CUAIV DUY SANG TAO IRONfi DAY HOC GIAI BiUTAP HlNH HOC KHONG GIAN 1̂ M O N G TRUNG HOC PHO THONG O TS CAO THI HA'''' D A O NGQC DONG" l T v d u y sdng tgo Tlieo ldi li$u (1) vd (2), h/duy sdng Igo (TDST)[.]
CUAIV DUY SANG TAO IRONfi DAY HOC GIAI BiUTAP HlNH HOC KHONG GIAN 1^ M O N G TRUNG HOC PHO THONG O l T v d u y sdng tgo Tlieo ldi li$u (1) vd (2), h/duy sdng Igo (TDST) cOa ngudi h mil dgng lu (TD) die lip, tgoraf h/dng mdi die ddo vd (^ hiiu qud gidl quyit vdn di cao TDST dupc hiiu td sv kit hpp d dinh coo, hodn thl|n nhdt cOa tu (TD) Kch eye vd TO ddc ldp nhdm hjo ro nhOng jf h/dng mdi d l gidl quyli vdn d l mdt cdch hi|u qud nhdt TOST Id TO ddcldp vi nd khdng phy thudc vdo nhung cdl dd ed Sdn phdm cOa TDST mang ddm ddu dn cOo mfii cd nhdn h ^ nd Cdc thdnh phdn cOa TOST Tdng hpp cdc kit qud nghidn cOu v l TOST cho lk\6y, TOST cd Knh chdt dfec frung o j bdn sou; - Tfnh mim dio: Dd Id ndng Ivc thay ddi, nhanh chdng Kip cdn dupc vdl h$ thdng tri ihOc mdf, chuyin h> gdc dd quan ni^m ndy sang gdc dp quan nidm khdc; djnh nghTa k;if sv v^t, ht|n hrpng, xdy dyng phuong phdp TO, h?o sy vdt mdi nhung mdf quan h$ mdi - Tfnh nhudn nhuySn cua TD t h i hl$n rS d hoi d ( ^ dilm; + Tinh da dpng cOo cdc cdch gidl quylt vdn d l gidl todn, khd ndng Hm dupc nhilu gidl phdp d cdc gdc dd vd Hnh hudng \A)dc DOng hvdc mdt vdn d l cdn gidi q u ^ , ngudi cd TO nhudn nhuydn nhanh chdng Hm vd d l xuat du^c nhilu phuong dn d l ed thi Hm dupc phuong dn ak uu; + Cd Hid ndng xem xdt md^ vdn d l audi cdc gdc dd khdc nhou, cd cdl nhin sinh ddng, todn df|n ddf vdl cdc sy vdt vd hi$n h;png chO khdng phdl cdl nhin bdt biin, phlln dl$n vd cOng nhdc - Tfnh die ddo: Khd ndng Hm kilm n>dt phuong phdp gfdf quylt vdn d l Ipliodc nhdt - Tfnh hodn thlin: Khd ndng ldp k l hopch, phdi hpp glOo ^ nghtvd hdnh ddng, phdt W i n ^ hjdng, kilm tra vd chOng minh jr tudng - Tfnh nbgy cdm vdn di: Ndng lye nhanh chdng phdt hl|n mfiu thufin, sal ldm, sy thilu k>gic, hvdc nhOng Hnh hudng cd vdn d l d l sOa chua, cdu hOc Ipl hpp If, hdi hdo nhdm tgo ro y hrdng mdi TS CAO THI HA' - DAO NGQC DONG" Cdc Knh chdt co bdn d h-dn cua TOST khdng tdch rdi md trdi Ipl, chi3ng cd mdi quon h^ mdt thilt, bd sung vd hfi trp Ifin Tinh m i m ddo cua TO h?o d i l u kl|n cho v l ^ Hm dupc nhilu gidi phdp dudi cdc gdc dd khdc (tfnh nhudn nhuySn); nhd d l xudt dupc nhilu phuong dn ndn cd t h i ttm thdy phuong dn Ip, ddc sdc (tfnh d0c ddo) Tdt cd cdc tfnh chdt ddc hvng dd cOng gdp phdn tpo ndn TDST - mdt dpng hop! ddng h-f t u | coo nhdt cua ngudi Tuy nhidn, hdu h i t cdc cdng trinh nghldn cuu khoa hpc vi TOST c^o t h ^ , tinh m i m ddo, tfnh nhudn nhuvin vd ddc ddo Id ba y l u td ca bdn nhdt, cdt Idl nhd't cOa TOST Sv b i l u h l f n cOa TOST cdc bdl todn hlnh hpc Ichdng gian Trong dpy hpc todn phdn Hlnh hgc ld}dng gian d hvdng THPT, hpc sinh (HS) cd rdt nhilu co hdi d l rdn luy^n TOST Cy t h i : 1} Tfnh mim d6o Vf dg 1: ChOng minh rdng hror>g mdt htnh tO dl$n, bdn dudng h-png hjyin ddng quy h;il mdt dilm Phdn tfch: D l gidi bdl todn ndy, HS thudng chOng minh hi/c H ^ bdn dudng hpng hiyln ddng Tuy nhldin, ddi vdl nhOng HS cd TO mim vd linh hopt, cdc em cd t h i chuylii h> bdi todn chOng minh ddng quy sang chOng minh dilm thdng hdng r Thdt vdy: G i d sO A A ' , BB', C C , DD* Idn lupt Id bdn dudng h'png hiy^n kd h> A , B, C, D Gpi E Id trung dilm cOa CD, hrong mp(ABE), gpi G Id giao d i l m ciJa AA' vd BB' Di chOng minh bdn dudng trpng ^>^ WIn/i * M i | B i bfc W PMH-B«i hfclUi N0vti ** CM bfc 17 - Tmttig I f i li9C itf pliHi, Il9i bH Tliii Npyti Tap chifiliJDdue s6 iki i - »/ioii) tuyin dSng quy ta cht DD" va C C cOng dl qua G, hay D, D', G ihang hdng vd C, C , G thing hdng G j l M , N ISn lupt Id trung dl^m BC vd AC Khi dd D' s B N ; B' € D N suy D, D', G e(BDN) MiJtkhdc: ly e A M ; A ' s D M n8n D, G, D- e|AMD| Khi dd D, G, D' thudc giao tuyjln ciJa hai mflt phdng |AMD| vd (BI^ID) Chiing minh luong ti/, ta cd C, G , C thing hdng V$y, m^t hlnh ti difn b{it kl b£n dudng trpng tuy^n d i n g quy tql m^t d\im 2) Tfnh nhuSn nhuySn W : Cho hlnh l^p phuong ABCD.A'B'CD' Chiing minh l i n g A C X mp(BDA') Ihlnh 2) Phdn tfch: Bdl todn ndy c6 nhl^u cdch gidl, lOy iheo «/ nhuin n h i ^ n v^ kl^n thiic cOa HS md cdc em cd th£ chpn cdch gidl quylft phu hpp Cd nhOng HS thdnh thqo vdl cdch chiing minh dudng Hinh t h i n g vudng gdc vdl m^t p h d n g bing cdch chiing minh dudng thing dd vudng gdc vdl hai dudng thing c i t n i m mt phing (ACCA') c i t (ADCB') theo gloo tuyin A C , suy ro A C (BDA') V / d y 3: Cho hlnh chdp tom gidc d i u S.ABC, cdc mdt bdn, cdc cpnh bdn tpo vdl ddy gdc a vd gdc y9, dd ddi trung dopn cOa hlnh chdp b i n g o C i t hlnh chdp bdl mjjt p h i n g cdch d i u cdc dinh hlnh chdp Tfnh didn Kch thlitdl$n tpo ihdnh [hinh 3) Ijp Chi Blao due s6 gd i ã a/Miô> Sv nhuin nhuyin kiln thiic Clio HS bdl todn ndy t h i hl$n qua cdc vd'n d l sou: tHS phdl n i m dupc mdt phing cdch diu b^n dinh cOa hi dl^n dl quo trung dilm ba cpnh d i n g quy Clio tii dijn hoijc Id m^t phing dl qua trung dilm hin cpnh i&\ dl|n ddi mdt; - HS phdl ihdnh thpo md'l quan h | glOo gdc Ipo bdl cdc mdt bdn, cdc cpnh bdn vdl ddy cOa hlnh chdp diu VI v ^ , dSl v6l bdl todn ndy c i n phdl x l l cd trudng hpp Bdn cpnh dd, HS phdl xdc d|nh diing cdc gdc da cho TO dd, to cd cdc cdch gidl bdl todn: Gpi D Id trung dilm ciia AB, O Id hlnh chllu cda S trdn mp(ABC) Theo gid thilt ta cd: DS = a; Z S C O = y»; vd Z S D O = a => tana = 2tan^ ^ " " " " j i ^ w ^ =>DO = DS.cosa = o.cosa vd DC « D O = So.cosa; DB = aS.cosa Trudng ht?p ? Thilt dl^n cin tim dl qua trung dilm cdc cpnh bdn ciio hlnh chdp Gpi (P) Id mdt phing cit hlnh chdp vd dl quo Irung dilm A,, B,, C, Clio cdc cpnh SA, SB, SC Do dd, mp(P) cdch d i u t6l cd cdc dinh hlnh chdp Khi dd, (P) cit hlnh chdp theo thilt dl$n Id tam gidc A,B,C, vd:AB,=^AB: C,B,=icB;/l,C,=iAC; S.= "^ 4.a+4lan'^) Trudng hqp Thid't d l # n dl qua trung dilm cdc cpnh A C , CB vd dl quo trung dilm cOa cpnh bdn SC (hlnh 3a) Khi d d , mp(P) c i t hlnh chdp SABC iheo thilt dl^n Id tam gidc MNP cd: S,.=-S^=-SD.AB; Hlnh 3a NP'j-AS; ABCD.A'B'CD' thda mdn » A; Ox » AC; Oy • AD; Oz • AD' ihl ylu cdu cOa bdi todn hnmg duong vdi vi$c chOng minh (ACD) (DAD'|, Wc " "" 4^741mV Trudng hgp Thilt dl|n dl qua trung dilm mdt bin vd mdt cdc canh AC, CB vd dl qua trung dilm cpnh bdn ddy ciJa htnh ldp SA, SB (hinh 3bj Khi dd, mp(P) cdch diu Kit cd phuong vudng gdc cdc dinh cOa hlnh chdp S.ABC vd cdt hlnh chdp vdl nhou Dl thdy DA Id giao tuyin theo Ihllt dl^n Id hlnh chii nhit MNTR To cd: cOa hai mdt phdng W , V , =-AB = aSmsa = 0^3-, (ACD) vd (ADD'); JU4III h^ong mpfADD'), cd DD' AD nln ' OC 20D la.cosa Hinh (ACD) (ADD*) 6^ = - i t , o = ~.:>lJ.Aa = — p cos^ oos^ COS/9 a'S , COS/JV' + ^ ' ™ ' / ' Quo m$t sd vi dv h ^ to nhdn thdy, Hinh hgc a'S S.,= cosPO + Aim'P)' Ididng gian Id m$t ndi dung h^dn hpc h^ nhilu cos^VI + ^ " " ^ CO hdi d l HS cd Ihl r^ luy|n, bdi dudng cdc 3) Tfnh die thdnh phdn co bdn cuoTOSTh'ong hpc tdp Gido ddo Tfnh d«c vidn cdn cd nhOng phuong phdp su phpm |^0 ddo cOo TD ddc hpp, glOp HS rdn luy|n dupc TDST thdng qua trung bdl cdc ylu vi|c gidl cdc bdl ldp todn D td' sou: Khd ndng tim ro (1) Tr^n Lu§n "D^y hpc sang 190 mdn Toan d tiuong nhung lidn tudng, phd thdng" Tap chi Nghiin cuu gido difc, s6 ttiang 3/ nhung md'l lidn 1995 (2) T6n Than Xdy dtpig hi thd'ng cdu hdi vd bdi tfyp hi mdi vd nhung Hinh 3b nhim bdi dudng m/}t sdyiu td cda tuduy sdng tqo kd't hpp mdi; cho hgc sinh khd vd gidi d trudng trung hgc ca sd Khd ndng Hm gidl phdp Ip dd cd nhOng Vlit Nam Vi$n Khoa hpc giao dye, 1995 gidl phdp khdc Vf dy 4; Cho gdctamdl^n Oxyz cd ZxOy= T&l ll$u tham kbio AyOz~ 45°; ^xOz - dO Chiing minh ring (xOy) Ho&ng Chung Rin luyfn nAng s&ng tfO t o ^ fafc d trudng phi th&ng NXB Gido dtfc H 1969 fyOz) [hinh A) G Polya Tofin hpc vi nhOtt^ suy li^n c6 li NXB Phdn Hch: Trong bdl todn ndy, theo cdch gidl Gido dvc H.196Z thdng ihudng, cd hai hudng d l chiing minh hoi G Polya S^g (90 toin hpc NXB Gido difc, H mdt phing vudng gdc dd Id ho$c cd m^t Ajdng 1978 thing cOa mdt phing ndy vudng gdc vdl mdt phing4 NguySn Thai Hoe Rin luyfn tir qua vifc giai kla hodc Id gdc too bdl mdt phing bing90° bit tf p to6n NXB Gido difc, H 2001 Theo hudng thi bdl todn chua cd sin dct Phan Huy Khai Toin bpc nfing cao cbo b^c sinh k l ^ d l chiing minh Theo hudng 2,taphdl tao Hinh h9C 11 NXB Dgi hgc qudc gia, H 1998 r a B A l B ; B C l B ; A € x , B y , C 0z, «JMMASY sau dd chiing minh ZABC « 90° Creative thirling Is understood osttwmost perTo cd: AOBA = AOBC => OA - CK Lpl c i fect comlsinatlon ofposlffve and independent tNnkZAOC = dO°=> AAOC diu ndn OA - OC - AC Ing aimed to create a great new idea with a good => AABC - AABO (c.c.c) Tu d i , suy ro /ABC = problem-solving capacity Creative thinking Is c^s known as independent thinking becouso It down't ZOBA-W deperKionwtKithast)eene)dshng.ltsindeper)dence Vdl cdch nghr ddc ddo vd IHn tudng bo gdc has reveled both In achleveat^e a^ns and sokjtkjn cd so 45°; 45°; dO° dd cho vdt cdc gdc tpollnc^ngs Ttie ttveetxak: elements of creative tt^r^d are: Beidbiiity; Fluency and Originality The geome bdl m$t cpnh cua hlnh l$p phuong vd hoi dudng ofspace In elementarysctKx^is^npc^iantlaKwIp^i cheo cua hai mdt,tatim dupc m$t Idi gidl mdi: and there are many opportunities for ^stwlnjiW^ Ddt ba tlo Ox, Oy, Oz vdo hinh ldp phuong bask:: elements of creative thinkingtorpupil "^^ ' # - Tgp chi Clao due so tin i - B/aou) ... phdl n i m dupc mdt phing cdch diu b^n dinh cOa hi dl^n dl quo trung dilm ba cpnh d i n g quy Clio tii dijn hoijc Id m^t phing dl qua trung dilm hin cpnh i&\ dl|n ddi mdt; - HS phdl ihdnh thpo md''l... vd:AB,=^AB: C,B,=icB;/l,C,=iAC; S.= "^ 4.a+4lan''^) Trudng hqp Thid''t d l # n dl qua trung dilm cdc cpnh A C , CB vd dl quo trung dilm cOa cpnh bdn SC (hlnh 3a) Khi d d , mp(P) c i t hlnh chdp SABC iheo... chOng minh (ACD) (DAD''|, Wc " "" 4^741mV Trudng hgp Thilt dl|n dl qua trung dilm mdt bin vd mdt cdc canh AC, CB vd dl qua trung dilm cpnh bdn ddy ciJa htnh ldp SA, SB (hinh 3bj Khi dd, mp(P) cdch