[lll!nGIllHIIII,illU;BI[IHllAVJIKHiUOUilIHIIA CHO HOC SIOH TROne DflV HOC HiOH HOC HHflOG GIRO If TRinf RG TRURG HOC PHfi'''' THORG O TS C A O THI H A * atrung hgc phd thdng (THPT), mdn Todn ed mdt vol t[.]
[lll!nGIllHIIII,illU;BI[IHllAVJIKHiUOUilIHIIA CHO HOC SIOH TROne DflV HOC HiOH HOC HHflOG GIRO If TRinf RG TRURG HOC PHfi' THORG O a trung hgc phd thdng (THPT), mdn Todn ed mdt vol trd quan frgng viee thyc hien cdc myc tieu chung cua gido dye phd thdng Ben egnh viee hodn thien vd'n kien thuc cho hgc sinh (HS), mdn Todn cdn gdp phdn vdo viec phdt triln ndng lye (NL) tri tue, hinh thdnh cdc NL suy ludn dde frung cuo todn hgc (1; 53) D l phdt trien fri tue cho HS dgy hpc todn, gido vien (GV) cdn hinh thdnh vd phdt trien cho HS nhirng hogt ddng tri tue co bdn nhu: phdn tich, tdng npp, so sdnh, khdi qudt hda, truu tupng hda ; Kr dd, giup ede em hinh thdnh nhirng NL tuong ung nhu: NL dgc biet hdo, NL xet tuong ty vd NL khdi qudt hda, dd Id nhung NL eo bdn vd quan trpng eua HS Hinh hpc khdng gian (HHKG) Id mot npi dung todn hpc khdng ehi cung cd'p nhirng kiln thuc ve cdc vdt t h i khdng gian md cdn tgo co hpi cho HSphdt trien ede NL tri tue Bdi viet de cdp v l vd'n de phdt triln mdt so NL tri tu§ ca bdn nhu: d^c biet hdo, Krong Kr hdo vd khdi qudt hdo cho HS frong dgy hgc phdn HHKG d THPT Phdt frien NL dgc biet hda cho HS t)dc bidt hda Id mdt cdc NL tri tue quan trpng cOo HS, giOp ede em nnin nhdn cdc vd'n de mdt cdch thd'u ddo vd chieu 6d; todn 1: Cho K> di6n A6CD cd dien tich tam gide ABC bdng dien tieh tam gide ABD Chung minh rdng dudng vudng gdc chung cuo AB vd CD dl quo frung dilm eua CD Chung minh: Theo gid thilt, ta cd: S^^^ = S^^ nin CB' = DA' (hai dudng cao tuong t/ng) (binh /; D l thdy, AC8'A'=ADA'fi'(viehOng d l u Id cdc tam gide vudng tai A ' v d B") Mdt khde, to Igi ed CB'= DA'; A'fi'chung Do dd; CA' = DB' N l u A'khdng trung 6', to xit h/ dien A'B'CD cd CB'= DA'; CA'= DB' nen dudng vudng gdc chung eua A'S'vd CD Id dudng ndi frung diem eua A'B'vd CD, hoy dudng vudng gdc chung eua AB vd CD di qua trung dilm cOo CD N l u A'frung 6', kit qud Id hien nhien • TS C A O THI HA* Ode biet hdo bdi todn to cd bdi todn Bdi todn 2: Cho tu dien ABCD cd dien tich mgt b d n g Chung minh rdng: a) Dogn thdng ndi trung diem cdc cdp egnh dd'i Id dogn vudng gdc chung eua ede cgp egnh dd b) Tir dien ABCD cd ede cdp egnh dd'i bdng Chung minh: a) Dung C H l A B ; KDIAB Hinh HC = KD Ggi O, M, N Idn luot Id trung diem HD, CD, HK To ed: ACHN = A D K N nen NC = ND Do do: M N l C D (binh 2) Mdt khdc, N O / / K D nen N O ± A B ; O M / / H C nen O M ± A B , suy M N l A B Vdy, dudng vudng gdc chung cOa AB vd CD Id dudng thdng M N di quo trung dilm cua CD Tuong Kr: S^^ = S ^.Q, suy dudng vudng gdc chung cua AB vd CD ^ q u o trung diem cOa AB Su dyng gid thiet bdn mdt eua tu dien cd diSn tieh bdng fa dupe dilu phdi chung minh b] Gid su M N id dudng vudng gdc chung cua AB vd CD Khi dd, M, N Idn luot se Id trung dilm euaCDvdABnenNA=NB;NH = NKnenHB=AK, suy A C H B = A A K D Vdy, CB = AD Tuong h/, ede cdp egnh ddi cdn Igl eua tu dien cung ddi mgt bdng Phdt frien NL K/ong tu hda cho HS Ben egnh viec xet cdc trudng hpp dde biet hogc cdc frudng hgp ey the de dua ro cdeh gidi bdi * Khoa TOM, Tnroig B« koc stf pMm - Oai hpc Thai Nfi)i«i Tap chi Glao due so 0 (ki a • la/aoia) todn thi ddi GV edn hudng ddn HS xet cdc y l u to Krong K/ cOa bdi todn cdn gidi quyet vdi cdc bdi todn dd bilt; tu dd, se giup HS ed sy nhudn nhuyen v l kien thuc, bilt lien Krdng gidi quylt vdn de vd d l ddng tim ro cdch gidi bdi todn 6d/ todn 3: Trong tam gide ABC vudng tgi A, dudng eao AH c d : / ; fiC^ = AB^ + AC; 2)^'-^*^; 3) AS' = 6H.8C; 4)A?C= CH.CB Nhu to dd biet, tuong ty vdi viec xet mdt tam gide mdt phdng Id viee xet tu dien khdng gian, frong dd, egnh cuo tam gide tuong ty vdi mdt eua tu dien, dudng coo cuo tam gide tuong ty vdi dudng thdng vudng gdc K> mdt dinh cOo tu dien den mdt ddi dien (dudng cao cua tu dien) Vdy, vd'n d l ddt ro Id xet mdt tu dien vudng SA6C, vudng tai S, cd nhirng hS thuc ndo giua cdc mdt cua tu diSn vudng cung nhu mdi lien he giua dudng cao vd cdc egnh eua tir di^n dd HS ed the xet cdc tinh chd't tinh tuong ty bdng cdeh khoi thdc tu he thuc lupng tam gide vudng vd dua ro dy dodn: Trong Hinh mdt tu diin vudng SABC, ta cd: 1) 5;,„ = s\,,„ + 5i„ + s\„.; Phdt frien NL khdi qudt hda cho HS Ben egnh NL tuong ty hda vd dde biet hda, NL khdi qudt hdo cOng Id mdt cdc NL tri Kje CO bdn cOa HS NL ndy khdng nhirng giup HS nhin nhdn vd'n de mpt cdch cd he thd'ng md cdn Id mdt cdc tien de de cdc em phdt triln NL sdng too Do vdy, dgy hoc, GV nen thudng xuyen tap luyen cho HS khd ndng khdi qud hdo bdi todn tu bdi todn dd cho (trong nhirng trudng hop ed the) 6d/ todn 4: Trong mdt phdng cho gdc xOy, dudng thdng d thay ddi ludn di qua mdt dilm I CO djnh thupc miln cuo gdc vd cdt cdc tia Ox, Oy Idn luot tgi M, N Qua I ke dudng thdng song song vdi Ox cdt Oy tgi E vd ke dudng thdng song song vdi J' Oy cdt Ox tgi D Ddt IE = a, ID = b Chung minh rang: v_ _ "' j Hinh Khai quat hoa bdi todn ndy bdng cdch md rdng vdo khdng gian, ta ed bdi todn sou: 8d/ todn 5: Cho hinh chop S.ABCD, ggi O Id giao diem cOa ede dudng cheo AC vd BD, I Id dilm cd djnh tren SO Mat phdng (P) thay dd'i ludn di qua I cdt cdc egnh ben SA, SB, SC, SD 21 '.JL.- J-:.-L Idn lugt tgi M, N, P, Q Chung minh: 1) Gid su SH (ABC) tgi H, suy Chung minh rdng tdn tgi H Id trye tdm eua tam gide ABC nen A^ ± BC bdn dogn thdng m, n, p, kji M Ta ed: SM BC (theo djnh li ba dudng q xde dinh cho: vudng gdc); s^, =-.-IM.BC; ã5.u(ô-=r'^'^'^C S^^ = S.\i.BC; Mdt khdc, tam gide vudng SAM ed SM' = HM.AM (binh 4), suy ro: • ^ viMT -".U Tuong ty, BC'.llM M/ =|Brv.VA/^ =(S„„ )^(1) ta cd: S„„ 5^„^ =(5^,«j'(2) 5««'-5^«' =(5^v,- )S- (3)- TO (1), (2) vd (3), suy ra: (5ô,.)- = (5^ô,)= -ãã(5^ô,.)= - H ( ^ « J HS eOng d l ddng chung minh dupe he thuc d cdu Tap chi Glao due s6 0 (ki a • la/aoiai 5A/ SN SP SC •-A >< Chung minh: Ap dyng kef qud cua bdi todn dd'i Hinh vdi mdt phdng (SAC), to ed: Ggi m, p theo thu ty Id dp ddi hoi egnh cOo hinh binh hdnh lA'SC, do: ^ + ^ = '(1) (binh 5) Xet mdt phdng (SBD),ta Igi ed: ^ + ^ = i (2) TO (1) vd (2), suy ra: ^ • * - ^ + # + ^ = - ã ãôã Nhu vdy, NL dde biet hda, td'ng qudt hda, hiong (Xem tiip trang 42) Sou dd xdy dyng xong ndi dung bdi gidng cd su dyng SDTD, chiing ta thyc hien cdc lien kit (hyperlink) len cdc dd'i tupng bdi gidng Ddy Id uu dilm ndi bdt, cdn khoi thdc tdi da cdc khd ndng lien kit Nhd cd khd ndng lien kit ndy md bdi gidng dupe td chirc mpt cdch linh hopt, thdng hn dupe truy xud't kjp thdi, HS d i tilp thu kiln thuc Budc 6: Sua chOa vd hodn thien SDTD Sou dd thilt k l xong SDTD, GV edn tiln hdnh kiem tro ede soi sdt, dde biet Id cdc lien kit de sua chOa vd hodn thien SDTD V(' du: Dudi ddy, chung tdi xdy dyng SDTD bdi: «Axetilen" (Hod hpc 9) Thyc tiin DH d cdc trudng phd thdng dd cho thdy, viee si> dyng SDTD nhd trudng dd ndng eao hieu qud day vd hpc Ode biet, SDTD giup HS hpc tap mdt cdch chu ddng, tieh eye, huy ddng dupe tdt ed HS tham gia xdy dyng bdi, ren luyen tu sdng too vd khd ndng ty hpc cho cdc em Su dyng SDTD edn ed the phdt triln cho HS cdc ndng Tyc nhu: biet he thing hda kiin thuc (huy ddng nhirng kiln thuc dd hpc trude dd), khd ndng hdi boa (hinh thirc trinh bdy, kit hpp hinh ve, chu viet, mdu sdc) Viec van dyng SDTD DH se ddn hinh thdnh cho HS tu mpch Ipe, hieu vd'n de mdt cdch sdu sdc, cd he thd'ng vd khoa hpc Su dyng SDTD kit hop vol cdc PPDH tich cue nhdm gdp phdn dd'i mdi PPDH Tuy nhien, khdng phdi bdt cu npi dung ndo, bdi hpe ndo cung ed t h i diing SDTD SDTD Id mdt phuong Hen DH nen cOng nhu vdi ede phuong Hen khdc, de phdt huy dupe tdi da tinh uu viSt eua nd, cdn su dyng dung luc, phO hpp vdi npi dung h/ng don vj kien thuc vd quan trpng nhd't Id phii hpp vdi ddi tupng HS; ddng thdi, ddm bdo ho trp tdi da cho viec truyen tdi ndi dung bdi hpc De dpt dupe dieu ndy, GV cdn linh hopt, mem deo, kheo leo kit hpp SDTD vdi ede phuong Hen DH khde d Tai lieu tham khao Bernd Meier - Nguy4n Van Cuong Li lu$n day hoc day hpc hien dai, tai lieu hue t$p ddi mdi phuong phap day hpc NXB D(ii li