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TE dc3NG DAI HQC DONG THAP Tap Chr Khoa hpc s6 24 (02 2017) KHAI THAC BAI TOAN HINH HQC K H 6 N G GIAN TRONG D^Y HOC TOAN d TRircnVG P H 6 T H O N G T H E O HirOOVG BOI DirOfNG NANG LlTC KHAM PHA TRI[.]
TE.dc3NG DAI HQC DONG THAP Tap Chr Khoa hpc s6 24 (02-2017) KHAI THAC BAI TOAN HINH HQC K H N G GIAN TRONG D^Y HOC TOAN d TRircnVG P H T H O N G T H E O HirOOVG BOI DirOfNG NANG LlTC KHAM PHA TRI THU'C MCfl CHO HOC SINH • Vo Xuan Mai'*' Tdm tat Trong bdi viit ndy, chung tdi de cdp din guan diim dgy hgc khdm phd cua Jerome Bruner vd van dung mdt so y tu&ng vdo viec to chuc hogt dgng Midm phd tri thiec todn hgc, tie khai thdc bdi todn hinh hgc khong gian & tru&ng phS thdng theo hu&ng bdi dudng ndng luc khdm phd tri thucm&i cho hgc sinh Tie khda: khai thdc bdi todn ndng liec khdm phd tri thiec m&i, dgy hgc khdm phd, hinh hgc khdng gian cau tnic toi uu cua nhgn tfaiic;fadnfaddngtimtdi, kfaam phd cua HS; ciu trdc ciia chuong trinfa day hpc vd ban chat ciia sy tfaudng - pfagt Quan ffilm day hpc kham phd cua Bruner dupc de cgp din bdi faai yeu t6 ttong md hinh dgyfapcnay, la cau true toi uu ciia nfagn tfaiic; hanh dpngtimtdi, kfaam phd cua HS Bruner dio rdng, rapt cau true nfaan tiiuc ^ i uu can cd ba dgc tinfa quan trpng: tmfa tiet kiem; kfad nang sdn sinfa cdi mdi vd sue mgnh cua can tnic Tinfa tiet kiem la kha nang don gidn fada cac tfadng tin kfaac ttong mpt linfa vuc, giiip cho ngudi hpc nhan dupc cai chung cai rieng, nhgn sy vat chi la phy cua mot sy vat khde, nfagn sy kien khdng giong t i t cd cac sy kien khde Cdn kha nang sdn sinh cdi radi vd siic mgnfa cua cau true la kfad ndng tim dupc su kipn mdi, hieu biet sau vd rpng faon nfaung thdng tin da cho, khd nang van dyng ki^ib thuc da fapc dupc vao viec giai quyet cdc tinfa huong rieng Theo Bruner, cd hai Ioai iing dung cau tnic: chi^en di cdc moi lien tudng, cac ki nang da tiep tfau dupc sang cac lien tudng, ki nang gan giong vdi nd vd chuyen di cdc nguyen tac, cac tfadi dp da cd vdo cdc tinh fauong kfaac - logi chuyen di ndy chinh la ttpng tam cua qua trinh dgy hpc, Id sy md Quan di^m day hpc kham pha cua rpng vd dao sau khdng ngung kien thiic theo Jerome Bruner va van dung vao vi6c to chiic rihiing y tudng, ngi^en tac t6ng qudt vd co ban, iTng vdi rapt c4u tnic nfadn thuc vd khung hoat dong Idiam pha tri thuc toan hoc cua HS 2.1 Quan diem day hoc kham pha cua chuong trinfa, Bruner de xuat rapt mdfainfahpc t ^ tim tdi kfaam pha nhu sau: trudc het BS la Jerome Bruner Theo [3, tr 59], J Bruner de xuat md hinh ngudi tu Iyc, tich cycfadnfadpng tim tdi, kham day fapc dupc ddc tnmg bdi bon yeu to chii yeu: phd doi tupng fapc tap de hinfa cfao minh cdc nguyen tdc, cdc y tudng co ban tir cdc tinh huong fapc tap cu th^ Trong fapc t ^ kfadm pha '"' Nghien ciiu sinh, Trucmg Dai hoc Su pham Ha Npi, D^t v^n de Day hpc kfadm pha dupc xuat pfadt tit li thuyet faogt dOng cua A N Leonchiep vd R L Rubinstien tu nfaung nam 1940 Tuy nfaien, ngudi cd cdng ngfaien cuu de dp dung tfadnfa cdng phuong phap vdo thuc tien dgy hpc Id Jerome Bruner vdi tac pham noi tieng "Qud trinfa day hpc" (The process of education, 1960) tren CO sd nghien ciiu va van dyng Ii tfauyet pfadt sinfa nh$n tfaiic cua Jean Piaget Hipn nay, day fapc khdm pha da dupc quan tam vd v ^ dyng vao qud trinh day hpc toan d trudng trung hpc tfadng, Pfauong pfadp day fapc ndy nham khuyen kfaicfa fapc sinfa (HS) ty tim tdi k i ^ thiic mdi, rut nfaung nguyen tac cho ban than tii nfaiing kinh nghiem, kien tinic da bidt Trong chuong trinh sdch gido khoa todn hipn hdnh, cd nhieu npi dung cd the kfaai thdc nham boi dudng cho HS kfaa ndng tim tdi, kfadm phd tri thiic mdi Vi vgy, cfaiing tdi ngfaien ciiu mpt so yeu to cfainfa quan diem dayfapckhdm pha cua Bruner, tir van dung nhiing y tudng vdo to cfaiic hoat ddng day fapc tfaeo hudng boi dudng nang Iuc khdm phd tri thiic toan hoc cua HS qua vipc kfaai tfaac cdc bdi toan hinfa hpc kfadng gian d trudng pfao thdng TRUdNG DAI UQC D N G THAP cho phep HS di qua ba giai dogn, ba hinh thuc hdnh dpng hpc t ^ : faanh ddng phan tich (thao tac vafaanfadpng tren cdc tai lieu da cd), faanfa ^ n g rad hinh hda (hdnh dpng ttdn cdc hinh dnh ve chung) vd hdnfa dpng ki faieu fada (nit dupc cac khdi niera, cdc qay tac cfaung tii nfaiing rad hinh dd) Yi vay, fapc t£tp kfaam pfad, gido vien (GV) can cung cap nhieu tinh fauong de HS cd Ifae dat can hdi, khdm pha vd tiiyc nghipm cfao den kfai tim dugc cac nguydn tac, cdc y tudng, cdc raoi lien he co ban cau true mdn fapc Can to cfaiic cfao HS tien faanfa cac fadnh ddng hpc tiq) tuong ling vdi cac Iiinfa tfaiic bieu faien cua can true (faanfa ddng pfaan ticfa, fadnfa ddng md fainfa hda, faanfa dpng ki faipu fada) tfaeo phuong phap chung Id suy lugn quy n^i 2.2 Van dung quan diem day hoc kham pha cua Jerome Bruner vao viec th chuc ho^t dong kham pha tri thuc toan hpc cua HS Theo [2, tr 159], tac gid da chi cdc yeu to CO bdn cua dgy hpc khdm pha Id: - GV nghien cira nOi dung bdi hpc den raiic dp sdu can thiet, tira kiem nfaung yeu to tao tinfa huong, tgo co hdi cho faoat ddng kfaara pfaa, tim tdi - Thiet ke cdc hoat ddng ciia HS, tren co sd dd xac dinh cdc hoat ddng cfai dao, to cfaiic ciia GV - Kfaeo leo ^ t ngudi fapc vao vi tri ciia ngudi khdm phd (khdm phd cdi mdi cua bdn tiian), to chitc vd dieu kfaien cfao qud trinfa n ^ dien mpt cdcfa tfauan Ioi de hi ngudi fapc xay dung kien tfaiic cfao ban tfaan Trong qua trinfa fapc tap tim tdi kfadm pfad, GV can tiiiet ke nfaihig tinfa fauong de HS kham pfaa tim cdc ngiQ^en tdc, cac y tudng ciia tri tfaiic mdi tten cac kien tfaiic da cd tfadng qua to cfauc cfao HS tien fadnh cdc hanfa ddng fapc t|p tuong ling vdi cac fainfa tfaiic bieu hien cua cau tnic: hanh ddng pfadn tich, hanfa ddng md fainh fada, hanfa dpng ki faieu fada vdi phuong phdp chung Id siQ* luan qity n ^ de riit cdc nguyen tdc chung, tim cdc sy kien mdi, hieu sdu sdc va rpng faon cdc thdng tin da cho ^^pc phdt hien cdi mdi Id ket qud ciia qua trinfa efauyen di cac moi hen tudng, cac ki nang da tiep tfau dupc sang cdc lien tudng, ki nang gan giong vdi nd; cfai^en di cdc ngayen tdc, cdc thdi dp da cd vao cdc tinh fauong kfaac nhau; nfagn dupc cai chung cdi rieng, nhpn sy vat chi Id phu cua rapt Tap chl Khoa hpc s6 24 (02-2017) sy vgt khac, nhgn sy kien khdng giong tat ca cac su kien khac Qua trinh phat faien tim tdi cai mdi keo tfaeo su pfadt trien tri tup cua HS, qua trinfa gan lien vdi vipc hinfa cdc so nhdn thirc mdi Khai thae cac bai toan hinh hoc Idiong gian & trudng diong tfaeo hirong boi duong nang luc kham pha tri tiiuc m6i cho HS 3.1 Nang Igrc kham pha tri tiiirc mdi Nang Iyc Id mpt van de kfaa trim tupng cua tam Ii fapc, kfaai ruera nang Iuc dupc nfaieu nfad nghien cuu ve Tdm li fapc va Gido due hpc tten the gioi ciing nfau Viet Nam quan tam; nang luc dupc faieu nfau sy thanfa tfago, kfad nang thyc hien Clia cd nhdn doi vdi mpt cdng viec, nang Iyc mang tinh cd nhan hda, cd the diroc hfaifa thanfa va phat trien thdng qua ddo tao, boi dudng va ty trdi ngfaipm qua thyc tien Nhu v ^ , nang Iyc Id hp thong nhung thupc tinh cua ca nhan ngudi (kien thuc, ki nang, kinh nghidm vd ngh$ tfauat Cling nfau tfaai dp), pfaii fapp vdi yeu cau cua hogt ddng va ddm bdo cho faoat ddng dat ket qud cao Tfaeo Tu ffien tieng Vipt, kfaara pfad la tim cai mdi, cai cdn an gjau Tfaeo [2, tr 159-160], su kfaam pfad lafaanfadpng pfadt faipn sau mpt qua trinfa tim kiem se tfaay dupc mpt sy vat bi che giau hay cfaua duoc tfaay Kfaam phd Id qua trinh hogt dpng vd tu duy, cd the bao gora quan sat, pfaan ticfa, nfagn dinfa, nSu gid tfaiQ^et, suy luan nfadm dua nfaung tinfa chat, q i ^ luat cac sy vpt,faipntupng vd moi lien fae giiia cfaung Til nfaiing phdn tich tren, cfaung tdi cfaorang "ndng luc khdm phd tri thiec m&i Id ndng liec hogt dgng cua ngu&i hgc nhdm tim ra, phdt hiin duac tri thuc m&i cho bdn thdn v&i nhieng tinh huong nhdn thiec khde qud trinh hgc tap" 3.2 Kfaai tfaac cac bai toan hinh hpc khong gian if truong thong theo huong boi du&ng nang luc kham pha cho HS Tren co sd phan ticfa tren, cfaung tdi khai thdc cac bdi todn lunfa fapc khdng gian Hinfa fapc 11 d trudng pfao thdng nfadm boi dudng ndng Iyc khdm phd tri tinic radi cho HS Tfaeo cfaung tdi, cdc tfaanfa to cua nang lyc khdm pha tri tfaiic radi gom cd: Nang Iyc chuyen di cac moi Hen tudng, cac ki nang da tiep thu dupc sang cac lien tudng, kl nang gan ^ o n g vdi nd, nang Iuc chuyen di cdc nguyen tdc, cac thdi dp da cd vao 23 TRUONG DAI HOC DONG THAP T?p ch( Khoa hpc s6 24 (02-2017) cac tinh hu6ng Ichac nhau, nang Iyc mo Wnh hoa H cua dilm Ofl-en[ABC) Tinh dien tich cac cac 16p doi tmmg toan hpc theo mpt so quan he tam giac HAB, HBC va HCA" Giai bai toan va tinh chit chung cua chiing va nang \\fc the liien quan diem bien chiing cua tu diiy toan hpc nhu sau (Hinh 1) Idiam pha tri thiic moi 3.2.1 Ndng life chuyen di cac moi lien tucmg, cdc ktnang da tiip thu duac sang cdc lien tuang, Id ndng gdn giong vdi no Theo tniong phai tiep cSn cua Thuyet hen tuong Tam li hpc, v&i de liSn tuong tu CO bon loai: Hen tudng giong nhau, hen tuong tirong p h ^ hen tuong ghx ve khong Hmhl gian va thoi gian, lien tudng nhan qua Nang luc duoc xem xet tren quan diem do, day GV Ta CO S^^g = Sg^^ cos a, frong " la CO th^ b6i duong cho HS chuyen di hen tuong giua cac y^u to tuong tu cua cac doi tupng goc giiia hai mat phang (OAB) va [HAB) mat phang va d6i tupng gan giong voi no jaV+bV+'A/ >ci,-ioF+ocf khong gian, tu hinh th thuc mdi tren co 'i a'+4' so nhihig tri thiic da co Vi du HS CO nhiing kien thiic da biet nhu L I.2„2 "Cho tam giac ABC vuong tai A, duong cao Vo' 2V +i 1 AJi Ta CO cac tinh chat: i)= S„,„ccea = AH'~ AB'"^ AC' ii)BO'= AB'+ AC' (Dinh H Pytago), iii) Tuong ttr ta CO : cos^B + cos^C = l " b'c' HS hen hanh phan tich, chuyen di lien tirong sang cac lien tudng, ki nang gan giong voi 2VaV+6V+cV' no Neu ta xem xet doi tupng tucmg tu voi tam giac vuong ttong mat phang la tii dien vuong ^«CA^SoaA'=°''r = khong gian, ta co the phat bieu duoc 2VaV+6V+cV' ket qua tuong tu nhu the nao? Til do, xet bai tap Qua ket qua ciia bai toan 1%, GV cho HS 17 [4, tr 103]: "Cho hinh tii di$n OABC co ba neu nh|n xet ve cac tinh chat trongflidien vuong: canh OA, OB, OC doi mpt vuong goc Chiing Nhqn xet tha I • minhrSng a) Tam giac ABC co ba goc nhpn b) Hinh chieu H ciia diem O trSn (ABC) Tii ta CO dang thiic s'^ = s'^^ +s'^^ +s'^ ming voi nvc tam tam giac ABC dupc gpi la dinh li Pytagp trpng fli dien vuong, flic la bmh phuong dien tich mat huyen biig c ) - ^ = — + — —L" tong binh phuong di?n tich cac mat vuong OH' OA' OB' ^ OC ' Nhdn xel thie 2: Nhu vay viec gim bai toan nay, HS co the ab kham pha dupc tmh chat i) tuong tu ni dien cosa = , vuong Ta tep tuc khai thae hai tinh chat lai 4aV + b'c' + c'a' qua bai tap [4, tr 120]: "Cho hinh fli dien Tuong tu ta co: OABC CO ba canh OA, OB, OC doi mot vuong g6c va O^ = a, OS = (,, 0 = c Goi hinh chi^u 24 Tap Chi Khoa hpc so 24 (02-2017) rRircflSlG DAI HOC DONG T H A P cosp = CO tinh efaat gan gi6ng vdi cos^ B + cos (7 = ttong tam gidc vudng ABC la oo^a+ca^fi+ccB^/ = X tac t6ng bmfa phuong edsin cua cac gdc giiia mgt vudng va mgt huyen bdng Nhu vay, khai tfaac hai bai toan tten, HS kfadm pfad dupc tri thirc mdi nhu bang sau: VS^TfevTT?' cosy = Do cos a + cos ^ + cos y = Nhu v ^ Bang Tuih chSt tuong tu giua tam gidc vuSng va tir dien vu6ng Taragidc ABC wudnQt^ A, AH J BC Tudian OABC vudng tai ^nfa O, ^^ AH^~ AB^^ AC^ ii)DinfaUPytago: BC^ = AB"" + AC'' '^ OH' iu) cos^ B + cos^ C = OA^ OB^ 0H1{ABC) OC^ ii) Dinh li Pytago: S\^ iii) cos^ a + cos^ >9 + cos^ Y = ^ Qua vi dy tten bdng faogt ddng efauyen di tii dien vudng Ngoai ra, GV ciing co tfae tgo tinfa cdc raoi lien tudng, kJ nang da tiep thu dupc sang fauong cfao HS kfaara pfaa tri tfaitc mod qua tfaao cdc lien tudng, ki ndng gan giong vdi nd, HS tdc tuong ty nfau bang sau: kfaam pfad dupc tri thuc radi ve cdc tinfa efaat tten Bang Yeu t6 tinmg tir giva tam gidc vd tir di£n Tam giac mat phing T u dien Idiong gian Tam mgt cka npi tiep tii dipn (ton tai diem cacfa deu cac mgt ciia tii di$n) Tdm ragt cau ngogi tiep tii dien (ton tai diem each deu cac dinh ciia tii dipn) Cac dudng cao cua tit dien kfadng dong qi^r (cdc dudng cao cua tu dien dong qi^^ cfaj kfai Id tii dipn tryc tdm ([4, tr 103]) Trpng tara ciia tam gidc (cac dudng trung Trpng tdm ciia tii dipn (cac dudng trpng tuyen cua tii dien dong quy) [4, tr 55] tuyen cua tam gjdc dong quy) Tam dudng trdn ndi tiep tam gidc (ton tai £ e m c^fa deu cac egnfa cua tam giac) Tam dudng trdn ngoai tiep tara gidc (ton tai £era cacfa deu cac £nfa cua tara gidc) Tryc tam tam giac (cdc dudng cao cua tara gidc dong qysy) 3.2.2 Ndng luc chuyen di cdc nguyen tac, thdi dd cd vdo cdc tinh huong khde Ve CO ban, nang Iyc efauyen di ndy kfadng pfadi Id hpc cac ki nang cu tiie ma la fapc rapt y tudng tong quat, nfaiing van de cy tiie cfai Id nfaiing truong fapp ddc tfau ciia ngiQ^en t ^ tong qudt da fapc Tfaeo Bruner, Ioai cfauydn di chinfa la trpng tdra cua qud trinfa d&y hpc, Id sy rad rpng va ddo sdu kfadng ngiing kien thiic theo nhiing y tuong, ngi^en tac tong qudt vd co ban Vi du Khi nghien cuu rapt so npi dimg Hinh fapc I I , cfaiing tdi tfaay rang npi dung khoang cdcfa giiia faai dirdng thing cfaeo nfaau bdi "Kfaodng cacfa" [4, tr 112], de c ^ d^n bdi todn ve sy ton tgi vd d i ^ nhat dudng tfadng cat vd vudng gdc hai dudng tiiang cfaeo nfaau cfao trudc, tir dd dan den khdi ruera ve dudng vudng gdc cfaung, doan vudng gdc cfaung vd khoang each giira faai dudng tfadng cfaeo nhau, sau nit nfaan xet ve moi lien hp giiia cdc khoang each da cd ttong bai cung vi du minh fapa Tvsy nhien, day Id ndi dung khd doi vdi HS, dgc biet la kfai HS can biet van dyng vdo tinh Idiodng cdcfa tinfa fauong cy tfae Vi tfa^ GV cd tfae kfaai thdc them tu bdi toan ve su ton tai va nhat dudng tfaang cdt vd vudng gdc faai dudng tiiang cfaeo 25 TRtfdNG DAI HOC DONG THAT T j p chf Khoa hpc sS 24 (02-201; cho trudc xay dung cho HS quy trinh xac dinh dudng vuong gdc chung ciia hai dudng thang cheo nhau, giiip HS buac dau hinh va v ^ dung k h o ^ g each vao bai toan cu thi Ta CO the xay dung dupc cac each dung vao doi tupng HS nhu sau: CocA^g7(Hmh2) Cdch dung (Tnidng hpp dac bi$t d± d' (Hmh4) • d Z Hiiili4 -Dung (or) chira rfva vuong gdc vdi rf J^ -Goi A = {a)nd,U -Viy BinliZ - Dung mat phang ( a ) chua d' va song song vdi d - Chpn M flen d, dung AffiT J ( a ) tai H - Tu H, dung dudng thing A song seng d, cSt d tai B - Tir B, dung dudng tfaang spng song vdi MH cat d tai A - Vay, 'a< = d(d,d)=MH.d(d.(a))^d(M(a)) Cdch dtfng (Hhthi) it AB = AB Id, Bed' d[d,d) Thuc Men chuyin di cac nguyen tac, cac thai dp da co vao fmh huong, GV yeu caii HS van dung nguyen tac vao bai tap 32 [4, fl- 117] "Cho hinh hop chir nhjt ABGD.A^C'l) co AB = AJC = a,AC' = 2a Tim ducmj vudng gdc chung va tmh khoang each giiia hai dudng thing AC va CD" HS can xem xet van dung ngigren tac da co vao bai toan nay, nhan thay iing C D ' ( y l s ' c ' D ) =^ C D ' J XC7' (v|n dpg each dvmg 3) (Hmh 5) D' Hiiili3 - Dung mat phang ( a ) vuong goc vdi A tai O - Dung hmh chieu vuong gdc (A) cfla rf' flSn ( a ) - Dung hinh chiiu vudng goc H cia O tren (A) Hmh T a c d CD' tam hinh (AB'O'D) vuong CC'D'D Ac', gpi IB ta co -litH, dung dudng thing song song vdi rf cat d taiB I = CD' r^ OHckdt^A"^' Ke IJ lAC'.J sAC Khi dd IJ chinh la dudng vuong gdc chung cua dudng thang AG va CD Tinh dd dai doan / / : -Viy 26 '"""' AB = d(d.d') * ^ « ^™^ =°"S vdi = OH (AB'O'D) Tap chl Khoa hoc s6 24 (02-2017) T R U ( N G D A I H O C DONG T H A P ^AC'D nen CO ACf ^2a,AD COSAC'D=— Trong = CfD = ayl2 AIJC' ta cd IJ = C'LcosACfD=- 3.3.3 Ndng luc md hmh hda cdc l&p ddi tuang todn hgc theo mdt so quern he vd tinh chdt chung cua chung Md fainfa fada cac lap doi tupng quan he Id pfauong phap chii yeu ctia toan fapc de nfagn Ifauc cac Idp ddi tupng vd quan he De thu dupc cac md hinh (sii dung ngdn ngu, kd hieu todn de md ta cdc lop doi tupng) ddi hdi ngudi hpc phdi tien hanh cdc tfaao tac nfau md td, so sdnfa, pfaan ticfa, tong fapp, kfadi qudt fada, trim tupng hda tu dd nit dupc cac tinfa diat cfaung tii cdc ldp doi tupng de dan den cdc kfaai niem, kien tfauc mdi i Vi d^ Theo tac gja Ddo Tam [5, tr 41], de fainh tfadnfa kfaai niem fainfa fapp theo quan diem cua Ii thuyet t$p fapp, ta co the tidn hanh thuc hien cac tiiao tdc sau: ' - Md td, phan tich, so sanh cac dgng hinfa fapp da dugc bidt ttong thuc tien (hinh lap phuong,fainfafappcfaii nhat, fainh fapp bdt ki) - Tong fagp nit tinfa chit chung: mpi hinfa fapp duoc xac dinh bdi dgi dien ba phuang ddi mpt cheo nfaau - Lien tudng den cac Idrai tiiiic: tdn tgi cap mat piling song song nhat lan lupt chiia faai duang tfaang cfaeo Canh ben khong vtiong goc mat - Hinh thanfa dinh nghia hinh hop: Cho ba dMbn% thdng ddi rapt cheo a, b, c kfadng Ian luprt ndm tten ba m^t phdng song song Goi D(a,b) la raidn kfadng gjan giiia hai mgt phdng song song ldn lugt chiia faai duong thing cheo a, va ke ca hai mgt pfaang Nhu v^y, giao cua ba mien kfaong gjan D(a,b), D(b,c), D(a,c) id mpt hinh hop - (Jua cdc thao tac tt&i, ta tfaay cdc Idp doi tupng ^infa I ^ pfauang, hinh hpp dbii nfaat, hinh hpp bat ki) da dugc md fainfa faoa, nhu vgy twf vdo vi tri tuong doi ciia cac dudng tfaang cfado nfaau ban d^u, ta cd tfae xay dung dugc fainfa fapp ngoai tiep nd Chang fagn, xet bai tap 26 [4, tr 112] "Ifinh hpp ABCD.AB'C'D' la hrah hop gi neu tiida raan rapt cac dieu kipn sau: a) Tir dipn AB CD' cd cac cgnh ^ i bdng nfaau; b) Tii dien AB CD cd cac cpnh doi vudng gdc nhau; c) Tu dien ABCD la tii dipn ^ u " Dua vao khdi lupm hinh hpp xay dyng d tren, HS cd tiie kfaam pfad dupc fahifa fapp ABCD.AB'C'D' ngogi ti% tii dien AB'CD' cd cdc egnfa doi bdng nfaau Id hinh hdp chii nfagt; Iiinfa fapp ABCD.AB'C'D' ngoai tiep tii dien AB'CD' CO cdc cgnh doi vudng gdc Id fainfa hop tfaoi; fainfa fapp ABCD.AB CD ngogi tiep tii dien deu AB'CD' la hinh I ^ phuang 3.3.4 Ndng luc the hien quan diem bien chieng cua tu todn hoc khdm phd tri thiec m&i Canh ben vudng goc mdt 6ay Hinh Sff Hb th£ hien tmh chat chung - riSng cua cac khai niem hmh ldng tru 27 TR.0ONG DAI HOC DONG THAI Tap chi Khoa hoc so 24 (02-2017) Nang luc the hien theo quan diem bi?n chat chung, tinh chat rieng cia chung nhu bilu chung gom quan h$ giua cac cap pham flii: npi dien tren so dung vi hmh thuc, cu thi va flroi hrpng, cai l-.''**^"!?, ^ „ , ^ ^, , , .A Alt, u,;r,n trii nhan iir-h Bai Viet da khai tfaac mot vai npi duug hi chung va cai neng O day, chung toi pnan nen , ,, • \ • T< , , ^ , • „„ ^„„„ „ian "