu iu tin ch nmtrong .Khi ang trong menu Edit bn hy n phm Shitf bn sthy c sthay i.


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Menu Hin th

Menu Dng hnh

Xin hy ch l bn mun dng mti 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 mnht). Trong hnh trn cc lnh u cha hiu dng.


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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 shin 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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CCHHNNGG 22.. CCCCII TTNNGG HHNNHH HHCC CCBBNN CCHHCCNNNNGG VV QQUUAANN HH GGIIAA CCHHNNGG

2.1. Cc i Tng Hnh Hc C Bn V Chc Nng Ca Chng

2.1.1. im

* Vmtim:

Bc 1: dng chut tri click vo cng cBc 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 st nhn cho im theo tn cc ch ci A, B, C. vang 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 bngcch dng cng c chn v di chuyn im i.* imchuynng: bn cng c th to ra mt im chuyn ng bng cch chn lnh Chuyn ng imtrong menu ng cnh hay trong Menu Hin th. Khi mt hp thoi nh s xut hin cho php bn iukhin s chuyn ng ca im. Nu bn chn thm Vt im th im va chuyn ng va li du vt.* imA di chuynnim B: trn mt phng bn v 2 im A v B. By gibn mun to mt button mkhi click vo button ny th im A s di chuyn n im B. Th bn lm nh sau:

Bc 1: dng cng cim vim 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 chBc 4: Click chut ln button mi xut hin .


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2.1.2. ng trn

Trong GSPng trn c th xc nh khi bit tm v bn knh hoc tm v mt im th hai thuc ngtrn.* Vng 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 thhai.

* im trn ng trn: sau khi v xong ng trn. Nu bn mun xc nh mt im trn ng trn th bnclick chut tri vo cng cim ri click chut tri ln ng trn. Lc im mi khi to s nm trnng trn. Bn hy th dng chut drag im mi to , v s thy n khng di chuyn t do na, m dichuyn trn ng trn.

2.1.3. on thng, ng thng v tia.Ba cng c von thng, ng thng, tia c gom chung vo mt nhm l Cng c dng on thng. Bnhy n v gi chut tri ln cng cCng c dng on thng bn s thy xut hin cc cng c cn li

.* Von thng :

Bc 1: click chut voBc 2: click chut vo 2 v tr khc nhau hoc 2 im phn bit trn mt phng.

* Vng thng:

Bc 1: click chut voBc 2: click chut vo 2 v tr khc nhau hoc 2 im phn bit trn mt phng.

* Vtia:

Bc 1: click chut voBc 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 bnkhng mun chn i tng th bn n phm ESC hoc click chut tri vo mt ch trng no trn mtphng. 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. Vit ch

Khi lm vic vi GSP bn c th vit ch xen k vi v hnh. Bn cng c th nhp nhng cng thc ton vcc cng thc hnh hc. Bn cng c th vit ch Vit vo bng v.* Vit ch

Bc 1: click chut tri voBc 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 Hc

Chng ta cn bit rng quan h gia cc i tng hnh hc l mt trong nhng iu cbn nht, ct linht xy dng nn mt phn mm hnh hc ng. GSP cng vy, ton b cc i tng hnh hc trong phnmm u c th kt ni vi nhau theo nhng qua h ton hc cht ch. Nhs kt ni gia cc i tng theoquan h ton hc cht ch ny m cc i tng ca phn mm c th to nn mt h thng ng. chnh lcha kha to ra sc mnh cho phn mm-khi mt i tng thay i, th nhng i tng c quan h vi n tnhiu cng thay i theo.

Quan h gia cc i tng hnh hc trong GSP l mt quan h cha- con (parent-children) hay cn gil quan h ph thuc. Ni nh vy khng c ngha rng tt c cc i tng tn ti trong mt phng ca phnmm 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 vmt cch c lp, tc l vim B khng ph thuc vo cch vim A th c th xem rng 2 i tng imA v B chng c quan h g vi nhau c, nhng nu bn v mt on thng AB, v tip bn v mt im Cnm trn an thng AB th lc ny thc s c mi quan h. on thng AB l i tng cha ca i tngim 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 nhvo s xc nh ca im A v im B. V thonthng 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 chuynA hoc B bn s thy rng cc i tng con ca chng l on AB v im C cng s di chuyn theo. Cn


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im C, n l i tng con ca on thng AB do bn khng th di chuyn n mt cch t do na, m nch c th di chuyn trn on thng AB. Do vy c th ni mt i tng c khi to trc l cha ca mti 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 lquan h mt-nhiu. iu ny c ngha rng, mt i tng trong GSP c th l cha ca nhiu i tng khc vngc 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 ci tng con.

Ngc li, bn mun xem nhng i tng no l cha ca mt i tng. Bn lm nh trn nhng bc 2bn thay bng lnh Hiu chnh > Chn tt ci tng cha.

2.3. i tng ng

Thit ngh, s c mt thiu sot ln nu khi tm hiu phn mm hnh hc ng (Dynamic Geometry) m khngnhc 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 itng m bn khng th no lm c vi mt cy bt v mt tgiy. 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 kchhot 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 can. Ngc li, nu mt i tng cha chuyn ng th tt c cc i tng con ca n cng chuyn ng theo.

Khi thm l nh Hin th > Vti tng hoc Click chut phi > Vti tng bn s thy qu tch ca mti tng khi n chuyn ng.


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CCHHNNGG 33.. DDNNGG HHNNHH VV QQUU TTCCHH

3.1. Cc Cng C Dng Hnh C Bn

3.1.1. Dng mtim trni tng.

Cng c ny cho php bn dng mt im mi l i tng con ca mt i tng cha no do bn chntrc. im mi khi to s khng b rng buc g thm ngoi vic n l i tng con ca i tng bn chntrc . thc hin lnh dng hnh ny bn dng lnh Dng hnh > im thucCn ch thm l khi bn cha chn mt i tng no dng im ln th n s b mnht i

Nhng khi bn chn th

3.1.2. Dng trungim ca mton thng

Lnh 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. Dng giaoim ca 2i tng

Lnh 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. Dngon thng, tia, ng thng.

Bc 1: Chn 2 im.Bc 2: on thng: Dng hnh > on thng (Ctrl+L)

ng thng: Dng hnh > ng thngTia: Dng hnh > Tia

3.1.5. Dngng thngi qua mtim v song song ving thng chotrc

Bc 1: chn ng thng hay on thng lm phng v im m ng thng cn dng i quaBc 2: Dng hnh > ng song song

3.1.6. Dngng thng vung gc ving thng cho trc

Bc 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. Dngng phn gic ca mt gc cho trc

V d ti cn dng ng phn gic caABC 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. Dngng trn bit tm v mtim thucng trn

Bc 1: chn tm v mt im thuc ng trn.Bc 2: Dng hnh > ng trn bit tm + im


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3.1.9. Dngng trn khi bit 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. Dng cung trnng trn

Bc 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 haibn chn l im bt u ca cung v im cui cng bn chn l im kt thc ca cung (cung c v theochiu dng)

3.1.11. Dng cung trni qua 3im

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

3.1.12. Dng min trong ca mti tng

Bc 1: chn i tng bn mun dng min trongBc 2: Dng hnh > Min trong (Ctrl+P)

3.2. Qy Tch Ca Mt im Hay i Tng

Mt trong nhng iu tht tuyt vi m phn mm GSP em li cho chng ta l kh nng tm qu tch camt i tng hnh hc. Tt nhin l GSP khng c kh nng chng minh c qu tch ca mt i tnghnh hc m n v nn qu tch. Nhng n c th gip chng ta hnh dung c qu tch ca i tng trckhi 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 thucvo 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 dngim 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 tchV y l kt qu m chng ta thu c khi thc hin nhng bc dng hnh trn.


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B n hy double-click vo nhn ca i tng no m bn mun thay i tn.

By gicng bi ton dng hnh v tm qy tch trn. Nhng chng ta khng mun GSP v nn qu tch nhanhnh 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 7bng 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 gicOAC. 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 dl 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 Dng

Bi tp 1: Hy dng cc cng c dng hnh cbn 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 dngxong, cc bn c th cho cc i tng khng cn thit n i, cn li hnh chnh, hnh m ta cn dng. (chni 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 thmA[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 trungim ca cc on thng ni trc tm vi cc nh ca tam gic th cng nm trn mt ng trn. Ngi ta ging 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 ngphn 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 Mkhi C thay i.

m

MO

B

C

Bi tp 5 Cho AB l on thng cnh. Ax, By l hai tia song song vi nhau v nm cng bso vi ngthng AB. Gi Am v An ln lt l hai ng phn gic ca cc gc xAB v ABy. Hy v qu tch giao imca hai ng phn gic .

Bi 6: Cnh ca mt hnh thoi ABCD c chiu di khng i, v tr ca AB cnh, 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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CCHHNNGG 44.. PPHHPP BBIINN HHNNHH

4.1. Cc Cng C Bin Hnh C Bn

4.1.1. Php tnh tin

Chng 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 ramc 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 trl Ta cc v Ta chnht.

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 hnhtheo 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 quay

Ta bit rng xc nh mt php quay chng ta cn c tm quay v gc quay. Trong GSP cng vy. quaymt i tng hnh hc, chng ta cng phi cn chn mt im lm tm quay v mt gc quay. Gc quay nychng ta c thnh du t mt gc no c trong mt phng hoc chng ta c th chn theo thng snhp 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 > nhdu 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, chophp bn chn gc quay. (chiu gc quay tnh theo chiu ngc kim ng h-chiu dng)


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By gigi s rng trong mt phng ta c mt gc XBY no v mt ng trn (O). Ta cn thc hinphp 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 gcBc 3: chn ng trn v dng lnh Bin hnh > Php quay

4.1.3. Php vt

Mt 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 phibit 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 nhdu t mt t s gia hai an thng no trong mt phng.

T s v tuc nhp thp thoi.

Bc 1: nh du tm quay. (chn im mun lm tm quay, ri dng lnh Bin hnh > nh du tm quay, vt 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 hinnh sau:


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By gigi s rng ta mun cn v tng 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 sBc 3: chn ng trn v dng lnh Bin hnh > Php v t

C

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, bnch cn di chuyn im B l php v t s thay i theo.

4.1.4. Phpi xng trc

Trong GSP mt php i xng trc sc xc nh nu c mt ng thng hoc mt on thng lm trc ixng. 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 trci 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 trcHnh sau y cho thy nh ca mt ng trn qua trc i xng l mt ng thng v mt on thng.

O2

O1O

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, thchng ta dng php quay v gc quay bng 180.


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4.2. Bi Tp p Dng

Bi 1: Cho ng trn (O) vi ng knh AB cnh, mt ng knh MN thay i. Cc ng thng AM vAN 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, Cl cc im i xng vi P ln lt qua cc ng thng AI, BI, CI. Hy xc nh giao im ca cc ngthng AA, BB, CC v drag im P trong tam gic ABC. C thm kt lun g v giao im ca 3 ng thngtrn?

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 gcC. Hy xc nh giao im ca cc ng thng ia qua A vung gc vi BC, i qua B vung gc vi AC, iqua 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 ngtrn, 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 lphp quay tm D gc quay l gc (DB,DA), F l php hp thnh ca V v Q. Hi php F bin tam gic ABDthnh tam gic no.

B

CO

I


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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 ngtrn, chng ta c th khng cn chn min trong m ch ch cn chn ng trn v dng lnh l .

5.1.4. Tnh so cung v di cung

Tnh so ca mt cung : chn cung ri chn lnh Php o > Gc ca cung hoc Php o > di cung

5.1.5. Tnh bn v ts

Bn 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/ACBc 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, tora 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 so ca mt i tng no Bn cng c th to ra

tham s mi yNt Hm s: bao gm cc hm lng gic sin(), cos(), tan(), arcsin(), acrcos(), arctan(), hm tnh gi tr tuyti (abs()), hm tnh cn bc 2(sqrt()), hm tnh lgagit N-pe(ln()), hm lgarit thp phn(log()), hm lmtrn(round()), hm ly phn nguyn(trunc()), hm ly du(sgn()).Ntn v : nh Pixels(im nh), centime(cm), inches, radians(ra-di-an), degrees().

5.1.7. Ta

tnh ta ca mt im hay nhiu im trong h ta ta thc hinBc 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 cphng trnh ca mt si tng khi c i tng trn mt phng chng hn nh phng trnh ngthng 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 ch trnhng lnh b t m.


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5.2. Bi Tp p Dng

Bi 1: Dng GSP thc hin cc yu cu sau:1. V 2 im trn mt phng ri tnh khong cch gia chng.2. Von thng ri tnh di on thng .3. Vng thng, ng trn ri xem phng trnh ca n.4. Von thng, ng thng ri tnh h s gc.5. V tam gic, t gic ri tnh chu vi, din tch.6. Vng trn, cung trn ri tnh chu vi, din tch.7. V tam gic v tnh so ca 3 gc.8. V cung trn ri tnh bn knh, di cung, so 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 ngtrn 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: Vng 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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CCHHNNGG 66.. TTHH VV HH TTAA

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 skhng gii quyt c vn . Vi GSP bn c th to ra h trc ta chun do GSP nh ngha trc,

hoc bn c th tnh ngha h trc to theo c nhn bn v nh du n. Bn cng c th v thca cc hm s phc tp hoc chn gin l xc nh ta ca mt im no . Bn cng c th tora cc bng gi tr, thy c s lin h gia hm s v cc bin

6.1.1. Xcnh h trc ta cho h thng

Nu nh GSP hin th ch Xc nh h ta trong Menu th th khi nu bn chn lnh ny th GSP shin th mt h ta mc nh cho bn.Nhng nu bn chn mt hay mt si tng no xy dng h trc ta th lnh trn c GSP thayth 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 lmgc 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 vo 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 trnmt phng. Sau , bn mun khi to mt h ta vi gc ta l tm ng trn v n v l bn knh cang trn (hay cn gi l ng trn n v) th lnh ny s gip bn. lm iu ny trc tin bn chnng 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 cchgia 2 im (bng di on thng AB) th lnh ny s gip bn. Nu bn chn mt trong 2 im A hoc Blm gc ta th khi khi to h ta mi, im A hoc B tng ng s l gc ta cn ngc li th gcta 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 ginu bn mun khi to h ta ch nht, vi nv trn trc honh v tung do bn chn trc th lnh ny s gip bn. lm iu ny bn hy chn mt dia 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 vtung l b.

6.1.2. nh du h trc ta cho h thng

Chng ta bit rng c th khi to nhiu h trc ta khc nhau trong mt mt phng. Trong GSPcng vy, trn mt mt phng bn hon ton c th khi to nhiu h trc ta khc nhau. Nhng bn

hy nhrng ti mi thi im ch c duy nht mt h trc ta c chn lm h trc ta chnh. Cngha rng cng l cc h trc ta , nhng cc i tng ca h kia s phi biu th thng qua h nymi cho n khi bn nh du mt h ta khc lm h trc cho h thng. lm iu ny bn thchin 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 thtrn mn hnh, th khi bn thay i h ta chng s cha c cp nht, v th mun cho chng hinthng bn phi tnh li.

6.1.3. Cc li ta hin th

GSP 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 sc tnh ta theo h ta cc v li hin th cng hin th theo ta cc.


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

Li chnht: Li ta ch nht (h ta ch nht). th > Kiu li > Li chnht

6.1.4. n hoc hin h ta v xcnhim c ta 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 noc 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 nhangMenu th v bn n Shift th lnh ny s trthnh 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. Dngim khi bit ta ca n

Lnh 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 > Vim th mt hp thoi s xut hin:

6.1.6. To ra tham s mi

Bn dng lnh th > Tham s mi to ra mt tham s mi trong bn v. Mt tham s l mt s c th ddng 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 thc 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 ththay i gi tr trong khong cho trc no . Hoc c th to ra mt tham s nhn gi tr t 0 n 360 chomt 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 thayi 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.


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6.1.7. To ra mt hm s mi

Trong GSP bn c th s dng lnh S> Hm smi to ra mt hm s mi. Khi thc hin lnh ny thchic 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 giithiu 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, so gc no do bn chn trc.Hm s: ti y bn c th s dng cc hm s cbn 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 thhm s

V th ca mt hm s bt k l cng vic khng d cht no i vi nhng ngi hc ton nu khng ni lkhng th lm c bng thc v compa. Tuy nhin giy, nu s dng GSP bn s cm thy nh nhn hn.Nu bn to ra mt hm s ri v by gibn 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 hinlnh th> V thmi. Khi chic my tnh con s xut hin cho bn nhp cc thng s cho mt hms.i khi hm s ny khng nm ht trong bn v, v gi tr ca x hoc y chy trong khong kh rng. giihn li gi tr ca x , bn hy Click chut phi vo th v chn thuc tnh khi mt hp thoi xut hin chophp iu chnh gi tr ca x. Hoc bn cng c thiu chnh n v di ca h trc ta .

6.1.9. o hm v tip tuynng cong

o 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 hmva tnh c v thc hin tnh o hm ln 2, 3 Khi thc hin tnh o hm xong, bn c th v th cao 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 shocS> o hm ca hm s.

Hnh sau y cho thy o hm cp 2 ca hm smc trn v th ca chng.

Tip tuyn ng cong

By gichng ta p dng o hm vo v tip tuyn ca mt ng cong no . Chng ta bit rng o hmca 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 + 31. V th ca hm s y = x 5x 3x + 3 bng cch thc hin lnh th > V th mi2. Chn hm s v tnh o hm ca hm s trn bng lnh S> o hm ca hm s.


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3. Dng mt im A no bt k trn th bng cch dng cng cim click vo th. Dng cngc 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 camy 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 thmi 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 thayi theo. V hnh sau y l kt qu:

6.1.10. Lp bng gi trtngng

C l nu ai tng cm mt tgiy v mt cy vit v ang chm ch theo di v ghi chp thng s camt 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 giy nhGSP bn c th lm iu mt cch d dngvi chc nng to bng gi tr tng ng ca GSP. to mt bng gi tr bng hy chn i tng mun tobng 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 sC

2R = , trong C l chu vi ca ng trn v R l bn knh.

By gichng ta s lp bng th hin gi tr chu vi ca ng trn, bn knh v t s ca chng khi ng trnthay i bn knh.

Trc tin hy vng trn (O,OA). Chn ng trn ri tnh bn knh bng lnh Php o > Bn knh, tnhchu 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

2Rbng lnh S> My tnh. By gibn hy cho ng trn (O,OA) thay i bng cch di

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


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By gibn s c 3 bng mi bng u c 2 dng v dng u tin mi bng th hin tn ca i tng vdng th 2 th hin gi tr ca i tng . Gichng ta thm d liu cho cc bng bng cch chn bng rihoc Click chut phi > Thm bng dliu hoc S> Thm bng dliu. 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 gil 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 thn p vo bng thm dng d liu mi v Shitf+Double-Click loidng d liu.

6.2. Cc H Trc Ta

GSP h trhin th v v th theo 3 h ta l: H ta cc (Polar Grid); h ta Descartes (SquareGrid); h ta ch nht (Rectangular Grid)

6.2.1. H ta cc

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. Ta Descartes v ta chnht.

chn ta Descartes thc hin: hoc l Click chut phi > Li vung hoc l th > Kiu li > Livung. hin th theo h ta ch nht ta thc hin: hoc l Click chut phi > Li ch nht hoc l th >Kiu li > Li chnhtKhi lm vic vi 2 h ta trn cc i tng c tnh ta theo dng (x,y) trong x l honh , y ltung .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 S

6.3.1. ng thng

ng thng cho bi phng trnh tham s: 00

x x at(d):y y bt

= += +

vi t l tham s

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 smi

Bc 3: Chn im A, tnh gi tr honh ca A bng lnh Php o > Honh (x) v tnh gi tr tung caA bng lnh Php o > Tung (y)Bc 4: Chn gi tr xA v a , thc hin lnh: S> Hm smi. 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 smi. Bn nhp hm s g(x) = yA + bxBc 6: Chn hm s f(x) = xA + ax v g(x) = yA + bx , thc hin lnh th > Vng 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

y b R sin t

= +

= +vi R l bn knh v (a,b) l ta ca tm.

6.3.3. ng Elip

ng elip cho bi phng trnh 0

0

x x acos t

y y bsin t

= +

= +vi (x0;) l tm elip v 2a, 2b ln lt l di trc ln v trc

b.


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6.4. Bi Tp p Dng

Bi 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 cosd. ng xon c logarit cho bphng 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):2 2

2 2

x y1

a b = trong a, b l s cho trc v Parabol (P): y2 = 2px

trong p l mt s cho trc

Bi 4: V th ca cc ng cong c cho bi phng trnh sau:

a. ng Cycloid x a(t sin t )y a (t cos t )

=

=

b. ng Astroid 33

x a.cos t

y a sin t

=

=

c. L Descartes 32

3

3atx

1 t

3aty

1 t

=

+

=

+


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CCHHNNGG 77.. CCNNGG CC NNGGII DDNNGG VV HHNNHH HHCC FFRRAACCTTAALL

7.1. Cng C Ty Bin

Khi lm vic vi GSP i lc chng ta cm thy bt tin v c nhng cng vic chng ta phi lm i lm li khnhiu 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 cbn nhim, thc k, compass. T nhng cng c ny chng ta c th dng nn nhng i tng hnhhc 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 tint 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 dngc mt tam gic.Thc cht ca vic lm trn l bn bt GSP ghi nhli cch dng mt tam gic, v sau mun dng limt 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 bnMenu ca Cng c ty bin bns thy cc bc dng nn tam gic.

V d 2: dng mt lc gic u.Bc 1: Von thng AB bt k


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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 choTn 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 mtthi gian, bn s cm thy thoi mi hn khi s dng GSP.

7.2. Hnh Hc Fractal

Hnh hc Fractal l hnh hc nghin cu v cc hnh tng dng. Mt hnh c gi l tng dng nu nhmi mu nh ca n u cha mt b phn ng dng vi hnh , tc l khi phng to mt b phn no cahnh theo mt t l thch hp ta s thu c mt hnh c tht chng kht ln hnh cho.Mi hnh tng dng th c gi l mt Fractal, cc fractal lun lun l mt tc phm p i vi nhngngi 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 thigian cho vic tnh ton, o c v v hnh Nhng giy vi lnh Bin hnh > Php lp ca GSP th bn cth to ra mt fractal mt cch d dng v nhanh chng hn bao giht min l bn bit lm cch no to rafractal .

By gi hiu r hn v chc nng ny ca GSP chng ta hy i to ra mt vi Fractal no .7.2.1. Thm Sierpinski

Bc 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 nhhnh 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 binthnh 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:


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

By gibn hy chn dng chut qut chn thm bn va to v sau nhn phm + hai ln bn s thu cchic thm nh hnh k bn.

hnh th nht, trong hp thoi Interate bn chn Number of interations: l 3. hnh th 2 do bn chnhnh 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 Koch

Bc 1: Von 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 tmB t s 2/3Bc 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 lpCho AA, BACtrl+A: AA,BBCtrl+A: AB, BBCtrl+A: AB, BBBc 6: Hin th > Ch lp ln cuiBc 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 Pitago

Bc 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 imC.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 lpCho 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 sdng 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 cci 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 ti tng t doban 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 binthnh 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 thhiu r n khng cn cch no khc l bn i thc hnh vi n.


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CCHHNNGG 88.. DDNNGG CCCCNNGG CCOONNIICC

8.1. Parabol

8.1.1. Parabol Cho Bing Chun V Tiuim.

dng Parabol khi bit tiu im v ng chun chng ta lm nh sau:1. Dng ng thng d lm ng chun ca Parabol2. 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 trng 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 trv sau bn c cngc dng Parabol khi bit tiu im v ng chun.

8.1.2. Parabol Qua Haiim V Bit Tiuim

1. 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. Elip

C rt nhiu cch khc nhau dng mt ng Elip nhng y ch xin gii thiu cch dng Elip khi bit 2tiu im v mt im th 3 m Elip i qua.

1. Dng F1, F2, P.2. Dng on F1F2 v trung im D ca n.3. Dng on F2P v tia F1P.4. Dng ng trn (P, PF2)5. Dng E l giao im ca ng trn (P,PF2) vi tia F1P.6. Dng on F1E v F l trung im ca n.7. Dng on FF1v ng trn tm D c bn knh bng on FF1.8. Dng ng trung trc ca F1F2.9. Dng ng trn tm F2 v c bn knh bng FF1.


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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. Hypebol

Dng 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 EB9. 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 Hypebol14.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 im

1. Dng nm im A, B, C, D, E.2. Dng ng thng AB, BC, CD, EA.3. Dng F l giao im ca DC v AE.4.

Dng E ty , dng E l nh ca E qua php i xng tm E.5. Dng na ng trn c tm l E v qua EE.(chn E,E,E v Dng hnh > Cung trn ng trn )

6. Dng im G thuc na ng trn .7. Dng ng thng EG.8. Dng H l giao im ca EG v AB.


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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 EG14.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 cchdng li cho tin dng sau ny.


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CCHHNNGG 99.. LLII KKTT

Bit s dng cc tnh nng cbn ca mt phn mm l mt vn hu nh khng bao gikh. 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 khnm mnh gp phi khi tip cn vi phn mm. T ch cha bit g, n ch s dng tng i ti cng phi mtmt 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 cthit k cho nhng ngi mi u lm quen vi GSP. Tuy nhin cng c th l ti liu tham kho, cng nhni 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 likhuyn tt nht l bn hy ng dng n vo vic gii cc bi ton bn ang dy hay ang hc hng ngyquaqu 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 thng dng n vo gii mt s bi tonhnh hc khng gian nht nh. Do c th ch thit k cho 2D nn bn s mt thi gian khi ng dng vo thgii 3D. Mt li khuyn thc sc l nu dng trong mi trng 3D th tt nht l bn nn s dng Cabri 3D, ns d dnh hn cho cc thao tc dng hnh ca bn. GSP l mt phn mm thin nhiu vng dng cho ton,tuy nhin bn cng c thng 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.