JOURNAL 01 SCH NCF Oi''''" IINUI I diicatioiial Sci 2012 Vol 57, No 9 pp, 10 19 QUI IKINH DAY HOC (;iAI HAI TAP H I N I I HQC THKO QUAN DIEM KIKN TAO CHO HOC SINH GIOI THCS N g u y e n A n h Tiian^*, Ph[.]
JOURNAL 01-SCH-NCF-Oi'" IINUI-: I-diicatioiial Sci 2012 Vol 57, No pp, 10-19 QUI IKINH DAY HOC (;iAI HAI TAP H I N I I HQC THKO QUAN DIEM KIKN TAO C H O H O C SINH GIOI T H C S N g u y e n A n h Tiian^*, P h i T h i T h i i y Van^ ' Truimg Dgi hgc Su phgm Ud Ngi '^ Sd Gido due vd Dao tgo lidi DUffng *E-mail: luandhsphn@gmail.com JVini 151 liiu hiio dai la v;i giai quyel van dc van dung li thuyel kien liin de xay dUiiy quy irinh day hoc giiu liiii lap hinh hpc cho hpc sinh yi()i d irUdng Irung hpc cif sii, ihUc hien diii nu'ii phUOng phap day hoc mon Toan ihco hifdng lich cUc hda hoal diing hpc lap, gdp phan nang cao chai lUOng day hpc loan vii bdi dUdng hoc sinh gidi mon Toan TUkhda: Ly thuyet kicn lao day hoc giai biii tap hinh hoc Md dau Day giai bai lap la mot nhflng tinh hudng day hpc die'n hinh Nhd qua trinh nay, ngifdi hpc hieu dUdc ban chat cua kien thflc, cd kha nang van dung linh hoat tri thflc va phUdng phiip da hpc qua dd phat trie'n nang life tU va nhflng kicn ihflc dd mdi trd nen sau s3c, trd vdn rieng ciia hpc sinh (HS) Tuy nhien, ddi vdi IIS THCS, tham chi ddi vdi HS gidi, giai bai lap hinh hpc gap kha nhilu khd khan Bdi lc, so vdi bai tap dai so, bai tap hinh hpc thudng khdng cd sSn mot qui trinh hay thuat giai de" cac em van dung, Van de dat la day hoc giai toan hinh hpc cho HS gidi d THCS, thay cd giao phai lam nhU thi nao dfi' cac em hpc tap mdt ciich hflng thu va chu ddng, tfl dd kich thich tri td md say me khoa hpc, linh ham hifi'u biit ddng thdi phat trie'n dfldc tfl qua irinh tim ldi ldi giai bai toan? Van dung li thuyet kiln tao day hpc giai toan la mpl nhflng bien phap cd the giiip giao vicn (GV) va HS thuc hien dfldc cac yeu c5u tren 2.1 N o i d u n g n g h i e n cij^u Van d u n g Ii thuyet kien tao day h o c giai t o a n h m h h o c cho H S gioi Tren cd sd van dung phoi hdp qui trinh day giai bai lap cua G Polia vao chu trinh nhan thflc cua HS theo quan diem kiln tao (Theo Brandt, 1997): Tri thflc da cd -)• Dfl doan -^ Kifi'm nghifim -^ (That bai) -> Thich nghi -¥ Tri thflc mdi, chung toi xay dflng mot qui trinh day hpc bai lap theo quan difi'm kiln tao cho HS gioi THCS gdm cac bfldc sau: 10 Quy trinh day hoc gidi hdi lap Hinh hgc iheo quan diiiii kien tgo 2.1.1 Bade Tiep can van de (Tudng u'ng vdi bfldc - G Polia) Trong bfldc GV to chflc cho HS thflc hicn ciic hoal ddng sau day: - HS sfl dung cac kiln thflc lien quan den bin loan dc chuyen ddi ngdn ngfl lfl Idi sang hinh vc, ngdn ngfl va ki hicu hinh hpc, lii" dd IIS ve hinh vii ghi gia thiel vii ket luan bai loan - HS dpc hinh ve (Nhin viio hinh vc neu gia thiet vii ket Uu'in cua biii loan) 2.1.2 Btfdc lYai nghiem lai tri thu:c da bict co lien quan tdi bai toan (TUdng u'ng vdi bufdc - G Polia) Trong budc GV de HS thUc hien cac ho;it dpng sail dfiy: / HS huy ddng (mat each cbi tiit hon) nbilng tri ibi'fc cd lien quan tdi bdi todn + Nhflng khai niem, linh chat cd mat gia Ihicl va kci luan + Bai toan (dang loan) cd lien quan da bict (nhan dang biii loan vii phUdng phap giai) HS phdn tich (so sdnh doi chieu dgc biel hda lifdng tu, ) de tien hdnh "ddng bda " niu bdi todn dd cho thu(}c dgng dd biil vd dd cd quy irinh gidi quyet Nfiu hoat ddng ddng hda cdng thi IIS tiep luc ihifc hien budc neu hoal ddng ddng hda chua cdng thi HS tiep tuc thUc hien budc 2.1.3 Bifdc Kham pha dfldng loi giai (Tuong u'ng vdi budc - G Polia) GV to chflc cho HS thuc hifin cac hoat ddng sau day dc thuc day qua trinh "ddng hda", hoac "dilu flng" nhflng kiln thflc da cd (Cac boat ddng ludn dan xen va bd trd cho nhau, thfl tu cac hoat ddng cd the' thay dd'i thudc vao bai loan) / SiJ[ dung cdc phep suy ludn xuoi, ngugc tien, nguoc lid Sfl dung cac phep suy luan xudi, ngUdc tien, ngUdc lui de khai thac gia thiet, phan tich kit luan hoac bien doi bai toan Dudodn Du doan mdi quan he gifla nhflng ddi tupng bai loan; udc lUdng mdt sd dai lupng bai toan; dU doan dUdng ndi gifla gia thiet va ket luan cua bai toan thdng qua cac hoat ddng quan sat, fldc Ifldng, dac, sfl dung phan mem hoac cac thao tac tri tue tUdng tu hda, dac bict hda, khai quat hda, cac phep suy luan xudi - ngfldc Kiim tra vd dieu chinh cdc du dodn Kiem tra va dilu chinh cac du doan bang cac vi du, phan vi du, hoac sfl dung phan mim day hpc, sfl dung phep suy luan xudi - ngfldc Ve dudng phu Ve dudng phu bai toan hinh hpc la mpt khau rat quan trpng, nhd cd dfldng phu HS cd the nhin rd hfldng giai bai loan hdn Trong cac hoat dpng tren GV lflu y hfldng dan HS cac thu thuat ve dfldng phu Sau day la mdt sd hfldng ve dfldng phu ma GV can phai thfldng xuyen ren luyen cho HS: - Hfldng i Ve dfldng phu dfla vao cac yeu to trflc quan cua hinh 11 Nguyen Anh l l i i i n , Plif Thi Thliy Van -1 lifOiig Ve ilifiing l)hu lao la cac hinh Ihcia niSn tifng bihic suy luan de tim ki^m lili gull ci'ia bai loan - IlKcing 3, Vc clKiIng phu dc lam xual hicn cac linh chSl dien hinh d mo hinh cua bill loan - liming Vc duilng phu dila vao vice xel eac trifitng hop dac biel ciia bai loan - lining Vi- duilng phu dc khai Ihac cac phep bien hinh 2.1,4, Xit li tinh huong be lac IrDng qua trinh suy luan Tiling qua uinh ,suy luan tim lili giai ciia biii loan, US nhieu gap cac linh huong be tac di viio ngS cut khong thii' suy luan dJOc ti6p, Iritdng hop GV phai ren luyen cho HS each dicu chinh hui'lng suy luan theo each sau: Cach Dui Ittlfing chiing minh Doi hUi'ing ehiing minh Ihco eiie hifiing sau; - Dfii hiTiing suy luan bSt dau III mot bUi'Ic suy luan nao - s a dung phuong phap loai dan hoac phuong phap gian ti6p lis mot budc nao ciia qua trinh suy luan hoac lif bUcJc dau tien - SiJt dung eae phep bic:n hinh Cdeh Giant hdi yeu ciiu ctid hdi todn - Giai mot phan eua bai loan - Xel truiing hdp dac biet ciia bai toan Cdeh Tim each sU dung het cdc dit lieu cUa bdi todn Trong qua trinh tim each giai cOa mol bai loan, can tan dung mpi dii kien ciia bai loan N6u edn mot dO kien nao chila sii dung den, hay lim each sil dung dii kien 2.1.5, Birdc 4, Trinh bay ldi giai bai toan (TiTdng ling vcri bu6c - G, Polia) Day chinh la qua Irinh HS thich nghi (bSng each lien hanh diidng giai bai loan do) de Ihu dUdc Iri thiie mdi; quy trinh giai bai loan Trong budc GV yeu cau HS thilc hien eae boat dong sau day; - Neu eac biidc giai bai loan dudi dang sd - Dua vao sd dd yeu c3u HS IU trinh biiy ldi giai bai loan 2.1.6, Birdc 5, Cung c6, ap dung va phat trien bai toan (TUdng ling vdi budc G Polia) Hoat dpng 1: Nhin lai Idt gidi bai todn De kiem tra ti'nh dung, chat che va hdp li ciia cac budc suy luan, tii dd cd the tim cae ldi giai khac cua bai loan Trong hoat ddng GV to chiic cho HS; Kiem tra lai su chinh xac ciia tiing budc chiing minh cac phep toan, sU hdp logic ciia lap luan dac biet lam ro dUdc suy lu§n c6 li cac budc suy luan viec tim l(Ji 12 Quy trinh day hgc gidi hai lap Hinh hgc iheo quan diem kiin tgo giai cua bai toan Tfl dd th4y dUdc Uu, nhupc die'm cua Idi giai va cd the lim dUdc phUdng phap giai mdi Uu viet hdn De lam rd dUdc suy luan cd li d cac budc suy luan vice lim Idi giiii cua bai toan, d mdi bifdc suy luan GV phai cho HS hieu dUdc vii tra ldi cac cau hdi lai lai theo hudng hoac chpn phUdng an nay, dong thdi HS thfl cac phfldng an cdn lai tfl dd la cd the tim each chflng minh mdi hoac cung cd the di vao ngd cut Tfl dd IS cd ihcm nhflng kinh nghiem thu phap de tim ldi giai cua bai toan Qua dd cung cd the md rdng dUdc bai toan theo cac each khac Hogt dfmg 2: Ap dung true liip GV cho HS ap dung phUdng phap giai hoac kit qua ciia bai loan I vao giai cac bai toan tUdng tfl hoac cac bai toan cd the suy kit qua nhd bai loan nham ren luyen kl nang giai toan cho HS Hogt dgng 3: Ap dung ndng eao GV cho HS ap dung phUdng phap giai hoac ket qua ciia bai loan vao khai thac, md rdng bai toan; giai cac bai loan khd, phflc lap hoac cd npi dung ihuc te Qua dd cd the lao dUdc vdn lilng kiln thflc mdt each sau, rong va phat trien kha nang tu sang tao cua hpc sinh gidi Trong hoat ddng GV td chflc cho HS IhUc hien cac viec sau day; - Khai thac md rpng bai toan theo cac hUdng sau day: + Lap bai toan dao + Dac biet hda bai toan + Khai quat hda bai toan + Thay doi mpt sd ylu td (cac ylu td difa vao khai thac mdt khau nao dd cua qua trinh chflng minh) de dUdc bai toan mdi - Giai bai toan nang cao hoac cac bai toan thflc tl Yeu cau HS van dung bai toan vfla giai vao nhflng linh hudng khd phflc tap va ddi hdi tong hpp nhieu kiln thflc Hogt dgng 4: Td chtic lgi cdc kien thtic lien quan den bdi todn ban ddu GV cho HS to chflc lai mdt so kiln thflc lien quan den bai toan vfla giai, tfl dd tao von lilng cho cac em de d l lien tudng kiln tao kiln thflc sau Mdt kiln thflc toan hpc hay mpt bai tap toan dfldc dfla khdng the tach rdi, khdng tfl sinh mot each dpc lap ma cd nhflng cd sd nhat dinh nam he thong kien thflc da cd trfldc dd J.A Kdmenxki da tflng ndi: "Day hpc la qua trinh tfl tfl va lien tuc, nhflng dieu cd hdm phai cung c6 cai hdm qua va md dfldng cho mai" Theo quan diem cua chung tdi, td chflc lai cac kiln thflc lien quan den bai toan ban dau theo cac hfldng sau day: - Nhac lai cac hfldng chflng minh quan he hinh hpc lien quan din bai toan Sau moi giai bai tap, HS cd the linh hpi them mdt hudng chflng minh mot quan he hinh hoc nao dd, trfldng hdp GV cin nhan manh va ddng thdi yeu can HS thong ke lai cac hfldng chflng minh thfldng dung cua quan he hinh hpc de tao "vdn 13 Nguyen Anh 'llian Phi Thi Thuy Viin lieng" cho I IS lim hitdng chifng miiih dinh li hoiic bai loan sau \'; du Sau giai \oiiji hai to;in "Tiong mdt lfl giiic tdng cac tich hai cap canh doi ludn Idn hon hoac hiing lich hai dUdng cheo", Dau bang xay va chi lfl giac ndi tiep (Hat dang ihflc ndlcmc), HS cd ihciii nidi phfldng phiip chflng minh tfl giac ndi liep, qua yen cau I IS nhiic lai c.ic hfldng chitng minh lfl giac ndi licp ma cac em da bill - Tap hpp Lac kicn thifc lien quan den mui kiln thflc nao dd bai loan Vidu: Sau giiii cac biu loan hen quan den trflc tiim GV cd the he thdng hda cho lis mdt sd kien ihi'fc lien quan den tufc tam de HS ghi nhd Uio nen vdn lilng cho cac em: Trong mpt (am guic bat ky: / Khodng edrh lif tnfc tdm den mdi dinb bdng hai ldn khodng cdeh lif ldm dudng iivn ngogi liip din cgnh doi dien TrUc ldm, trgng tdm vd tdm duiing trim ngogi tiip ndm tren nu'u dififng thdng (ggi Id difimg thdng 0-le) khodng (dch tif tnmg tdm din irifc tdm bdng hai ldn kluuing edch lif Irgng Idm din ldm duifng iron ngogi liep Cde diem ddi xdng vdi mu tdm qua ede eanh ndm tren duifng iron ngogi liep Clia tam gide dd Chi'fng minh diem dtn xt'fng cua irifc tdm H qua trung diem ede cgnh i ua tam gidc ABC Iriing vdfi diem ddi xi'fng eiia dinh ddi dien qua O vd difi'm dd ndm tren duifng trdn Chin diem gdm ba trung diem eua ba cgnh chdn duifng cao, ba trung diem eua ba dogn thdng ndi lir true tdm den dinh eua tam gidc ndm iren nwt duifng trim co tdm Id trung diem cua dogn thdng niii true tdm vdi tdm ciia duifng trim ngogi tiip vd hdn kinh hdng niia bdn kinh eiia ducfng trim ngtfgi tiep (duifng trim dd dUffe ggi Id duifng trdn 0-le) - Nhiin manh phUdng phap giai bai toan ban dau neu dd la phUdng phap mdi (trong dd lUu y den each ve them dUdng phu neu cd) - HS nhin lai cac menh dc tren de thay cac kiln thflc, cac bai lap (hoac he thdng bai tap) lien quan den bai toan ban d5u Trong mdi budc gdm cd cac hoat ddng cua GV va HS cac hoat ddng dan xen va bd trd cho cd nhflng hoat ddng cd the dfldc lap lai Tuy nhien, d mdi bai toan khac tflng budc cd the sfl dung mot va mpt so hoat ddng cua bfldc dd 2.2 Vl du ap d u n g Sau day chung tdi xin neu mdt vi du minh hpa cho qui trinh tren: Bai Cho tam giac deu ABC ndi tilp dfldng trdn {()) Diem M chay tren cung nhd BC Chflng minh MA = MB + MC (Bai 20 trang 102 sach bai tap loan Idp tap 2, NXBGD, Tdn Than chu bien) Trong bai bao nay, chung tdi qui fldc: (?) Cau hdi hoac cau dan dat cua GV (!) Cau tra ldi mong dpi cua HS ( ! ) Sfl suy nghi (im lang) cua HS 14 Quy trinh day hgc gidi hdi lap Hinh hgc theo quan diem kiin Igo Bude } Tim hieu ndi dung hdi todn (?) Hay sfl dung cac kicn thflc Hen quan den bai loan dc chuyen ddi ngdn ngd tfl ldi sang hinh ve, sang ngdn ngU va ki hicu hinh hoc, tfl dd IS vc hinh vii ghi gia ihicl va kel luan bai toan Vdi Iflu y HS phai neu dupc each ve tam giac deu ndi tiep dfldng trdn bang thudc va compa (!) Gia thiet: (O); A, Z?,r Ihudc (C;);/4/:J - AC /ir.'; A/thudc cung/:;6'(Hinh 1), Kll luan: MA MB + MC Budc Trdi nghiem (Hen he vdi vdn Iri thu'c da cd) GV dua cac cau hdi yeu cau IS triii nghiem kiln thflc da hpc: (?) Cac em hay nhd lai nhflng khai niem, dinh li, bai toan va cac phfldng phap chflng minh cac quan he hinh hpc lien quan din bai loan nay? (!) HS cd the nhd lai din : - Tinh chat cua tam giac deu ndi tilp dudng trdn, cac gdc ndi tilp cua dudng trdn - Cac hudng chflng minh mdl doan thang Hinh L bang tong hai doan thang khac nhu sau: Hudng } Chia doan thang ldn hai phSn, mdt phan bang mot hai doan thang cdn lai Ta phai chflng minh phSn cdn lai bang doan thang Hudng Tao mpt doan thang bang tdng hoac hieu cua hai doan thang, sau dd chflng minh doan thang mdi tao bang doan thang thfl ba (?) Cd the ap dung trUc tiep cac tinh chat, cac dinh li hoac cac bai loan da biet de giai bai toan dUdc khdng? (HS thUc hien qua trinh ddng hda) (!) HS khdng thuc hien dUdc hoat ddng ddng hda, GV tiep tuc chuyen sang budc Budc Khdm phd dudng loi gidi GV td chflc cho HS kham pha dfldng loi giai nhu sau: (?) Hay sfl dung cac phep suy luan xudi, ngUdc de khai thac gia thiet va phan tich kit luan cua bai toan (HS sfl dung phep suy luan) A (!)HS cd the dfla hai hfldng: Hudng L Chia doan MA hai doan mot doan bang mpt hai doan chang han bing doan MB Phai chflng minh doan cdn lai bang MC (Hinh 2) Hudng Tao doan thang bang tong hai doan thang MB va MC Ta se chflng minh doan Hinh 15 Nguyen Anh 'I\iiui, Phi Thj Thuy Viin tliiiiig nidi tao bring tloaii thiing MA (7) Miiy chon mdt hai lulling Ircn dc ehiing minh bai toan, chang han hudng Tlie hi chia tloaii 1/,1 Ihimh hai doan mol doan bang mol Irong hai doan ehiing han bang Joan MB Phin ehiing minh doan edn lai biing MC ('*) r;ic cm hiiy liim dieu dii di (!) Tren doan A/.l lay dicm X cho ,'1/A' MB (HS thife hien hoal dpng ve MC (Iloae tren doan MA lay diem X difdng phu) Ta phiii ehdng minh XA eho -I.V MIS Ta phai chiing minh MX = MC) (•.') Hay chiing minh A'.'1 - MCI (!) HS cd Ihi: dit doiin ehifng minh tam giiic 4BX hicn hoal dong du doiin chiing minh) (?) Hay kicm Ira xem hai tam giac ABX biing lam giiie C'BM (HS thifc vii lam giiie C 13.M cd bang hay khdng? (!) Hai tam giiie ABX vii tam giiie CBM thife hicn hoat dpng kicm tra du doan) bang irudng hdp (cgc) (HS Btlfic Trinh bdy lili gidi hdi tudn - Neu Ciic blidc giai bai toiin dudi dang sd Lay X tren doan MA eho MX tam giiic deu f^ABX -= /.CBM = MB Tif dd la cd tam giac BMX =* IA' = MC => AM MB + la MC - Dua vao sd dd yeu cau HS tif trinh bay ldi giai bai loan Lay X tren doan MA cho MX = MB Tam giac BMX co MX = MB va /.BMX = /BCA = 00° nen tam giac BMX la tam giac deu Xet cac tam giac ABX va CBM cd AB = BC BX = BM/ABX = /CBM (vi cung cdng vdi goe CBX bang 60°) Suy hai lam giac bang nen I.V = MC^ IChi dd ta diidc AM MB+ MC(\) Buac Nhin lgi ciing co vd phdt trich hdi todn Hogt dpng 1: Nhin lai ldi giai bai loan (?) Hay kiem Ira lai sif chinh xiic cua titng bitdc chiing minh cac phep loan, sil hop logic cua lap luan dae biet lam rd ditoc suy luan cd li fl cac bade suy luan viec tim Idi giai eua bai loan TO dd thay duac Uu, nhupc diem cda ldi giai va cd the tim dlldc phudng phap giai mdi uu viel hdn (!) Ciic budc suy luan dSu chinh xac va cd ihS' thay dUdc them ba each giai cua bai loan Hogt dpng 2: Ap dung triic tiep GV cho HS giai cac bai loan sau day de nim vung phudng phap giai bai toan (hoac dang loan nay) va ciich ap dung bai toan trudng hdp ddn gian: Bai Cho tam giac deu ABC npi tiep dudng tron ( ) Diem M chay trfin cung nho BC Xac dinh M de MB + MC ldn nhat (TO kk qua MB + MC = MA bai loan trgn, de MB + MC ldn nhk tudng dUdng MA lon nhat, tiic la MA la dudng kinh cua dudng trdn Hay M la Him d6i xiing Quy trinh day hgc gidi bdi tap Hinh hgc theo quan diim kien tgo cua A qua O) Bai Cho hai dfldng trdn (O; /?) va (0'\ /?') tilp xuc ngoai lai D Vc lam giac deu ndi tilp dudng trdn (O) Ke cac tilp tuyen 4/1', BB' CC vdi dirdng trdn (()') a)Tmh A.A' theo AD R R' b) CMR: Trong ba doan AA', BB', CC cd mdl doan bang tdng hai doan thang a) Dua vao he thflc lUdng lam giac vudng ti'nh dUdc AA'^ AD • AD' (D' la giao diem thfl hai eua AD vdi dudng trdn {O'), dua vao hai tam giac ddng dang ADO va D'O'D ta tinh AD' theo AD /?, 7?' TU dd tinh dUdc AA' theo AD /?, /?' b) Ap dung kit qua cua bai toan ban dSu coi diem D nam iren cung BC ta cd AD = BD + CD kit hdp vdi cau a va ti'nh difdc BB'theo BD R, R', tinh CC theo CD, R R' suy dilu phai chflng minh Hogt dgng 3: Ap dung nang cao - Khai thac md rdng bai toan Ddi vdi bai toan I, GV din dat HS the md rdng va khai thac bai loan theo hudng khai quat hda nhu sau: Thay gia thiet tam giac ABC la deu lan lUdl b3ng cac trUdng hdp tam giac vudng can, tam giac can va tam giac bat ki (?) Xet trudng hdp tam giac ABC vudng can tai A ndi tilp dudng trdn (O) Diem M chay tren cung BC khdng chfla A Tim he thflc lien he gifla MA MB, MC Thfl xet mpl vai vi tri dac biet cua diem M Khi 71/ = JB ta cd; MB + MC = BC:MA AB.YiABCvixdngcannenBC = ABnentad\idQ&nMB+MC ^ MA (2) (?) Cac em hay kiem nghiem dU doan tren? Bang each chflng minh tUdng tu vdi bai toan ban dSu HS cd the neu dUdc each chflng minh nhfl sau; Chflng minh: (Kinh 3) Ha BX vudng gdc vdi AAL Ta cd: ZAMB == ZACB = 45« (hai gdc ndi tilp cung mdt chan cung AB) Khi iy suy tam giac BMX vudng can tai X, suy MB = ^/2 MX{\) Xet tam giac ABX va tam giac CBM cd: ZBAM = /.BCM (hai gdc ndi tiep cung mdt chan cung), ZBXA == ABMC vi cung bang 90" , suy hai tam giac ddng dang Nen MC : AX ~ BM : BX = ^/2 , suy MC=s/2AX (2) Tfl (I) va (2) suy dieu phai chflng minh MB + MC ^ MA (?) Hay neu kit qua vfla chflng minh? ^ Hinh (!) Tam giac ABC vudng cSn tai A ndi tilp dfldng trdn (O), diem M chay tr6n cung NgiiyCn Anh 'Rliin, Phi Thi Thiiy Van Hf • khdng ehiiii , I TttciiMll I A/f ' - W/1 (Ta coi day la bai toan 4) (7) Tifilng Ilf mi't ipng hiii uuin eho tnfdng hpp lam giiie can dc cd ket qua sau; l!:ii Tiim giiic AlIC eiln liii ,1 npi licp dttdng Iron {(;), dicm M ehay tren cung HI • khniis; chifa Ta eo MB I MC - — • MA ('.') Mil long eho irifiing hdp tam giiie AIK ' lii b'll ki npi licp dudng trdn (O), diem M chay Ircn cung lIC khong chiia A Khi la sc cd he thiic lien giiia MA MB, MC nhu the nao? Nguili ta ehiing minh diing thife MA • BC - MB • AC f MC • AB.Bo ehinh lii luii dung eii.i dinh li Ploleme; Trong mpl tti giiic npi licp lieh hai dudng cheo bang long Ciie lich hai cap Ciinh ddi dicn (?) Md ldng truimg hpp tam giiie dcii ABC thiinh IU giiic deu, ngu giiic deu, that giiic dfiu ta ed Ciie kel qua gi'' (?) Cac cm h.iy tim hieu va chUng minh mpt so kcl quii sau; Bai 6, Cho hinh \ udng BCD npi tiep ((;; /?), 1/ la dicm chuyen dpng tren cung B C D Chiing minh rang A/D + MB = MA (suy lif bai 4) Bai 7, Cho ngu giiic deu / l i / l / l , v l | / l ; npi liep duilng Iron (O), 1/ la mot diem trencung/1,/i,r, Chiing minh ilng A//I2-I-A/Zli "= I'.'li t ^lA, \-MA-, (Ap dung dinh li Ploleme vao cac tii giac ndi liSpfl//l|.l2-^i M A,A,.-\i MAiA2A'J Bai Cho that giac dSu A,A.2 Ay ndi liep dudng trdn (O), M la mpt diem Uen cung A^Aj Chitng minh rang MAj + MA3 + M.A-, + A/.I7 == MA, + U.I, + M.Af (Ap dung dinh li Ploleme vao cac ui giac noi tiep MAiAiA'i, MAiA.iAi, M.AiA.jA-^ MA,A,.A„ ,l/.-l,.l -l7) GV cd the khuy§n khich tri td md ciia HS bang eae eau gdi md sau day; (?) Cd the md rpng bai loan tren cho trudng hdp da giac deu la ed ket qua that thu vi HS se dupe hpc d cac Idp tren - Giai cac bai loan nang cao Bai Cho tam giac deu ABC cd eac canh bang n (n > 0) , Tren AC lay diem Q di dpng, tren tia doi cua tia CB lay diem P di dpng eho -XQ • BP = a^ Goi M la giao diem cCia BQ va AP ChUng minh rang; A.M + );f' - BM (D4 thi vao midng THPT chuyen Le Quy Ddn - Thi \ii Ddng Ha - Quang Tri nam hoc 2005- 2006) Bai 10, Cho dudng trdn tam {0) va diem M nSm dudng trdn Cac day AiBj,A2B2, AsB-i di qua M{A,,B.i, A3, Bi, ,42, B3 theo thd tu nam tren dudng ttdn (0) ) va ddi mdt tao vdi mdt gdc 60" Chiing minh rang; MAi-\-MA2-t-MA3 = A/B1 + A/B2 + A/B3 Hogt dpng 4: Td' chde lai cac kien diilc lien quan den bai loan ban dau Trong hoat dpng yeu cSu HS rut dUdc cac nhan xet sau day: Nhan manh lai each chiing minh mot doan thing bang tdng ciia hai doan thang khae da sii dung bai toan Rtit kSt qua; Trong ba doan thang noi tii mdt diem tren dudng tron den ba dinh 18 Quy trinh day hoc gidi bdi lap liinh hge theo quan diiin kicn tgo cua tam giac deu npi tilp dfldng trdn dd cd mot doan thang bang tdng ciia hai doan thang cdn lai Nhin lai cac bai loan lien quan den bai loan I - Dien dat ket luan bai toan theo each khac ta thu difdc bai loan - Md rdng trfldng hdp tam giac deu ciic lam giac vudng can, can, tam giac bat ki (bai 4, 5, 6, 7, 8) - Ap dung ket qua bai toan de giai cac bai loan nang cao (bai 9, 10) Ket luan Tfl viec nghien cflu ly thuyet kien tao va van dung day hpc hinh hpc cho HS gidi d THCS chung ldi da xay dUng quy trinh bUdc day hpc kiln tao giai bat tap hinh hpc va lam rd each thflc lien hanh cijng vdi minh hpa thdng qua vi du cu the Theo quan dicm cua chflng tdi, khdng phai bai tap nao cung cd the day theo phUdng phap nay, ma chi cd nhflng bai tap dai dien (hat nhan) eho mdi Idp bai tap cimg mdt phUdng phap giai Cling ap dung mdt kll qua nao dd, hoac eung lien quan den mdt md hinh hinh hpc Tinh dai dien cua bai toan dupc the hien d cac phudng dien sau day: - Phuong phdp gidi Id tieu bieu eho mot ldp nhu'ng bdi ciing logi hay kit qud diffJe sii dung de gidi hdng logt nhifng bdi tap khde tif trang bi cho cde em cdc thii phdp gidi todn - HS cd the nhdn dgng dUdc bdi todn tdt cd cde bien dgng eua nd dn cdc bdi todn cd lien quan, delif ndy sinh phiUfng phdp gidi bdi tap - Nd ed vai tro nhu mdl cong cu thUe hdnh ddc lUc cho HS gidi mgt lap cde bdi todn TAI LIEU THAM KHAO [1] Nguyin Ba Kim, 2009 Phuang phdp dgy hge man Todn Nxb Dai hpc Su pham Ha Npi [2] Ton Than va cac tac gia, 2005 Todn tap (Sdch gido khoa) Nxb Giao due Ha Ndi [3] Tdn Than va cac tac gia, 2011 Bdi tap Todn tap Nxb Giao due Ha Ndi [4] Tdn Than va cac tac gia, 2005 Todn tap } (Sdch gido vien) Nxb Giao due Ha Ndi ABSTRACT Process of teaching good pupils doing exercises in geometry in secondary school following constructivism theory The Authors set and solve a problem applying constructivism theory to build up the process of teaching doing exercises in geometry to pupils in secondary school, innovating method of teaching maths with active learning orient, contributing raise quality of teaching maths and trainning for good maths pupils 19 ... dfldng cho mai" Theo quan diem cua chung tdi, td chflc lai cac kiln thflc lien quan den bai toan ban dau theo cac hfldng sau day: - Nhac lai cac hfldng chflng minh quan he hinh hpc lien quan din... 4: Td chtic lgi cdc kien thtic lien quan den bdi todn ban ddu GV cho HS to chflc lai mdt so kiln thflc lien quan den bai toan vfla giai, tfl dd tao von lilng cho cac em de d l lien tudng kiln tao... hpp Lac kicn thifc lien quan den mui kiln thflc nao dd bai loan Vidu: Sau giiii cac biu loan hen quan den trflc tiim GV cd the he thdng hda cho lis mdt sd kien ihi''fc lien quan den tufc tam de HS