Đang tải... (xem toàn văn)
Tgp chi Khoa hgc Trudng Dgi hgc Can Tho Phdn C Khoa hgc Xd hgi Nhdn van vd Gido due 33 (2014) '''' Tap chl Khoa hoc Tru''''dng Oai hoc Can Thd website sj ctu edu vn V^N D U N G PHirONG PHAP TOA D O D E GIAI[.]
Tgp chi Khoa hgc Trudng Dgi hgc Can Tho Phdn C: Khoa hgc Xd hgi Nhdn van vd Gido due: 33 (2014): ' Tap chl Khoa hoc Tru'dng Oai hoc Can Thd website: sj.ctu.edu.vn V^N D U N G P H i r O N G P H A P T O A D O D E GIAI BAI T O A N HINH H O C KHONG GIAN Nguyen Thi Tuyen' ' HQC vien cao hgc lap Ly ludn vd phuang phdp dgy hgc bg mon Todn, khda 19, Khoa Suphgm Thong tin chung: Ngdy nhgn: 29/04/2014 Ngdy chdp nhgn: 29/08/2014 TUle: Applying the coordinate method toward the stereometric problems Td khda: Phucmg phdp tga do, tga dg hoa Keywords: Coordinate method, coordinates chemical ABSTRACT Stereometry is an important part of the mathematics curriculum high school today.The stereometric problems are pretty complicated, requiring learners to have good and critical thinking Solving some stereometric problems is relatively difficult and takes more time, but the use of coordinate method will make them much simpler In this article, we would like to introduce how to apply coordinates method toward the stereometric problems T6M TAT Hinh hgc khdng gian la mgt bd phgn quan trgng cua chucmg trinh todn trung hgc phd thong hien Cdc bdi todn hinh hgc khong gian khd phuc tap, ddi hdi ngudi hgc phdi cd tu tdt Viec gidi mdt sd bdi todn hinh hgc khdng gian tuang ddi kho vd tdn nhiiu thdi gian nhung neu gidi theo phucmg phdp tga dg se dan gidn hon Trong bdi viit ndy, chiing tdi xin gidi thiiu cdch van dung phucmg phdp tga di gidi bdi tgdn hinh hgc khdng gian DAT VAN DE ,.i,::lHmhvhpp^khdh^iaff'la mdn hinh hpc kha trOru tugng nen da sd hpc sinh e ngai hpc vd phdn ndy Trong cac dd thi tuydn sinh Dai hpc - Cao ddng gdn ddy, phdn hinh hpc khdng gian dugc dudi dgng ma hgc sinh cd thd gidi bang hai phuang phdp: Phuong p h ^ hinh hoc thudn tiiy vd phuang pbap tpa dO Vide gidi bai todn hinh hgc klidng gian bdng phuang phap hinh hpc thuan tfty gap nhidu khd khdn ddi vdi hpc sinh vfta hgc xong ldp 12 vi da phdn cde em it nhidu da quen gidi cdc bdi todn tpa dO khdng gian Vipc gidi bdi toan hinh hpc khdng gian bdng phuong pbap tpa cd rdt nhidu uu vidt, nhidn hpc sinh cung gap khdng it khd khdn Bdi vi, phuong phap ndy chim dugc dd cgp nhidu ttong cac sdeh giao khoa, hpc suih phd tiidng it dugc tidp can, va phuang phdp ndy chi tdi uu vdi mOt ldp bdi todn ndo dd ehu khdng phdi luc ndo nd ciing td hieu qua Dd eac em hpc sinh Idp 12 cd thdm phuong phap gidi toan hinh hpc khdng gian, chuan bj cho ki thi cudi cdp Trong khudn khd bdi bdo, chung tdi chft ydu tap trung vao cac van dd sau: Ddu hieu nhdn bidt vd cae budc gidi bai toan hinh hpc khdng gian bang phuang phap tpa dO- Dua mgt sd each dgt hd ttuc tga dg vdi mOt sd hinh dac bidt Trinh bay mot so bdi tap hinh hgc khdn^ gian dugc giai theo phuong phap tpa dd va mdt sd bdi tap dugc gidi theo hai phuong phap: Phucmg phap tdng hgp va phuang phdp tpa dO Dieu ndy giup hgc sinh ren luydn ki ndng gidi todn bang tpa dO vd cd thd ttd ndn linh hoat viec lya chgn phuang phap giai cho phu hop vdi timg bdi toan Tgp ehi Khoa hgc Trudng Dgi hgc Cdn Tho Phdn C: Khoa hgc Xd hgi Nhdn van vd Gido dvc: 33 (2014): 98-105 NQI DUNG NGHIEN CUtJ 2.1 Mpt sd dau bi|u nhan biet bai toan hinh hpc khoDg gian cd thd giai bdng phuong phap tpa dp Hinh da cho cd mOt dinh la tam didn vuong Hinh chdp cd mOt canh bdn vudng gdc vdi day va day la cdc tam gidc vudng, tam gidc deu, hinh vudng, hinh chft nhdt, Hinh lap phuang, hinh hOp chft nhat - Hinh da cho cd mdt dudng thdng vudng gdc vdi mat phdng, mat phdng dd cd nhtrng da gidc ddc biet: Tam giac vudng, tam giac ddu, hinh thoi, MOt vdi hinh chua cd sin tam dien vudng nhung cd the tao dugc tam didn vudng chang han: Hai dudng thdng eheo ma vudng gdc, hoac hai mdt phdng vudng gdc Ngodi ra, vdi mOt so bdi todn md gia thiet khdng cho nhftng hinh quen thudc nhu dd ndu d ttdn thi ta cd thd dya vdo tinh chdt song song, vudng gdc efta cdc doan thdng hay dudng thdng ttong hinh ve dd thiet lap he true tga dO2.2 Cac dgng todn thudng gdp Tinh dO ddi dogn thdng, kliodng cdch tu diem den mgt phSng, khodng cdch tft diem ddn dudng thing, khodng cdch gifta hai dudng thdng - Tinh gdc gifta hai dudng thdng, gdc gifta hai dudng thdng, gdc gifta hai m|lt phdng Tinh thd tich khdi da didn, dipn tich thidt didn Chiing minh quan he song song, vudng gdc 2.3 Cdc budc giai bai todn hinh hpc khdng gian bang phirong phdp tpa dp Budc 1: Chpn hd true tpa dO Oxyz thich hgp vd tim tpa dO cdc didm cd lien quan ddn ydu cau bdi toan - Budc 2: Chuydn bdi toan dd cho vd bdi toan hinh hgc gidi tich vd gidi Birdc 3: Gidi bdi toan hinh hpc gidi tich ttdn Budc 4: Chuyen kdt lugn efta bai toan hinh hpc gidi tieh sang tinh chdt hinh hpc tuang ftng 2.4 Thidt lap h$ tryc tpa dd Vdn de quan ttpi^ nhdt ttong vide gidi bdi toan hinh khdng gian bdng phuong phjqi tpa Id thidt lap he tga dO cho phu hgp Sau ddy chftr^ tdi xm gidi thieu mdt sd phuong phdp d% thidt Igp hd tpa dO(1) Thiit Igp hi tga dg doi vdi tam dien Vdi gdc tam didn vide tpa dd hda thudng dugc thyc hidn khd dan gidn, dac bidt vdi; - Tam dien vudng thi bd tryc tpa dO vuong gdc dugc thidt ldp ttdn tam didn dd - Tam didn cd mOt gdc phdng vudng, dd ta thidt lap mOt mat cua he true tga dO ehfta gdc phdng dd (2) Thiet lap h^ tga dg cho hinh chdp Vdi hinh chdp, vide tpa dO hda thudng dugc thyc bidn dya ttdn d^c tinb hinh hpc ciia chftng Ta cd cde trudng hgp thirdng gdp sau: Hinh chdp ddu thi he tpa dO dugc thidt ldp dya trdn gdc ttftng vdi tdm efta ddy va true Oz trimg vdi dudng cao ciia hinh chdp Hinh chdp cd mOt canh bdn vudng gdc ven day thi ta thudng chgn ttyc Oz la canh ben vudng gdc vdi day, gdc tga dO trftng vdi chan ducmg vudng gdc - Trong cdc trudng hgp khdc ta dya v^o dudng eao cua hinh chdp va tinh chdt da gidc ddy de chgn hd tpa dp phft hgp (3) Thiit lap hi tryc tga cho hinh hop chU nhdt Vdi hinh hOp chft nhdt thi vide thidt ldp he tpa dO kha dan gidn, thudng cd hai each: Chpn mOt dinh ldm gdc tpa dO vd ba true ttung vdi ba cartii efta hinh hop chft nhat Chpn tdm cua day lam gdc tpa dd vd ba true song song vdi ba cgnh efta hinh hOp chft nhdt (4) Thiit lap hi tga dg cho hinh lang Py Vdi lang try dftng thi ta chpn tryc Oz thing dftng, goe tpa dO la mOt dinh ndo dd efta day hoac tam cua day ho§c didm ndm ttong m$t ddy Id giao efta hai dudng thdng vudng gdc Cdc true Oy, Ox thi dya vdo tinh chdt efta da gidc ddy ma chpn cho phu hgp Tgp chi Khoa hgc Trudng Dgi hgc Can Tha Phdn C: Khoa hgc Xd hgi, Nhdn van vd Gido due: 33 (2014): 98-105 Vdi lang try xien, ta dya ttdn dudng cao va tinh chdt cua ddy dd chgn he tpa dO thich hgp Ngoai cdc trudng hgp ttdn, ttong cdc trudng hgp khac ta dya vao quan he song song, vudng gdc va cdc tinh chdt efta dudng cao, ddy, dk tiiidt lap he tpa cho thich hgp 2.5 Hf true tpa dp Oxyz Hp true tga dO vudng gdc Oxyz ttong khdng gian Id hd gdm ba true x'0x,y'0y,z'0z ddi mOt vudng gdc Diem O la gdc tga dO Ox gpi Id tryc hoartii Oy gpi Id tryc tung Oz gpi Id tryc eao Tren cdc tryc Ox, Oy, Oz Idn lugt chua ba vecta don vi I, J, k Cdc mat phdng (0xy),(0yz'),(0xz) vudng gdc N6u /,/, K Ian luat thuoc cac tia Ox, Oy, Oz C'u = 01 thi y„ = o ; (z„ = OK = MM' Ngu l,J,K lin luat thuOc cac I x„ = ~0I Ox', Oy', Oz' M\y„ = -0] (z„ = -OK = -MM' 2.6 Mdt so bai toan Bai toin 1: (SGK Hinh hoc NC lap 12) Cho liinh chop 5.^BC CO duong cao 5i4 = h.i&y litam giac ABC vuong ^C,AC~b,BC = a Gpi M la tnmg diim cua AC va N \h diim cho 5W = \rB a) Tinh dp ddi doan thang MN b) Fun sy lien he gifta a, b, h dh MN vudng gdc ddi mOt Tpa dO eua vecta: u = (x; y; z) 4, BC) = d(BC, (SAN)) = d(B, (SAN)) Vi HB n (i/lN) = ,4 nen ta co: d^aXSAN)) _ AB a=(^;0; ^ ) , M = (f;0;^) [S2,S5] = ( ; ^ ; ) d(H.{SAN)) ~ AH~ = -m , ^6 ' -' The tieh ciia khoi chop S.ABC la AW (SHN) =» (SAN) (SHN) ''^•^??#-ilMFli^l#-^