SUf DUNG PHUONG PHOP DIEN TICH TRONG DAY HOC GIAI CAC DAI TOAN HINH HOC CHO HOC SINH Tl iu HOC O TS NGUY§N IVIANH CHUNG'''' CthI hilu, phuong phdp difn Kch Id mft uong phdp gldl lodn, dung d$ gidi cdc ll[.]
SUf DUNG PHUONG PHOP DIEN TICH TRONG DAY HOC GIAI CAC DAI TOAN HINH HOC CHO HOC SINH Tliu HOC O TS NGUY§N IVIANH CHUNG' C thI hilu, phuong phdp difn Kch Id mft uong phdp gldl lodn, dung d$ gidi cdc ll todn v l olfn Kch md khdng sii dqng hvc tilp cdc cdng thiic tinh difn flch (1} Phuong phdp diin Kch cung la CO sd cho vlfc gldl cdc bdi todn v l cdt ghip hinh Ddy Id mft pnuong phdp khd I I I vdiliqc sinh |HS| difn dqi hd nin SGK c6 d l cf p nhung hjqng bdi t f p ddnh cho vdn d l ndy cin it nhou vd cd chilu coo cOng bdng nhou thi cd s i cqnh ddy bdng nhou Cdc bdi todn v l Knh d i f n Kch, so sdnh d i f n tfch gfOg cdc hinh VI dv I; Cho tom gidc ABC cd difn Kch bdng 200cm^ Kio ddi AB mft doqn BM bdng AB, kio ddi BC mft doqn C N bdng BC vd kio ddi CA mft doqn AP bdng AC N l i cdc dilm I*, N , P Tfnh difn Kch tom gidc MNP (hinh 1) Gldl: Di gidl bdi todn ndy, GV c6 rill gql y d H & hqc, HS da duqc hqc v l difn Kch cdc hinh nhu: hinh chO nhf t, hinh vudng, hinh cho HS so sdnh difn Kch d o cdc tam gidc sou: tom gidc Cdc cdng thiic v l difn Hch cOo cdc ABPvdABC;BPAvdBPM hinh ndy chu y ^ duqc HS ling dqng gidi cdc bdi Khi dd, HS d l ddng nhdn riily: Tom gidc ABP tfp Knh lodn cd Ilin quon d ^ difn Kch D l bit vd tam gidc dudng, phdt h-lln ndng Iqc gidi todn cho HS K I U ABC cd chung hqc thdng quo vlfc gidl cdc bdi todn hinh hqc dudng coo hq bdng phuong phdp difn Hch, gido vlin (GV) cdn h i B v d A P = AC bj cho cdc em ndm vOng mft s i Knh chdt non vioB ^ ^Aflc " hinh hqc sou: 1) N l u mft hinh duqc chia ihdnh 0 c m ' (1) cdc hinh nhd thi tdng difn Hch cOo cdc hinh nhd Tom gidc BPA bIng difn Kch cua hinh Idn bgn ddu; 2) N l u ghip vd torn gidc cdc hinh nhd k;i d l duqc mft hinh Idn Hil difn BPM cd chung Hinh I Kch hinh Idn thu duqc bdng tdng difn Hch cOa dudng coo hq cdc hinh nhd dem g h i p Iqi; 3) N l u hat hinh cd hiPvdAB = BM difn Kch bdng nhou cOng bdt di mft phdn chung nin S ^ - S , „ - S,,^^ = 200cm' (2) Ihl hai phdn cdn \gl cung cd difn Hch bdng nhou; Tu (1) vd (2), suy ro: S , ^ = S ^ + S ^ = 4) N l u to thim vdo hai hinh c6 difn flch bdng 0 c m ' + 0 c m ' = 0 c m ' (3) Tuong h;, ta cd: mft phdn chung thi to nhf n duqc hot hinh SôN - ScN, = 'ã00cm' (4) Tli (1), (3) vd (4), suy oi difn Kch bdng nhau; 5| Khi s i cqnh ddy ra: S ^ - SAK + S ^ + S ^ + S a , = 200cm' + khdng ddi ihl difn Kch vd chllu coo cua mft tom 0 c m ' + 0 c m ' + 0 c m ' = 400cm' gidc UI hoi dqi luqng K If thuf n; 6) Khi chllu coo Bdng phip suy luf n hjong h; nhu hong cdch khdng ddi ihl sd difn Hch vd s i cqnh ddv gidi bdi todn h i n , HS cd Hil gidi duqc bdi tadn la hoi dqi luqng H If thuf n; 7) Khi s i difn Hch sou: «C/io to aide ABCD, kio ddi AB mdt doqn khdng d i i thi » cqnh ddy vd chllu cao cOo BM bdngAB, kio ddi BC mdt doqn CNbdng BC, ilifl tom gidc Id hoi dqi luqng H If nghjch; 8| kdo ddi CD mdt doqn DP bdng CD, kto ddi DA Nlu hoi tom gidc cd chilu ddi cqnh ^ v d dudng mdt doqn AQ bdng DA Ndt cdc didm M, N, P, o n bdng nhou thi difn Kch cOa chOng bdng nhou; Q Tfnh dt$n Hch lu gidc ABCD, bidt rdng dl$n ' ) N l u hgi tom gidc cd difn bdng nhgu vd cd sd Hch Id gidc MNPQ Id 20cm" cqnh ddy bdng nhou thi cd chllu coo bdng nhau; 10| N l u hot tom gidc cd diin Kch bdng ãIiMi|i)illôcMi|Bit Tap chi Glao due s6 (w a • s/aon) VI dl/ 2: Cho hinh in vdl BP Ijnlnh 4) j cho nhfl ABCD, hin AB ^ Gldl: so sdnh BA vdi BP, GV cdn gql ^ choj ldydllmM,h«nCDldy HS chuyin vl bdi lodn so sdnh difnflchci5a hoi dllmN.ANcdtDMhjl tom gidc ndo dd cd chung dudng cao, nhfn BA l,CMc4tBNhjiH So vd BP hiong ling Idm hai cqnh ddy Ti> dd, gllp sdnh difn Kch cOa hi HS hr vd djnh hudng hong vifc Hm kit gldl gidc IMHN vdl tdng Hinh Theo gid Hiilh AN - 4xNC nin S^^ - x S_, *d S , ^ - ^ " SQ^, ta duqc: S,!,,, - X Sc^ (11; difn flch haitomgidc Iql cd: MC - 2xMB nin S ^ - x S ^ (2) AIDvdHBCf/.(n/>2; Ti)(l)vd(2)suyro:S,>,„.8xS « S Gldl: bdi todn ndy, GV cd ihl hudng ddn HS dug difn Kch hi gidc IMHN thdnh ting difn X S~,-> BA - x BP Vfy, df ddi doqn Ihdng Hch cOa hattomgidc ndo dd Khi dd, HS d l ddng BA gdp Idn df ddi doqn riling BP Cdc bdi todn khdc nhfnriidydifn Hch cOa hi gidc IMHN bdng ling VI i>) /: Cho torn difn Hch cOa hoitomgidc IMN vd MHN AAf t khdc:tomgidc AND vdtomgidc MDN gidc ABC cdM,N Idn c6 chung cqnh ddy DN, du M xudng DN (do AB AC soo cho: AB AM X 3, AC song song vdl DC) nin: At^x3lhlnh5l f,, , SAW, - SMB - > SAIO - S„N (">n8 bd» * ^ Hch cOatomgidc DIN); hfong h;: S,^^^ •> S,^ - > g) Tfnh difn Kch ' r Hinh ^ww ' ^ (cOng bdt di difn tfch cOgtomgidc tom gidc A/«V>I, bilt rdng tgm gidc ABC c6 difn Kch 9Ccm' NHQ Tg suyra:S „ ^ - S~, + S™ b) Tli gidc AtfCB Id hinh gl? VI soo? Cdc bdi lodn v l Hnhdf Hdi vd so sdnh Gldl: al Vdl bdi todn ndy, HS d l ddng Knh df ddi giOg cdc cqnh VIA) I: Chotomgidc duqc:i.„=l5„ = ixij„=90:9.10 (cnfl vudng cd hgl cqnh gdc vudng Id 3cm vd 4cm b^ Ap dqng kit qud cdu a),tood: Tlnh cqnh huyln cug tgm gidcdd S.«: =*»«;= T * « c VI hoitamgidc BMC vd Gid/: GV hudng ddn BNC cd difn Hch bdng nhou, c6 chung cqnh ddy HS cdt 4tamgidc vudng BC nln dudng cno xudt phdt Ki dinh M, N xudng bdng nhou cd cqnh gdc Hinh cqnh ddy BC cOng bdng nhou, suy MN//BC, vulng Id 3cm vd 4cm rli ghip Iqi vdl nhgu nhu hinh vi bin Ijnirh 3) Khi hgyBMNCldhlnhthgng V7 d^ 2: Cho lorn gidc ABC, M Id mft dilm ddtocd: hinh vudng nhd cd df ddi cdc cqnh Id bdt kl h«n BC (M khdc dilm BC) Hay vi 1cm, nin hinh vudng nhd cd difn Kch 1cm' Hinh vudng kin si cd difn Kch bdng tdng difnqua M mft dudng thing soo cho dudng riiong Kch tgm gidc vd difn Kch hinh vudng nhd Vfiy,dd chia tom gidc ABC thdnh hot phdn c6 difn difn Kch hinh vudng kin Id: 4x6 + - 25 (cm') Hch bdng nhgu [hinh dfl Gldl: Trude hit, GV hudng din HS phdn Kch Suyrahinh vudng Idn cd df ddi cqnh Id 5cm (vl S:fS 25), nghTg Id cqnh huyln cOgtomgidc cdc gid riii^ cOg bdi lodn V I M Id mft dilm bdt kl hfn cqnh BC, nin khdng mdt Hnh tdng qudt, to vudng cd df ddi 5cm gid Sli: BM < MC Khi dd, gql N kb dilm V/(^2:Chotom BC Tii N vi NP//AM, nil M vdl P, HS si chiing gidc ABC, hin BC Idy minh Aiqc MP Id doqn Hidng cdn Hm dilm M soo cho MC Thdt v4y, tom gidc ABN cd difn Hch bdng - 2MB, N Id dilm hin AC soo cho AN • 4xNC Kio ddi MN cdt BA hjii P So sdnh df ddi hai cqnh BA F ^ * ^ ^ -difn Hchtomgidc ABC Gqi I Id gigg cOg AN H(nA4 vd MP VI NP//AM nin difn Kchtomgidc AMN bdng difn Kchtomgidc AMP, suyraJ f n Hdi hi Tap chi Glio due s6 gd » g/aom gidc APMB bdng difn tfch lam gfdc ANB vd bdng mft niio difn tfch tam gidc ABC V/dv3(tfnhgld hj Clio bilu thiic): F~\ P~l Hinh Cho tom gidc ABC c6 bo gdc diu nhqn Gqi O Id gloo dilm ciio bg dudng ego AA,, BB,, CC, Tfnh td'ng '^ABD~'^ACE- ^AOE-T^^E xS.«c(l)=>«£«p=Vo(2) (3);S.c T OA - OM (7), Tii kit qud ndy, gii; nguyIn gidriiiHbdi lodn oS chung ddy BC n i n : ^ = ^ E ; luong h/, to I vd thay kit luf n cOa bdi todn I bdng kit qud (7), ta cd bditodnsou: 8d/ lodn 2: Cho tom gidc ABC, hin cdc cqnh ' BB^ SBCA CCi 5cu AB, AC Idn luqt Idy cdc dilm E, D soo cho AB = X AE; AC = X AD Cdc doqnrildngBD vd CE Vfy: cdt tql O, AO cdt BC tql M Chiing minh OA, , OB, , PC, rdng: AO = OM cdch AA, Tuong BB, h/CC, gidi bdi todn ndy, Col kit qud bdt lodn I Id gid riillt vd ddo gid riilAriidnhk^lufn,to HS si gldl duqc bdi cd bdi lodn ddo cuo lodn sou: Cho tam bdt lodn I nhu sou: gidc ABC, O Id Bdt todn 3: Cho , dlim bd't kl Irong tom gidc ABC, gqi M tam gidc Kio ddt Hinh Id trung dilm ciia BC, AO, BO, CO, O Id dilm cOo diOng Idn luqt cdt BC, CA, AB tgl A B„ C, Tinh td'ng: AM BO kio dat cdt ACh9iD,COkiodai CA.^OB, , PC, cdtABtqlE(hin/i^ AA, BB, CC, • Hinh Chiing minh ring: Sli dqng phuong phdp difn tfch, GV cd rill kulng ddn HS gidi cdc bditodnhinh hqc vl chiing AB-3xAE;AC = xAD minh dudngrildngding quy, chiing minh G/d/: VI OA=OM, BM = MC nin S.„ = S„ dl&n thing hdng, Khoi llidc hf thdng bdi Ifp hi mft bdi todn SAOB =—>CD=2xAD^AC=AD;S^3 Gldl: Ti gid riiilt: AB = x AE; AC - x AD, Tucmg h/: (Xem Hip Irang 51 j tacd: Tap chi Glao due so pa »• 5/»on) Nhin chung, cd PPDH trSn d6u cd chung c6c inj dilm Id gdn If thuylit vdl thyc hdnh, tu vd hdnh ddng, phdt huy tfnh ty Iyc, tfnh trdch nhlfm; ph6t triin khd ndng sdng tpo; r^n luyf n ndng Iyc gi6l quy^t nhOng vdn d l phuc hpjs; rdn luvfn h'nh bin bl, kidn nhSn; ndng Iyc cfng tdc ldm vlfc; phdt tri^n ndng Iyc D G ; cho ph6p phdn hdo nhjp d f vd trinh a $ cOo HS Tuy nhidn, cdc Iruong phdp ndy ddi hdi nhilu ihdl glon; ndng li/c, nghlfp vy su phgm cOa GV; sg ty gidc, Hch eye COQ HS; vd'n d l tdi chfnh; phuong Hfn, co sd vftchdt DH VI vdy, cdc PPDH ndy khdng thay thi cho phuong phdp thuylt trinh vd luyf n l$p md Id htnh thOc DH bo sung cdn thilt cho cdc PPDH truyin thdng D Tii Ufu tham khdo Ptian T r ^ B ^ Phmmg p h ^ gling d^y Am nhfc NXB Guto B E - x A E = > A C = A E x T i l llfu tham khdo Nhu vdy, to m$t bdi todn gdc, chl cdn thay Nguyfin Mpnh Chung Bdi gidng mdn phuong ptidp do\ mft sd dilm gid thilt hodc kit ludn to dtfy hpc todn tliu hpc (tdi lifu da duyc bO mOn duoc cdc bdi lodn khdc nhung cdch gldl Todn - Khoa Su phpm ti^u hpc - Thidng Dpi hoc Hdng lucmg ty, dilu ndy giOp HS cd khd ndng ly v$n Ddc thim dinh), 2010 dgng cdc p h ^ suyludn diin dfch, suy ludn quy D6 Trung Hi$u - D6 Dinh Hoan - Va Duong Thvy rap di khai thdc ^ n d l nhdm hilu sdu kll^n thOc Va Qatk Chung Phmmg p h i p dpy bpc mAn T o i n dcGng nhu rto luyf n tu k>glc, tu sdng tgo tiiu h9C NXB £>