Geogebra 4

7/30/2019 Geogebra 4

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Hng dn s dng phn mm Geogebra

Ch gii Cc nt cng c ca Geogebra. Menu ng cnh:

Right Click vo i tng hnh hc s xut hin mt menu m ta gi l menu ng cnh (Thng tinit v menu ng cnh s c trnh by chng Qu tch).

9. Hp thoi thuc tnh:* Double click vo i tng s xut hin hp thoi thuc tnh cc i tng hin th trong bn v

* Ta cn c th click vo th properties menu ng cnh cng s xut hin hp thoi thuc tThng tin chi tit v hp thoi thuc tnh s c trnh by chng Qu tch).I. Cc nt cng c ca Geogebra:

im A

H to cc.

Hin th i tng

Hin th tn i tng

To vt

i tnnh ngha li

Xo

Thuc tnh cc i tng

Menung

cnh

y l hp thoithuc tnh cacc i tng,gi tt l Hp

thoi thuc tnh


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1. Trn thanh cng c ca Geogebra c 9 nt cng c:

Mi nt cng c c mt chc nng khc nhau, cc nt cng c cn l ni lm xut hin trnh

cha mt nhm cng c khc dng hnh.Mun s dng cc cng c khc ca nhm ta click vo du (nm pha di bn phi ca cc nt c

c trn) s c mt trnh n ta chn.

Khi ni: Click nt cng c hoc ta phi hiu: Nu

hanh cng c c nt th ta click vo , nu trn thanh cng c khng c nt th ta phi click

du ca nt cng c i din v sau click vo v tr trn tn.

2. ch chn 1 i tng, hoc di chuyn mt i tng

3. di chuyn mt i tng quay quanh 1 im vi khong cch khng ti

4. ch to thm mt hoc nhiu im mi.

5. ch to giao im ca 2 i tng.

6. ch tm trung im ca 1 on thng (hoc im chnh gia cim), tm ca cung trn, ng trn, ng cnic.

7. ch v ng thng i qua 2 im.

8. ch v 1 on thng i qua 2 im.

9. ch v 1 on thng i qua 1 im, c di cho trc

10. ch v 1 tia i qua 2 im.

11. ch to 1 vector i qua 2 im.

12. ch to 1 vector i qua 1 im, song song v bnvector cho trc.


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13. ch to 1 a gic n cnh.

13. ch to 1 a gic u n cnh.

14. ch to ng vung gc i qua 1 im v vung gc vi 1 hng (c th l on thng).

15. ch to ng trung trc ca 1 on thng cho trc.

16. ch to cc ng thng song song vi 1 ng thng (c th l hng) v i qua 1 im cho trc.

17. ch to cc ng phn gic ca 1 gc.

18. ch to cc ng thng i qua 1 im v tip xc vi 1 i tcho trc.

19. ch to dng ng ng cc.

20. ch to ng trn i qua 1 im v c tm rc.

21. ch to ng trn i qua tm v bn knh rc.

22. ch to ng trn i qua 3 im.

23. ch to na vng trn qua 2 im (2 mt knh).

24. ch to cung trn bit tm v 2 im.

25. ch to cung trn i qua 3 im, trong cim u mt cung.

26. ch to qut trn bit tm v 2 im.

27. ch to 1 qut trn i qua 3 im thuc cung trong c 2 im u mt cung.


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28. ch to 1 ng conic i qua 5 im.

29. ch v, nh du cc gc bt k.

30. ch v, nh du cc gc vi s o cho trc.

31. ch o chu vi mt hnh, o di cung trn, o khocch gia hai im (hoc gia mt im vi mt ng thng hoc gia hai ng thng),

32. ch o din tch ca a gic, ng trn, qut trn, elip

33. ch o h s gc ca ng thng.

34. ch to hp kim tra s n hin ca i tng.

35. ch khi to cc gi tr s, di hoc gc c th bin i trn thcun ngay trn mn hnh (gi l slider)

36. ch to t ng cc hnh sinh bi s chuyn ng ca 1 s imquan h cho trc.

37. ch thc hin php i xng mt i tng qua tm.

38. ch thc hin php i xng mt i tng qua 1 trc.

39. ch thc hin php quay mt i tng quanh 1 im (quay) bi 1 gc.

40. ch thc hin php bin i tnh tin mt i tng tmt vc t.

41. ch thc hin php bin i v t mt i tng t

im bi mt t s.

42. ch chn v iu chnh mt vn bn vo mn hnh.

43. ch chn v iu chnh hnh nh t cc tp nh vo bn v.

44. ch xc nh mi tng quan gia hai i tng.


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45. ch dch chuyn ton b cc i tng trn bn v.

46. ch phng to hnh v trn mn hnh.

47. ch thu nh hnh v trn mn hnh.

48. ch cho php chn n hoc hin cc i tng hnh hc trn mhnh

49. ch cho php chn n hoc hin tn i km i tng.

50. ch cho php sao chp cc thuc tnh th hin (mu sc, rng,...) i tng sang cc i tng khc

51. ch cho php xo cc i tng trn mn hnh.

DNG HNH (CONSTRUCT)

. Chn i tng Di chuyn i tng:1. Chn i tng:

* Click nt cng c hoc .

* Click vo i tng cn chn. i tng sau khi chn c nt m hn.* Mt i tng c nhiu yu t, mun chn yu t no th click vo yu t .* Khi ta click vo v tr ca i tng cn chn m chng trng nhau th s xut hin hp thoi ta click n i tng cn chn.

2. Chn nhiu i tng:

* Click nt cng c hoc .* To ra mt hnh ch nht bao trm ln cc i tng cn chn bng cch: Click vo nh gc vung pri, bn trn hnh ch nht ri drag theo ng cho n nh gc vung pha phi, bn di hnh ch nhoc click vo nh gc vung pha phi, bn trn hnh ch nht ri drag theo ng cho n nh

vung pha tri, bn di hnh ch nht.3. Di chuyn i tng bt k n v tr khc trn bn v:

* Click nt cng c hoc .* Click vo i tng cn di chuyn, sau drag i tng n v tr mi.* Mt i tng c nhiu yu t, mun di chuyn yu t no th click vo yu t . V d khi v mt rn i qua mt im v c tm cho trc th ta c: tm, ng trn v im thuc ng trn.


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Khi chn di chuyn tm th im thuc ng trn khng di chuyn v ng trn ph thuc tm v imrn ng trn.Khi chn di chuyn im thuc ng trn th tm khng di chuyn v ng trn ph thuc tm v im

rn ng trn.Khi chn di chuyn ng trn th tm v im trn ng trn di chuyn theo v chu vi ng trn kh

hay i.* Nu i tng a ph thuc i tng b th i tng a ch di chuyn c trn i tng b. V d imhuc ng thng d th khi di chuyn im A vn lun lun trn d.

4. Di chuyn mt im quay quanh mt im c nh:

* Click nt cng c hoc .* Click vo im cn c nh, sau click vo im cn di chuyn v drag im quay quanh im c Khi quay khong cch 2 im khng thay i.5. Di chuyn ton b cc i tng trn bn v:

* Click nt cng c hoc .* Drag vo bt k v tr no trn bn v di chuyn n.Khi i tng di chuyn th nhng g c lin quan n i tng ca s i s (Algebra window) cng ti theo.

Mun hu bt k lnh no ca Geogebra ta ch cn click nt cng c .I. Dng im:

1. Dng im:

* Click nt cng c hoc .* Click vo v tr cn dng im, click bao nhiu ln trn bn v th c by nhiu im.* Trng hp click trn mt i tng khc th im thuc i tng .*Algebra window hin th to ca im dng (phn free objects)2. Dng giao im:

* Click nt cng c hoc .* Click vo hai i tngcn tm giao im. (i tng trong trng hp ny l: on thng, tia, hng, ng trn, conic, th ca hm s).

*Algebra window hin th to giao im dng (phn dependent objects)

3. Dng trung im:

* Click nt cng c hoc .* Click mt on thng xut hin trung im.* Nu click vo 2 im bt k ( c hoc cha c trn bn v) th trung im ca on thng ni hai im c to ra.

*Algebra window hin th to trung im dng (phn dependent objects)


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4. Dng tm cung trn, ng trn, ng cnic:

* Click nt cng c hoc .* Click mt cung trn (ng trn, ng cnic) xut hin tm.*Algebra window hin th to tm dng (phn dependent objects)II. Dng ng thng, on thng, tia, vector:

1. Dng ng thng qua hai im:

* Click nt cng c hoc .* Click vo 2 im bt k ( c hoc cha c trn bn v) th s c ng thng i qua hai im .* Nu hai im click trn i tng no th hai im chnh l giao im ca ng thng vi i t.*Algebra window hin th:

To ca hai im thuc ng thng (phn free objects).

Phng trnh ng thng (phn dependent object).2. Dng on thng ni hai im:

* Tng t nh dng ng thng ta click nt cng c h

dng on thng. Hai im tu chn chnh l 2 mt ca hng.

*Algebra window hin th:To ca hai im hai mt ca on thng (phn free objects). di on thng (phn dependent object).

3. Dng on thng i qua 1 im v c di cho trc:

* Click nt cng c hoc .* Click vo 1 im bt k hoc 1 im c trn bn v s xut hin hp thoi.

* Nhp di ca on thng vo hp thoi. Click kt thc.*Algebra window hin th:

To ca hai im hai mt ca on thng (phn free objects). di on thng khng i (phn dependent object).

4. Dng tia qua hai im:

* Click nt cng c hoc .* Click vo 2 im bt k ( c hoc cha c trn bn v) th s c tia i qua hai im v nhn im crc lm gc.

*Algebra window hin th:To ca hai im thuc tia, im u l gc tia (phn free objects).Phng trnh ng thng cha tia (phn dependent object).


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5. Dng vector ni hai im:

* Click nt cng c hoc .* Click vo 2 im bt k ( c hoc cha c trn bn v) th s c vector ni hai im v nhn im crc lm gc (im u) v im chn sau lm ngn (im cui).

*Algebra window hin th:To im u v im cui ca vector(phn free objects).To ca vector(phn dependent object).

6. Dng vector i qua 1 im v bng mt vector cho trc:

* Click nt cng c hoc .* Click vo im m vector i qua v vector cho trc. (khng cn theo th t nhng c im v vector pc trc)*Algebra window hin th:

To im cui ca vector(phn dependent object).To ca vector(phn dependent object).V. Dng a gic n cnh:

1. Dng a gic n cnh bt k:

* Click nt cng c hoc .* Click vo v tr cc nh a gic ta cn dng.* kt thc vic dng a gic ta click vo nh u tin. Nu khng thc hin ng tc ny th hnh ta c ch l cc nh ca a gic.*Algebra window hin th:

To cc nh a gic (phn free objects) di cc cnh v din tch a gic (phn dependent object).2. Dng a gic u n cnh:

* Click nt cng c hoc .* Click vo v tr hai nh lin tip ca a gic s xut hin hp thoi.

* Nhp s cnh ca a gic u vo hp thoi. Click kt thc.*Algebra window hin th:

To hai nh a gic chn trc (phn free objects).To cc nh cn li, di cc cnh v din tch a gic (phn dependent object).

V. Dng cc ng c bit:1. Dng ng thng i qua 1 im v vung gc vi mt ng thng cho trc:

* Click nt cng c hoc .* Click vo im ( c hoc to mi) v ng thng cho trc. Khng yu cu theo th t.*Algebra window hin th:

To im to mi (nu c) (phn free objects).


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Phng trnh ng thng va dng (phn dependent object).2. Dng ng thng i qua 1 im v song song vi mt ng thng cho trc:

* Click nt cng c hoc .* Click vo im ( c hoc to mi) v ng thng cho trc. Khng yu cu theo th t.*Algebra window hin th:

To im to mi (nu c) (phn free objects).Phng trnh ng thng song song va dng (phn dependent object).

3. Dng ng trung trc ca mt on thng:

* Click nt cng c hoc .* Click vo on thng (hoc 2 im c hoc 2 im to mi) cn dng ng trung trc.*Algebra window hin th:

To hai im to mi (nu c) (phn free objects).

Phng trnh ng trung trc va dng (phn dependent object).4. Dng ng phn gic ca mt gc:

* Click nt cng c hoc .* Click vo 2 tia (hoc 2 ng thng hoc 2 on thng) to thnh gc th ta s c c hai ng phn grong v ngoi ca gc .

* Nu click vo 3 im to thnh gc (im th hai l nh ca gc, im th nht v im th ba trn 2ca 2 cnh ca gc) th ta c ng phn gic trong ca gc .*Algebra window hin th:

To ba im to mi (nu c) (phn free objects).

Phng trnh ng phn gic va dng (phn dependent object).5. Dng tip tuyn ca mt ng trn:

* Click nt cng c hoc .* Click vo ng trn v mt im ngoi ng trn ( c hoc to mi) th ta s c 2 ng tip tuk t im n ng trn.* Nu click vo ng trn v 1 im trn ng trn( c hoc to mi) th ta s c 1 tip tuyn vi rn k t im .

* Nu click vo ng trn v 1 im trong ng trn th ta s khng c nghim hnh.*Algebra window hin th:

To im to mi (nu c) (phn free objects).Phng trnh cc ng tip tuyn va dng (phn dependent object).

6. Dng ng ng cc ca mt im i vi ng trn:

* Click nt cng c hoc .* Click vo ng trn v mt im tu th ta s c ng ng cc ca mt im i vi ng trn.*Algebra window hin th:


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To im to mi (nu c) (phn free objects).Phng trnh ng ng cc va dng (phn dependent object).V. Dng ng trn, cung trn, qut trn, conic:

1. Dng ng trn i qua 1 im v c tm cho trc:

* Click nt cng c hoc* Click vo 2 im bt k, im u tin l tm ng trn, im th hai l im thuc ng trn.*Algebra window hin th:

To tm v im thuc ng trn (to mi) (phn free objects).Phng trnh ng trn va dng (phn dependent objects).

2. Dng ng trn c tm v bn knh cho trc:

* Click nt cng c hoc* Click 1 im bt k ( c hoc to mi, im l tm ng trn).

* Nhp di bn knh ng trn vo bng ri nhn . ng trn c tm v bn knh cho trkhng thay i hnh dng khi ta di chuyn bt k yu t no ca ng trn.*Algebra window hin th:

To tm (nu to mi) ng trn (phn free objects).Phng trnh ng trn va dng (phn dependent objects).

3. Dng ng trn i qua 3 im:

* Click nt cng c hoc* Click vo 3 im khng thng hng bt k (c ba im u thuc ng trn).*Algebra window hin th:

To 3 im (nu to mi) thuc ng trn (phn free objects).Phng trnh ng trn va dng (phn dependent objects).

4. Dng na ng trn i qua hai im:

* Click nt cng c hoc* Click 2 im bt k (c sn hoc to mi, l 2 u ca ng knh).*Algebra window hin th:

To 2 im (nu to mi) hai u ng knh (phn free objects). di na ng trn (phn dependent objects).

5. Dng cung trn i qua hai im v c tm cho trc:

* Click nt cng c hoc* Click 3 im bt k (im th nht l tm, im th hai l u mt ca cung trn, im th ba trn tiagc l tm v i qua mt th hai ca cung trn).*Algebra window hin th:

To 3 im trnh by trn (nu to mi) (phn free objects). di cung trn (phn dependent objects).


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6. Dng cung trn i qua 3 im:

* Click nt cng c hoc* Click 3 im bt k.(c 3 im u thuc cung trn, im th nht v im th ba hai u mt ca cung*Algebra window hin th:

To 3 im trnh by trn (nu to mi) (phn free objects). di cung trn (phn dependent objects).

7. Dng qut trn bit tm v 2 im thuc qut trn:

* Click nt cng c hoc* Click 3 im bt k (im th nht l tm, im th hai l u mt ca cung trn thuc hnh qut, im ba trn tia c gc l tm v i qua mt th hai ca cung trn hnh qut).*Algebra window hin th:

To 3 im trnh by trn (nu to mi) (phn free objects).

Din tch qut trn (phn dependent objects).8. Dng qut trn qua 3 im:

* Click nt cng c hoc* Click 3 im bt k.(c 3 im u thuc qut trn, im th nht v im th ba hai u mt ca cuim th hai trn cung trn thuc hnh qut).*Algebra window hin th:

To 3 im trnh by trn (nu to mi) (phn free objects).Din tch qut trn (phn dependent objects).

9. Dng conic i qua 5 im:

* Click nt cng c hoc* Click 5 im bt k thuc cnic. (tu theo v tr ca 5 im conic c th l: elip, parabol hoc hyperb).*Algebra window hin th:

To 5 im trnh by trn (nu to mi) (phn free objects).Phng trnh ng cnic (phn dependent objects).

V. Dng gc:1. Dng mt gc:

* Click nt cng c hoc* Click vo 2 tia bt k (hoc hai ng thng hoc hai on thng), th ta s c du gc v tn gc hin rah km theo s o ca gc) giao im ca chng (nh ca gc).

* Click vo 3 im bt k, th ta s c du gc v tn gc hin ra (c th km theo s o ca gc) imchn th hai (nh ca gc).*Algebra window hin th:

To ba im thuc gc (phn free objects).


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ln ca gc (phn dependent objects).2. Dng mt gc c s o cho trc:

* Click nt cng c hoc

* Click vo mt on thng bt k (hoc 2 im bt k). Nu l on thng th nh l mt ca on thdng trc, trng hp chn 2 im th im th hai l nh.* Nhp s o gc. C 2 la chn: counter clockwise (ngc chiu kim ng h); clockwise (chiu kim h). Ta mun tia cn li ca gc pha no th ta click vo la chn .

* Nhn kt thc vic dng gc.*Algebra window hin th:

To hai im hoc hai mt on thng thuc gc dng trc (phn free objects). ln ca gc, to im th ba ca gc (phn dependent objects).

VI. o c:1. o chu vi ca mt hnh, di cung trn:

* Click nt cng c hoc* Click vo hnh cn o chu vi hoc cung trn cn o di th ta s c khung vn bn ghi s o chu vi

mt hnh hoc di cung trn .* Khi dng on thng (hoc cnh a gic) th di ca chng hin th phn dependent objects.*Algebra window hin th: Chu vi ca hnh hoc di on thng (phn dependent objects).2. o khong cch gia hai im, khong cch gia mt im vi 1 ng thng, khong cch gia ng thng:

* Click nt cng c hoc* Click vo 2 im cn o khong cch (hoc 1 im vi 1 ng thng, hoc 2 ng thng) th ta skhung vn bn ghi khong cch cn o.*Algebra window hin th: Khong cch cn o (phn dependent objects).3. o din tch ca a gic, ng trn, qut trn, elip, :

* Click nt cng c hoc

* Click vo hnh cn o din tch th ta s c khung vn bn ghi din tch ca hnh .*Algebra window hin th:

Din tch cn o (phn dependent objects).

4. o h s gc ca ng thng :

* Click nt cng c hoc .

* Click vo ng thng cn tm h s gc ta s c khung vn bn ghi h s gc ng thng .*Algebra window hin th: H s gc ng thng (phn dependent objects).


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VII. Chn vn bn:

1. Chn vn bn:Mun chn mt vn bn vo bn v ta lm nh sau:

* Click nt cng c hoc* Click vo bt k mt v tr no trong bn v. Nu ta click vo mt im th vn bn cn chn c chc nnh mt label.

* Nhp vn bn cn chn. Nhn , lc vn bn c chn vo bn v.2. Chn vn bn ng:+ Khi ta mun n (hide) ca s i s v hin th mt vi s liu ca ca s i s ca s hnh hc thphi chn mt vn bn, trong vn bn ny s c nhng gi tr thay i khi cc i tng hnh hc di chuyn

gi l vn bn ng.+ Mun chn mt vn bn ng vo bn v ta lm nh sau:

* Click nt cng c hoc ri click vo bt k mt v tr no trbn v s xut hin khung ta ng nhp vn bn.* Nhp vn bn (khng thay i), ri click vo mt gi tr trong danh sch i tng ca s i s (giny s thay i khi i tng hnh hc di chuyn), sau nhn apply.V d: Mun chn mt vn bn ca s hnh hc hin th di ca on thng AB ( hin th cai s a = 2,34) ta lm lm xut hin khung ng nhp vn bn v nhp: a = , sau click vo v tr a = 2 ca s i s ta s c c vn bn hin th ca s hnh hc: a = 2,34 ; gi tr ny s thay i khi hai

A v B di chuyn.+ Ta cng c th chn mt vn bn ng vo bn v ta lm nh sau:* Lm xut hin khung ng nhp vn bn nh trn.* Nhp vo khung vn bn theo c php: vn bn thng + tn i tng hnh hc. Lc trn ca s hhc s xut hin vn bn thng v gi tr ca i tng hnh hc.V d: Nh v d trn ta nhp vo khung vn bn: a = + a , sau nhn apply, ta cng thu c kt qu rn.

VIII. Chn hnh nh:1. Chn hnh nh:Mun chn mt hnh nh vo bn v ta lm nh sau:

* Click nt cng c hoc* Click vo bt k mt v tr no trong bn v. Nu ta click vo mt im th hnh nh cn chn gn lin im .* Tm file cn chn. Nhn open, lc hnh nh c chn vo bn v.2. Cc thuc tnh ca nh:V tr ca nh c xc nh bng ba im ba gc ca hnh:


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* Gc th nht: gc tri bn di nh, gc ny dng di chuyn nh.* Gc th hai: gc phi bn di nh, gc ny chnh chiu rng ca nh.* Gc th t: gc tri bn trn nh, gc ny chnh chiu cao ca nh.Mun thay i v tr v kch thc ca nh ta c 2 cch sau:Cch 1:

* Dng ba im chnh l ba gc ca nh ( trnh by trn).* Chn hnh nh vo ti im th nht (gc nh th nht).* Right click vo nh chn s xut hin menu ng cnh.

* Click s xut hin hp thoi thuc tnh ca cc i tng, click vo th positionnh v cho 3 gc nh (corner 1; corner 2; corner 4).* Click th close, lc nh s l mt hnh bnh hnh nhn 3 im dng lm 3 nh ca n.Cch 2:* Dng mt im (hoc c sn) chnh l gc th nht ca nh.* Chn hnh nh vo ti im va dng (gc nh th nht).* Right click vo nh chn s xut hin menu ng cnh.

* Click s xut hin hp thoi thuc tnh ca cc i tng, click vo th positionnh v cho 3 gc nh.* Nhp vo corner 2 v corner 4 nh v cho hai nh cn li theo c php: tn gc nh th nht + (x;* Click th close, lc nh s l mt hnh bnh hnh nhn 3 im dng lm 3 nh ca n.X. Mi tng quan gia hai i tng:Mun bit hai i tng c bng nhau khng ta lm nh sau:

* Click nt cng c hoc* Click vo hai i tng cn xc nh mi quan h.

* Mn hnh s xut hin bng thng bo v mi quan h gia hai i tng .XI. Trnh din cc bc dng hnh: trnh din cc bc dng hnh ca bn tho ta tin hnh cc bc sau:.Bc 1: Cho hin th thanh iu hng cc bc dng hnh, nt play, nt hin th bn tho dng hnh

* Click vo trnh n view.* nh du vo cc mc: Navigation bar for constructionteps; Play button v Button to open construction protocol b

cch click vo cc mc .2.Bc 2: iu khin cc nt lnh trnh din theo nhu cu ca mnh.

li bcng hnhu tin.

Th t bc dng / Tngs bc dng.

Trnh din ccbc dng hnh

Thi gian gia hai bcdng (tnh bng giy)

Hin th bcdng k tipTr li bc dngtrc Hin th bcdng cui cng Hin th bn tho ccbc dng hnh


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Geogebra 4.0 mi vi nhiu tnh nng t ph mnh lit

1. im trong a gic v hnh trn

Trong cc phin bn trc y ca Geogebra, chng ta khng th to ra mt im chuyn ng t do bn trong mtam gic hay hnh trn. Gi y vi Geogebra 4.0, chng ta c th d dng thc hin c iu ny.

Trn thanh cng c chng ta d dng nhn thy nt cng c mi , chnh l cng c cho php to ra mt imhuyn ng t do bn trong mt i tng (khp kn) khc.

To i tng bn trong mt a gic

Sau khi dng cng c a gic to ra mt a gic (khp kn) bt k trn mt phng:


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Sau s dng cng c , nhy chut bt k vo bn trong hnh a gic s to ra cc im ch chuyn ng bn trong a gic ny.

Hnh nh 3 im E, F, G chuyn ng bn trong t gic ABCD. Cc im ny c khi to bi cng c .

To i tng chuyn ng bn trong mt hnh trnVi cng c trn chng ta cng c th to cc im chuyn ng t do bn trong mt hnh trn bt k. Cc bc nhau:

Dng cng c vng trn to ra mt vng trn bt k nh hnh di y.

Mc nh cc vng trn to ra s c nn l rng. thay i nn ca hnh trn, hy nhy chut phi ln vng trn, x


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hin bng chn nh hnh sau:

Nhy chn Thuc tnh.

Xut hin giao din thuc tnh vng trn nh hnh di y.

Nhy TAB Kiu, ti v tr Tnh chn sng, nhy chut r thc o sang phi 1 to l . Nhy nt ng. Khi hn

rn c dng nh hnh sau:


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By gi hy dng cng c to ra cc im chuyn ng t do trn hnh trn nh hnh di y.

Sau khi to xong cc im cn tm, vo li ca s thuc tnh ca hnh trn v im khin kiu nn (trnh chn snv 0. Ta thu c hnh sau:

Nh vy ta to c cc im chuyn ng t do bn trong mt hnh trn bt k.

To i tng chuyn ng bn trong mt hnh ellipse

Cc thao tc to i tng im chuyn ng bn trong hnh ellipse tng t nh vi hnh trn. Qui trnh nh sau:


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To hnh ellipse mc nh.

Thay i kiu nn ca hnh ellipse c chn sng > 0 bt k.

S dng cng c to ra cc im chuyn ng bn trong ellipse.

Thay i kiu nn ca ellipse c chn sng v 0.

2. im chuyn ng t ng trn on, ng thng v ng cong

Trong rt nhiu bi ton hnh hc cn quan st s chuyn ng ca mt hnh hay mt i tung no khi yu cu mim chuyn ng trn mt ng thng hay cong. Cc bi ton qu tch l mt v d in hnh ca yu cu ny.

Trong cc phin bn trc y ca Geogebra cha c chc nng iu khin chuyn ng t ng ca mt im trn

mt i tng khc l on, ng thng, ng cong. Mun thc hin cng vic ny phi thng qua mt i tngh 3 l Slide.

Nhng nay t phin bn mi Geogebra 4.0 tr i chc nng ny c a vo phn mm. Sau y l gii thiunhanh tnh nng quan trng ny ca phn mm Geogebra 4.0.

Thit lp / t ch chuyn ng t ng ca im trn on, ng thng v cong

Geogebra 4 h tr chc nng cho 1 im t ng chuyn ng trn 1 i tng khc trong cc trng hp sau:

im trn on thng / vector.

im trn tia hoc ng thng.

im trn vng trn hay cung trn.

im trn ng cong nh ellipse, parabol hay hyperbol.

im trn mt th hm s bt k.

thit lp ch t ng chuyn ng ca im trn mt i tng khc ta thc hin nh sau:

Nhy chut phi ln im, mt bng chn xut hin, nhy vo dng Hiu ng trn.


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Sau lnh trn im ny s t ng chuyn ng trn i tng.

Dng / Stop chuyn ng t ng

V nguyn tc kt thc chuyn ng ca mt im, chng ta c th thc hin li thao tc trn, nhy chut phi lim (ang chuyn ng) v chn, hy Hiu ng trn.

Tuy nhin thao tc ny rt kh v im ang chuyn ng nhanh, rt kh nhy chut phi chnh xc ln im ny.

C 1 cch khc n gin hn nh sau:

Bm t hp phm Ctrl-E, hay lnh Chnh sa ---> Thuc tnh t thc n chnh ca phn mm.

Xut hin hp hi thoi Thuc tnh nh sau.


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Dng chut chn i tng im trong danh sch bn tri v trong ca s bn phi nhy chut hy chn ti v tr Hing trn.

3. Qu tch

Cng c Qu tch mi c a vo t phin bn mi Geogebra 4.0. y l cng c kh quen thuc thng crong cc phn mm hnh hc ng khc (v d c trong phn mm Cabri 2 plus).

Cng c ny nm ti v tr:


22/60

ngha ca cng c ny nh sau:

Gi s cn tm qu tch ca i tng A (thng thng A l mt im). Qu tch ca A c xc nh khi c mt iB no c dch chuyn t do trn mt i tng no (v d on thng, tia, ng thng, ng cong, ....).

Thng thng bi ton qu tch ny c thc hin ging dy trn phn mm nh sau:

t vt cho im A (khi di chuyn, im A s to ra 1 vt trn mt phng.

GV thc hin thao tc cho im B chuyn ng t do trn i tng ca mnh (c th dng chut to chuyn ngrc tip hoc cho B t ng chuyn ng), khi A s chuyn ng v v ra mt ng cong trn mt phng,

hnh l qu tch cn tm.

Tuy nhin cng c qu tch m ti mun gii thiu hm nay c 1 ngha v vai tr khc bit.

Cng c c chc nng to ra cc i tng hnh hc chnh l cc qu tch no ca hnh ny. Trong v d v

nu, cng c khng ch v th hin ng qu tch ca im A v n cn to ra hn mt i tng hnh hc mhnh l qu tch ca im A khi B chuyn ng t do.

i tng qu tch ny c k hiu l: Quitich[B, A] hay Locus[B, A].

thc hin vic to i tng qu tch ca A chng ta cn thc hin ln lt cc bc sau:

Chn cng c qu tch .

Nhy chut ln im A (chn im s to ra qu tch).


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Nhy chut ln im B (chn im l nguyn nhn xut pht ca qu tch).

minh ha r hn chng ta cng lm bi tp sau:

Cho 1 ng trn tm O v ng thng d nm ngoi ng trn. Mt im C chuyn ng t do trn vng trn.

ng thng OC ct d ti E. Tm qu tch trung im I ca CE.

Chng ta s s dng cng c tm v v qu tch ca im I. Cch lm nh sau:

Chn cng c qu tch .

Nhy chut ln im I (l im to qu tch).

Nhy chut ln im C (l im gc xut pht ca qu tch).

Sau lnh trn chng ta s thy xut hin trn mn hnh 1 ng cong chnh l qu tch ca I. C th thao tc vi ing qu tch ny nh cc i tng khc trong hnh, v d c th i mu cho ng qu tch ny nh hnh sau.

Trong Danh sch cc i tng ca hnh hin thi, qu tch ny s hin trong mc cc i tng ph nh hnh di


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Nh vy cc i tng qu tch c khi to bi cng c s l mt i tng hnh hc bnh thng nh cc ng khc.

Chng ta c th to cc im chuyn ng t do trn cc ng qu tch ny, c th v ng vung gc, song songip tuyn, ... Thm ch c th v c qu tch ca qu tch. chnh l ngha ca cng c mi qu tch ny ca ph

mm Geogebra 4.0.

4. a gic cht (mnh ghp a gic)

a gic cht (rigid polygon) l mt cng c mi c c a vo Geogebra t phin bn 4.0. y l mt c

tuyt vi c nhiu ng dng trong thc t ging dy Ton trong nh trng ph thng.

V tr ca cng c ny trn thanh cng c ca phn mm:


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ngha ca cng c a gic cht

Cng c ny cho php khi to cc a gic gn tng t nh cng c a gic. im khc bit l cc a gic ny saukhi c khi to s l "cht" theo ngha khng th iu chnh, thay i v tr tng i gia cc nh c na. Chh thc hin c cc thao tc dch chuyn v xoay ton b a gic. Hay ni cch khc, a gic cht sau khi c k

o s khng th thay i hnh dng c na.

Thao tc to cc i tng l a gic cht

Thao tc khi to a gic cht hon ton tng t nh vi a gic thng: dng chut ln lt nhy chn cc im lnh ca a gic trn mt phng, kt thc khi nhy chut li vo im u tin.

Kt qu a gic cht hin nh hnh di y, ch c 2 im u v im th hai l hin trn mn hnh, cc nh trungian s n hon ton.

iu chnh a gic cht

i vi a gic cht ch cho php thc hin 2 thao tc sau:

Dch chuyn hnh: nhy v r chut ln nh u tin hoc vng trong ca a gic s lm hnh dch chuyn trn mhnh.

Xoay hnh: nhy v r chut ln nh th hai s lm xoay hnh theo gc xc nh bi chut.

Nh vy chng ta thy cc a gic cht ch c th dch chuyn hoc xoay do s khng thay i hnh dng, v nun gi hnh dng ban u khi c khi to. Tnh cht c bit ny c nhiu ngha v ng dng trn thc t. Sau

y chng ta s cng xem mt vi v d.


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Cc v d ng dng a gic cht

V d 1: Xp hnh

Tp mu: Xep_hinh.ggb. S dng cng c a gic cht to nn cc hnh a gic con tng ng, cc hnh ny cn

ghp li to ra mt hnh ln theo mun. GV d dng thc hin vic to cc hnh nh ny.

Trong hnh trn bi tp l xp cc hnh con bn tri to thnh hnh tam gic ln bn phi.

V d 2: hnh ng dng

Tp mu: Sao_chep_hinh.ggb. GV to mt hnh gc bng cng c a gic cht, sau sao chp cc hnh ny thnhnhiu bn, cho cc hnh ny xoay i cc gc khc nhau to ra cc hnh ng dng trn mn hnh.

Trong hnh trn cc hnh no l ng dng vi nhau?

Lnh sao chp i tng hnh hc trong Geogebra 4.0

v c cc hnh trong v d 2 nu trn, chng ti s dng mt tnh nng rt mi ca Geogebra 4.0, lhc nng "copy/paste" cc i tng hnh hc.
http://www.schoolnet.vn/georoot/geogebra4/Xep_hinh.ggbhttp://www.schoolnet.vn/georoot/geogebra4/Sao_chep_hinh.ggbhttp://www.schoolnet.vn/georoot/geogebra4/Xep_hinh.ggbhttp://www.schoolnet.vn/georoot/geogebra4/Sao_chep_hinh.ggb


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Chc nng ny c thc hin mt cch d dng trong phn mm khi chng ta mun sao chp t 1 hnh gc thnhnhiu hnh khc ging nh vy.

Thao tc ny n gin nh sau:

Nhy chut chn mt i tng hnh hc trn mn hnh (c th chn nhiu i tng).

Nhy t hp phm Ctrl-C (sao chp vo b m).

Nhy t hp phm Ctrl-V (dn). Sau lnh trn, i tng hnh hc s xut hin ti v tr u con tr chut nhng chdn vo hnh.

Di chuyn chut n v tr mun dn hnh.

Nhy t hp phm Ctrl-V. Sau bc ny, hnh s c dn ra mn hnh ti v tr con tr chut, lnh kt thc.

5. a gic vector v a gic im (ng gp khc)Hai i tng mi na lin quan n khi nim a gic mi c a vo phn mm Geogebra 4.0 l cng c a g

vector v ng gp khc (a gic im) .

V tr cc cng c ny trn thanh cng c:

a gic vector (Vector Polygon)

S dng cng c to cc a gic vector.

Thao tc khi to a gic vector hon ton ging nh i vi a gic thng: nhy chut ln lt ln cc im ca gic, nhy chut ln im u tin kt thc to a gic.


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S khc bit gia a gic thng v a gic vector ch l thuc tnh ca im u tin (trong hnh di, A l imu tin).

Khi dch chuyn im u tin, ton b a gic vector s dch chuyn theo. Nh vy im u tin ca i tng agic vector ng vai tr nh mt "nh ca vector a gic" vy.

ng gp khc (Polyline)

S dng cng c to ng gp khc hay a gic im.

Cch to ng gp khc hon ton ging nh cch to a gic, dng chut nhy chn ln lt cc nh ca ng khc, qu trnh to kt thc khi nhy chut li vo im u tin.

Ch rng nhn bn ngoi ng gp khc ny ging nh khi ta to ra cc on thng lin tip nhau. Vy s khc ngia i tng ng gp khc ny v cc on thng ni nhau l g?

. ng gp khc ny l mt i tng hnh hc hon chnh. Chng ta c th dch chuyn v tr cc nh, nhngng gp khc vn ni lin chng.

2. Nu dch chuyn bng chut trn cc cnh ca ng gp khc th ton b i tng s dch chuyn theo.


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. Khi ton b ng gp khc l mt i tng hnh hc hon chnh th chng ta c th thc hin c nhiu thao tv chc nng th v dnh cho i tng ny, v d:

Cho 1 im chuyn ng t do trn ng gp khc.

Tnh chiu di ca ng gp khc.

Thay i kiu ng, mu sc ca ton b ng gp khc.

Ch :

Phn mm Geogebra 4.0 vit ha khi nim ny bng t "a gic im" chc v cch to i tng ny tng tnh a gic. Tuy nhin t gc ting Anh l Polyline nn phi dch l ng gp khc mi chnh xc.

6. Dn, hy dn im. Tip tuyn v ng i cc ca ng trn

Dn, hy dn im

Cng c dn, hy dn im mi c a vo Geogebra 4.0 l mt cng c kh hay v c nhiu ng dng nharn thc t.

V tr ca cng c ny trn thanh cng c nh sau:

ngha chnh ca cng c ny l t / hy thuc tnh ca mt im l nm trn mt i tng khc. Trn thc t kh

hc hin cc thao tc vi im, v nhiu l do khc nhau, c thc hin 1 cch khng chnh xc. V d:

Gi s ta mun to ra 1 im nm trn mt vng trn. Nhng khi nhy chut to im th im ny b trch v khnm trn vng trn ny.

Cng c khi xy ra trng hp sau: Gi s ang c 1 im chy trn 1 vng trn, nhng by gi gio vin li munim ny khng thuc vng trn na.


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Tt c nhng tnh hung trn u c th c gii quyt rt nhanh bng cng c Dn / Hy dn im .

Cc thao tc chnh vi cng c .

. Dn im t do vo i tng.

Nhy chut chn cng c .

Nhy chut chn im, sau nhy chut chn i tng cn dn im.

2. Hy dn im: a im ra khi i tng.

Nhy chut chn cng c .

Nhy chut ln im cn hy dn (trc im ny cn nm trn i tng).

Sau y xt 1 vi v d:

V d 1:

Gi s c tam gic ABC (c khi to bi cng c a gic) v 1 im t do D ngoi tam gic. Gi s chng tamun dn im D vo bn trong tam gic.

Chn s dng cng c , nhy chut ln im D, sau nhy vo bn trong tam gic ABC, chng ta s thu hnh sau:


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Trong hnh trn im D c dn vo bn trong tam gic ABC v s ch c php chuyn ng bn trong tam gny.

V d 2:

Gi s chng ta ang c im C chuyn ng trn 1 vng trn tm O. By gi chng ta mun C s thnh im t dohon ton, khng nm trn vng trn na.

Chn s dng cng c , nhy chut ln im C. Khi C s lp tc ra ngoi vng trn v tr thnh 1 im t rn mt phng nh hnh di y.


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Tip tuyn vi ng trn

Cng c c chc nng t ng v cc ng tip tuyn vi vng trn t 1 im cho trc trn mt phng. V a cng c ny trn thanh cng c:

Thao tc nh sau:

Chn cng c .

Nhy chut ln im v sau nhy chut ln vng trn s to ra hai ng tip tuyn t im ny n vng trn

hn.

Hnh sau m t trc v sau khi thc hin lnh.

ng i cc ca ng trn

Cng c mi c chc nng t ng to ng thng i cc ca mt ng trn.


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i cc ca 1 im i vi ng trn

ng thng i cc ca mt IM A i vi ng trn tm O l mt ng thng d vung gc vi AO ti v tr ao cho OP.OA = R2, vi R l bn knh vng trn.

Nu A nm ngoi vng trn th ng i cc ca A s ct vng trn ti 2 im chnh l chn cc ng tip tuyn A n vng trn ny.

Nu nm trn vng trn th ng i cc chnh l tip tuyn vi vng trn ti A.

Nu A nm trong vng trn th ng i cc s nm ngoi vng trn nh hnh nh trn.


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i cc ca 1 ng thng i vi ng trn

ng i cc ca 1 ng thng i vi 1 vng trn chnh l ng thng vung gc vi ng thng ny v i qum vng trn.

Thao tc vi cng c .

Chn cng c .

Nhy chut chn vng trn.

Nhy chut chn im hay ng thng.

Ch : c th chn theo th t ngc li: chn im / ng thng trc, chn vng trn sau.

7. Cng c v t do (Pen Tool)

Cng c v t do (pen tool) hay cn gi l Cng c BT l mt cng c hon ton mi trong Geogebra 4.0. C ny cho php ngi s dng c th v trc tip bng chut ln bt c v tr no trn mn hnh bng cc nt bt t

V d hnh nh sau cho ta thy kt qu ca cc nt bt v t do nh vy.


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Cc cng c ny rt hay c dng trn thc t. Khi ging dy, GV cn c cc ch thch thm vo hoc gii ngha thrn mn hnh khi cng c v t do ny c bit c ngha. Hay dng hn c l i vi cc thit b bng tng th cng c ny ng vai tr nh mt chic bt hay vin phn GV trc tip thao tc trn mn hnh khi ging dy.

V tr ca cng c ny trn thanh cng c nh sau:

C 2 cch s dng cng c v t do trong phn mm nh sau:

S dng cng c bt v t do trong mt khung ch nht

Theo cch ny, chng ta s dng cng c bt to ra mt hnh v t do trong mt khung hnh ch nht cho trc. S

khi v xong, hnh v ny s l mt i tng ha trn mn hnh v ngi dng c th thc hin cc thao tc dchhuyn, xoay, co gin, xa nh mi i tng hnh hc khc.

Thao tc thc hin nh sau:

S dng cng c (hoc nhy phm ESC quay v cng c mc nh ny).


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Dng chut k mt khung ch nht trn mn hnh (s to i tng v t do trong khung ny).

Nhy chn cng c .

Bt u tin hnh v t do bng cch r chut tri trn mn hnh.

Mun xa cc ng v th nhy v r chut phi s thc hin nh mt bt xa trn mn hnh.

Kt thc bng cch nhy chn mt cng c bt k khc, hay n gin th bm phm ESC.

Kt qu ca vic v t do s l mt i tng ha nh hnh di y.

By gi chng ta c th dch chuyn, xoay hoc co gin i tng ny bng cch dch chuyn 2 im ti hai v trkhung di ca i tng ny. Mun xa i tng ny th nhy chn v bm phm Delete.

Ch 1:

Trong qu trnh v t do c th iu chnh mu sc v kiu ng v t do bng cc cng c tinh chnh ngay pha tra mn hnh.

Ch 2:

Sau khi kt thc vic v t do (v khi to xong i tng ha ny) th khng th dng li cng c ny xamt phn ca hnh v t do c na.

S dng cng c bt v t do khng gii hn

Theo cch ny chng ta khng cn to trc 1 khung ch nht trc khi s dng cng c v. Khi chng th to cc ng v t do bt c v tr no trn mn hnh. Sau khi v xong th i tng hnh v ny s mc n khng th di chuyn v xa c.


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Hnh nh ca i tng c to bi cng c bt v t do trn mn hnh nh sau:

Ch :

Mi ln s dng cng c v t do to ra cc hnh v trn mn hnh, phn mm s to ra mt i tng ha. Ci tng ny nm chng ln nhau trn mn hnh.

Cc thao tc nng cao i vi cc hnh v t do

Phn ny dnh ring cho cc gio vin c hiu bit su hn v phn mm Geogebra.

Cc i tng ha c to bi cng c khi s dng t do trn mn hnh thc s vn l nhng i tng ha bnh thng ca phn mm, nhng chng s c gn mc nh cc thuc tnh sau:

L i tng ph. Do mc nh khng hin trong ca s Danh sch cc i tng ca phn mm.

c gn thuc tnh "C nh" v "Khng th la chn c", do vy chng ta khng th xa hay thay i cc ing ny.

Do vy ch cn xa 2 thuc tnh "C nh" v "Khng th la chn c" l chng ta s thao tc vi cc i tng ha ny mt cch bnh thng trn mn hnh.

Sau y m t cc thao tc c th iu chnh tham s ca cc i tng ha ny.Trc tin chng ta hy thu nh mn hnh chnh li (bng cch s dng nt chut gia) v s nhn thy ngay cc i

iu khin cc i tng ha ny trn mn hnh.

Hy lm xut hin ca s Danh sch cc i tng (bng cch, v d, g Ctrl-Shift-A), sau cho php hin c cci tng ph, chng ta s nhn thy ngay cc i tng hnh nh ny trong danh sch nh hnh di y.


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Nhy chut phi ln cc i tng ny trong danh sch v nhy hy thuc tnh C nh i tng, by gi c thhoc xoay cc hnh ny.

Mun thay i thuc tnh Cho php la chn hy vo ca s thuc tnh ca cc i tng ny v nhy chn thuc Cho php la chn nh hnh di y ch ra.

By gi chng ta c th chn cc i tng ha ny bng cch nhy chut ln chng v c php dch chuynhng bt k trn mt phng. Gi y cc i tng ny hon ton ging nh trng hp chng ta v chng trong m

khung ch nht.


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Trong hnh nh trn cc i tng ha c v trong ch t do tr thnh cc i tng hnh hc bnh thn

8. Cng c vn bn (mi nng cp)

Trong phn mm Geogebra chng ta c th chn cc on vn bn vo bt c v tr no ca hnh. Cc vn bn ny cnhiu ngha khi minh ha cho cc i tng hnh hc v h tr rt tt cho vic hc v dy ca GV v Hc sinh. C

to cc i tng vn bn ny l c t cc phin bn trc y ca phn mm. V tr ca cng c ny trhanh cng c nh sau:

Trong phin bn mi Geogebra 4.0 cng c vn bn ny c rt nhiu nng cp mi vi nhiu tnh nng mi mannh t ph.

khi to mt i tng vn bn mi, ch cn thc hin thao tc sau:


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Chn i tng .

Nhy chut ti v tr bt k trn mn hnh mun chn vn bn.

Xut hin hp hi thoi nhp vn bn, nhp xong nhy nt OK kt thc.

Thanh cng c thuc tnh ca i tng vn bn

Khi i tng vn bn c chn trn mn hnh chng ta s nhn thy 1 thanh cng c nh pha trn ca mn hnh (di thanh cng c chnh) cho php thay i cc thuc tnh ca vn bn ny nh mu sc, c ch, kiu ch, ... Tnhnng ny s gip ngi s dng nhanh chng thay i thuc tnh ca cc vn bn trn mn hnh.

Trong ca s nhp vn bn c 1 ca s nh Xem trc cho php quan st trc tip kt qu ca i tng vn bnny trn mn hnh.


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H tr rt nhiu k t v biu tng ton hc

Trong phin bn mi Geogebra 4.0 h tr thm rt nhiu cng c h tr cho vic nhp v th hin cc cng thcon hc trong cc i tng vn bn ny.

Cng thc Ton hc c g bng ngn ng Latex gi y c th chn mt cch tng minh trong ca s nhp vbn. Nhy chiut ln v tr Cng thc Latexchng ta s nhn thy mt bng chn ln vi nhiu mc khc nhau chophp la chn nhp cc loi cng thc ton hc khc nhau. Tnh nng ny rt thun tin cho vic nhp cng thcTon hc.


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Mt nng cp rt mnh khc l phn mm cho php nhp, chn cc k hiu, biu tng ton hc rt phong ph hngp nhiu ln so vi cc phin bn trc y.

Nhy chut ln v tr Cc biu tng chng ta s nhn thy mt bng chn xut hin cho php la chn nhiu k hion hc khc nhau, rt phong ph.

Lin kt trc tip vi cc i tng hnh hc

Mt tnh nng mi rt ni bt na ca i tng vn bn l kh nng kt ni bn trong trc tip v trc tuyn vi ci tng hnh hc khc. Tnh nng ny rt c ngha trn thc t, v d chng ta c th a cc gi tr s tnh tonrc tuyn ca cc i tng hnh hc (v d nh di, din tch, ...) vo bn trong cc vn bn.

Xt 1 v d sau (tp chu_vi_ABC.ggb).
http://www.schoolnet.vn/georoot/geogebra4/chu_vi_ABC.ggbhttp://www.schoolnet.vn/georoot/geogebra4/chu_vi_ABC.ggb


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Trong v d trn i tng vn bn (dng ch Chu vi tam gic ABC = ...) lun th hin chnh xc chu vi ca tam gi

ABC trn mn hnh.

thc hin c vic to mt lin kt trc tuyn t 1 v tr ca vn bn vi 1 i tng hnh hc bn ngoi chng hc hin thao tc sau: nhy chut ln v tr Cc i tng, s xut hin DS cc i tng hnh hc, nhy chn ing hnh hc mun lin kt.

Trong v d trn chng ta s chn i tng l chuvidagiacTamgiacABC trong DS cc i tng hnh hc to likt.


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Vn bn kt ni trc tip vi cc i tng hnh hc

Cc i tng vn bn c th l cc i tng t do trn mn hnh hoc c th c gn cng vi mt i tng hnhc khc trn mn hnh. Khi i tng hnh hc ny chuyn ng th vn bn cng chuyn ng theo.

Thao tc to vn bn kt ni vi mt i tng hnh hc c trn mn hnh (v d im, on, ng, vng trn, ..nh sau:

Chn i tng .

Dng chut nhy chn i tng hnh hc mun kt ni.

Nhp vn bn trong ca s, nhp xong nhn nt OK.

V d sau cho ta hnh nh mt vn bn lun gn kt vi im A ca tam gic ABC.

Khi dch chuyn im A, dng vn bn ny lun chuyn ng theo.

9. Cng c chn nh (mi nng cp)

Cng c chn nh khng c nhiu im mi trong bn Geogebra 4.0 mi, tuy nhin y l mt cng c rt qurng cho php a cc hnh nh bitmap vo trang mn hnh.

V tr ca cng c chn nh trn thanh cng c chnh nh sau:


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Thao tc chn 1 file nh vo trang mn hnh.

Nhy chn cng c chn nh

Nhy chn 1 im bt k trn mn hnh.

Xut hin hp hi thoi m File. Tm tp nh trn my tnh v chn m tp ny, hnh nh s c a vo mn hna phn mm nh hnh di y.

Ch rng mc nh cc hnh nh c chn vo bi cng c s l cc i tng ph.

Hnh nh sau khi c chn vo c th d dng di chuyn hoc xa.


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Chn nh t Clipboard

chn 1 nh ang c trong Clipboard thc hin cc thao tc sau:

Nhy chn cng c chn nh

Nhn gi phm Alt v nhy chut ti 1 im bt k trn mn hnh.

Sau thao tc trn hnh nh c trong Clipboard s c a ra mn hnh ti v tr va nht chut.

Gn im iu khin cho nh

Mc nh cc hnh nh c chn vo mn hnh ca phn mm Geogebra ch c th xa hoc dch chuyn, khng thhc hin c cc thao tc nng cao hn nh xoay, co gin hnh.

Mun thc hin cc thao tc nng cao ny, trc tin cn hiu cc v tr im t 1 n 4 ca mi hnh nh c m trong s sau.

V tr u tin khi chn nh vo chnh l im s 1.

Cc chc nng nng nng cao hn i vi cc hnh nh chn trong Geogebra c thc hin theo nguyn tc sau:

Xc nh trc cc im A, B, C ln lt ng vai trn cc im 1, 2 v 4 ca hnh.

Thc hin thao tc gn cc im A, B v C vi cc nh 1, 2 v 4 ca hnh nh.

Ch :


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Nu ch gn cc nh 1 v 2 hoc ch 1 v 4 th hnh nh s gn vi 2 im v c th thc hin c cc thao tc nhxoay, co gin (khng mo) v dch chuyn hnh.

Nu gn c 3 nh 1, 2 v 4 th hnh nh s t ng co gin (mo) sao cho cc nh ny trng vi cc im A, B, Crn mn hnh.

Xt cc v d sau:

V d 1: ch gn cc nh 1 v 2

Gi s c 2 im A, B trn mn hnh nh hnh di y.

Nhy chut phi ln hnh nh v chn lnh Thuc tnh.

Xut hin hp hi thoi thuc tnh sau:


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Chn TAB V tr, sau gn cc v tr 1 v 2 cho cc im A, B nh hnh di y:

Nhy nt ng hon tt vic gn, khi hnh nh s c gn v gn cht vi 2 im A, B nh hnh di y:


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By gi chng ta c th dch chuyn cc im A, B xoay v dch chuyn hnh nh theo nhiu hng khc nhau. Tnhin hnh nh vn ng dng vi hnh gc.

V d 2: gn c 3 nh 1, 2 v 4

By gi gi s chng ta c 3 im A, B, C nh hnh di y:

Chng ta tin hnh cc thao tc gn nh trong v d 1, nhng by gi gn c 3 im: nh 1 --> A, nh 2--> B, nh--> C.


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Khi hnh nh c gn vi 3 im A, B, C v ta thu c hnh di y:

R rng trong trng hp ny do hnh phi ko cng vi 3 nh nn n s b mo i.

10. Cng c nhp trc tip tham s v d liu

Trong cc phin bn trc y ca Geogebra c cng c dng khi to v iu khin cc tham s t do.Cc tham s ny rt c ngha trong phn mm dng xc nh cc di on thng, bn knh, dng knh vngrn, tiu c ca ng cong hoc tham gia vo cc biu thc i s.


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Cng c cn cho php ngi dng iu khin cc gi tr ca tham s tng ng bng cch r chut trn mthanh trt nh. Tnh nng ny c rt nhiu ng dng trn thc t, cho php GV iu khin cc gi tr s chuyn n

dc theo mt thang trc s qua quan st th hin cc i tng hnh hc tng ng trn mn hnh.

Tuy nhin trn thc t trong rt nhiu bi ton v v d s yu cu thc hin nhp cc tham s ny mt gi tr c th

, v d m = 3, a = 8, .... Trong cc trng hp ny vn c th dng thanh trt nhp s, nhng cch ny khnh xc li mt thi gian.

Trong phin bn mi Geogebra 4.0 mi b sung mt cng c mi cho php ngi dng nhp trc tip t bphm 1 gi tr c th ca cc tham s t do trong phn mm. Cng c ny rt hu ch trong cc trng hp mun ggi tr c th no cho mt tham s ca phn mm.

V tr ca cng c ny trn thanh cng c ca phn mm.

Ch : cng c nhp d liu ny ch cho php nhp cc gi tr ca cc tham s t do, khng th nhp cc tham s phhuc.

Sau y ta xt cc thao tc to hp nhp d liu cho mt tham s c th trong phn mm Geogbra 4.0.

Cc thao tc to hp Input gi tr ca tham s t do

Chn cng c .

Nhy chut ln v tr trn mn hnh mun to hp nhp d liu. Xut hin hp hi thoi sau:


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Ti v tr Tiu g dng vn bn s hin trn mn hnh ti hp nhp d liu. Ti v tr i tng lin kt chham s cn gn cho hp nhp d liu, v d nh hnh di y.

Sau khi nhp xong nhy nt p dng.

Chng ta s thy xut hin ti v tr con tr hp nhp d liu nh sau:

di ca hp nhp d liu c the iu chnh bng thuc tnh " di" trong hp hi thoi thuc tnh ca hp nhpiu ny.


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Sau y xt 2 vi d.

V d 1: Tp cc_nhap_tham_so_1.ggb

Trong v d ny xt mt tham s t do m v phng trnh hm s

y = (x-m)/(x+1)

Hp nhp trc tip gi tr m c xc nh ngay trn mn hnh cho php nhp d liu trc tip vo gi tr m.

V d 2: Tp cc_nhap_tham_so_2.ggb
http://www.schoolnet.vn/georoot/geogebra4/cc_nhap_tham_so_1.ggbhttp://www.schoolnet.vn/georoot/geogebra4/cc_nhap_tham_so_2.ggbhttp://www.schoolnet.vn/georoot/geogebra4/cc_nhap_tham_so_1.ggbhttp://www.schoolnet.vn/georoot/geogebra4/cc_nhap_tham_so_2.ggb


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Trong v d ny xt tam thc bc 2:

y = ax2 + bx + c

vi a, b, c l cc tham s cho bi cc thanh trt trn mn hnh.

S dng cng c to ra 3 hp nhp trc tip d liu vo cc tham s a, b, c.

By gi chng ta c th iu khin cc tham s a, b, c hoc bng thanh trt hoc bng cng c nhp trc tip trn mhnh.

11. Ca s th v ha th 2

Mt trong nhng pht trin t ph na ca phin bn Geogebra 4.0 mi l tnh nng th hin hai mn hnh hng thi trn mn hnh.

y l tnh nng rt c bit ca phn mm Geogebra 4.0, n cho php:Ngi dng c kh nng quan st c ng thi 2 ca s ha trn mn hnh. Ngi dng c th thao tc ng

hi vi cc i tng ha trn c hai ca s ny.

Mt i tng c th hin th trn 1 hoc ng thi c 2 ca s trn. Tnh nng c bit ny s h gip ch rt nhiho GV khi th hin cc i tng hnh hc trn 2 khung ca s ny, h tr qu trnh ging dy ca gio vin.


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Phn mm d dng cho php ngi dng

Lnh th hin / n cc ca s ha chnh ca phn mm Geogebra 4.0 nm ti thc n Hin th (View) trong cc r sau.

C th s dng phm nng:

Bt / tt ca s ha 1: Ctrl-Shift-1

Bt / tt ca s ha 2: Ctrl-Shift-2

Trc khi thc hin cc thao tc lin quan n th hin cc i tng hnh hc trn cc ca s ha ny chng ta h

xt mt vi v d sau.

V d 1: Tp do_hoa_2a.ggb
http://www.schoolnet.vn/georoot/geogebra4/do_hoa_2a.ggbhttp://www.schoolnet.vn/georoot/geogebra4/do_hoa_2a.ggb


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Trong hnh trn chng ta nhn thy 2 ca s ha chnh ca phn mm, mt nm bn tri v mt nm bn phi. Ca s ny u th hin cc i tng hnh hc ca phn mm.

th hm s y = (x+1)/(x-1) mu c th hin trn c 2 ca s. Ch rng ta nhn thy 2 th nhng ch i tng ton hc.

im A chuyn ng trn th, mt tip tuyn vi th i qua A. Hai i tng ny ch th hin trong ca s bri.

th hm s th 2 (hnh parabol) ch hin trong ca s bn phi.

V d 2: Tp do_hoa_2b.ggb
http://www.schoolnet.vn/georoot/geogebra4/do_hoa_2b.ggbhttp://www.schoolnet.vn/georoot/geogebra4/do_hoa_2b.ggb


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Trong v d ny chng ta nhn thy trn c 2 ca s ha hnh nh ca bi ton ng thng Sim sn. Tuy nhinc i tng nm trn 2 ca s ny l khc nhau.

GV c th cho HS quan st cc cc v tr khc nhau ca ng thng Simson trn 2 mn hnh hoc cho hai tam girn 2 ca s thay i v tr HS hiu r hn v bi ton ny.

By gi chng ta s cng nhau hc cc thao tc chnh trn 2 ca s ha ca phn mm Geogebra 4.0.

Ca s ha hin thi (Active)

Trong 2 ca s ha hin trn mn hnh lun ch c 1 ca s l hin thi (Active). Cc i tng hnh hc c nh dng Input s hin th mc nh trn ca s Active ny.

Mun chuyn 1 ca s thnh Active ch cn nhy chut ln v tr bt k bn trong ca s ny.

Ci t la chn cho php hin th i tng hnh hc trn mt hoc c hai ca s ha

Khi mt i tng ha uc khi to, mc nh i tng ny s hin th trn mt trong 2 ca s ha.

Mun thay i hin th sang ca s khc, hoc mun cho i tng ny hin trn c 2 ca s hy thc hin thao tcau:

Nhy chut phi ln i tng v chn Thuc tnh.

Xut hin hp hi thoi Thuc tnh ca i tng ny nh hnh sau:


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Chn TAB: Nng cao. pha di chn vng lm vic hin thi (ca s 1) hay th 2 cho ca s 2. Ch : ng hnh hc c th hin trong 1 hoc 2 ca s hoc hin trong c 2 ca s ha ca phn mm.

Nhy nt ng.

Sao chp mt i tng hnh hc t ca s ny sang ca s khcTrong phn mm Geogebra 4.0 b sung mt tnh nng rt c bit l thao tc sao chp (copy), dn (paste) i c i tng ha. Tnh nng ny rt hu ch trong nhiu trng hp. C th copy, ct, dn trn cng mt ca s

hoc trn 2 ca s khc nhau.

Sau y m t thao tc sao chp cc i tng ha t 1 ca s ny sang ca s khc ca phn mm Geogebra.

Gi s chng ta c 1 hnh bao gm 1 s i tng hnh hc th hin trong ca s 1 nh hnh di y. Gi s chngmun sao chp cc hnh ny sang ca s th 2. Thao tc ny s to thm cc i tng hnh hc khc trong phn m

Bc 1: chn cc i tng hnh hc mun sao chp. Hnh nh cc i tng c chn s th hin nh hnh di


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Bc 2: g t hp phm Ctrl-C (lnh Copy).

Bc 3: dng chut nhy trn ca s 2 v g t hp phm Ctrl-V (paste). Hnh nh ca i tng s hin ra ti v tron tr nh hnh di y.

Bc 4: di chuyn chut n v tr mun t cc i tng hnh hc sao chp v nhy chut. Cc i tng nyh hin trn ca s th 2 nh hnh di y.


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Tp do_hoa_2c.ggb

Trong hnh nh trn hai nhm i tng th hin trn 2 ca s ha khc nhau ca phn mm. y l hai nhm ng khc nhau, nhm i tng trong ca s 2 thu c bng cch thc hin thao tc sao chp cc i tng t c 1 sang.
http://www.schoolnet.vn/georoot/geogebra4/do_hoa_2c.ggbhttp://www.schoolnet.vn/georoot/geogebra4/do_hoa_2c.ggb

Geogebra 4

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Transcript of Geogebra 4