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KHAI THAC MOT BAI TOAN CO BAN (HINH HOC S)
li
O D O A N THAI A N *
T
rong hoqt ddng dqy vd hqc Todn ndi chung, mdn Hinh hqc ndi rieng, vdn de khoi thdc, nhin nhdn mdt bdi todn co bdn dudi nhieu gdc do khde nhau nhieu khi cho nhQng ket qud khd thu vj. O trudng phd thdng, viec dqy todn hqc cho HS thyc chdt Id viec dqy cdc hoqt dqng todn hqc cho hq. Cy the nhu khi truyen thy cho hqc sinh (HS) mdt dan vj kie'n thuc thi ngodi viec cho HS hep cdn, ndm vung dan vj kien thuc d d , mdt viec khdng kem phdn quon trqng Id vdn dyng don vj kien thuc dd hqc vdo cdc hoqt ddng todn hqc, mdt hoqt ddng md thdng quo d d , gido vien (GV) dqy cho HS phuang phdp tu hqc - nhiem vy quan trong cuo ngudi gido vien dung Idp .Xudt phdt tu quon didm tren, vdn d l khoi thdc vd cung HS khoi thdc mdt bdi todn co bdn trong SGK de tu dd xdy dyng duqc mdt he thd'ng bdi tdp tu CO bdn den ndng coo den bdi todn khd Id mdt hoqt ddng khdng the thieu dd'i vdl ngudi GV.
Dudi ddy Id vi dy minh hoq cy the khi dqy bdi
«Ddl xung true" - Tie't Luyen tqp (Todn 8 , tqp 1).
Bdi todn I: Cho hoi diem A vd B ndm ve hoi phia cuo dudng thdng a. Hdy fim tren o mdt diem M soo cho A M -I- MB Id ngdn nhd't.
G i d l : Nd'i A vdl B cdt o t q i d i e m M . '^'^ / ° D l d d n g
c h u n g minh Hinhl die'm do thdo
mdn bdi todn.
Thdt v d y , tren a Idy mqt diem M ' khde diem M. Ta thd'y rdng, AN< -i- M'B > AB = A M -i- MB. Ddu «=" xdy ro khi M ' ^ M (hinh 1).
Khoi thdc bdi fodn 1, GV duo ro cdu hdi:
Ne'u hoi diem A,B ndm trong mqt nuo mdt phdng bd a thi cdch fim diem M nhu the ndo?
Bdi todn 2 (bdi todn 39 b (tr 88 SGK): Bqn Tu dong d vj tri A cdn den bd sdng de ldy nudc rdi
Hinh 2
dl den vj tri B (hinh 2). Con dudng ngdn nhdt md bqn Tu nen dl Id con dudng ndo?
Hudng ddn gidi (hinh 2): Ldy A ' ddi xung vdi A quo a. Nd'i A'B cdt a tqi M Id diem cdn hm.
Chung minh: Theo tinh ' chdt ddi xung truc ta cd
M A = M A ' .
^ A M -H MB be nhd't khi A M ' -i- MB be nhdt khi vd chi khi A ' , M , B thdng hdng.
Tie'p tyc khoi thdc bdi todn 2, GV dua ra finh hudng: Neu cho A vd a c d djnh cdn B thoy ddi tren mdt dudng trdn (O), ta cd bdi todn sou:
Bdi todn 3: Cho Mqt diem A vd mdt dudng thdng a c d dinh. Mdt dudng trdn tdm O ndm trong cung mdt nuo mdt phdng vdi A cd bd Id dudng thdng a. Hdy fim tren a mdt diem M , tren (O) mdt diem B soo cho A M -t- MB Id be nhd't
Hudng ddn gidi (hinh 3):
Ldy A ' dd'i x u n g v d l A q u o d u d n g thdng a
Nd'i A ' O cdt a d M , cdt (O) d B d l
chung minh duqc M , B Id 2 diem cdn hm.
Tiep tyc khoi thdc bdi todn 3 ta cd bdi todn 4 Bdi todn 4: Cho hai dudng trdn (O, R) vd (0',r) ndm cung phio vdl dudng thdng a hdy xdc djnh tren (O, R), (0',r), a Idn luqt cdc diem A , B, M, soo cho A M + MB be nhd't
Hudng ddn gidi (hinh 4).
Dyng (O") ddi xung vdi (O') quo a Nd'i 0 " 0 cdt (O") tqi A ' cdt (O') tqi B vd cdt a tqi M Idy A
Hinh 3
* Trifclng Trung lipc cO sd Quach Xuan Ky - Bo Trach - Quang Binh
Tap chi Giao due s6 2 2 8 (ki 2 -12/20091
Hinh 4
ddi xung vdl A ' . Cdc diem A, M, B Id cdc diem cdn fim.
Tie'p tyc khoi thdc bdi todn 2 to cd bdi todn 5.
Bdi todn 5:
Tren m d t n u o mqt phdng bd Id dudng thdng o cho trudc hoi diem A, B tren a hdy fim hai diem M, N (MN = d cho trudc) soo cho AM -i- M N -i- NB be nhd't.
Hudng ddn gidl: Ldy A ' ddi xung vdi A qua o, Ndi A'B cdt a tqi M. Tren a ldy M N = d (soo cho BN be nhd't) cdc diem M N Id cdc diem cdn fim.
Bd; todn 6: cho hoi dudng thdng a, b song song vdl nhau vd cdch nhou mdt khodng khdng ddi d. Tren nuo mdt phdng bd a khdng chuo b
Idy mdt diem A. ^ Tren nuo mqt
hdng bd b
hong chuo o ldy mqt diem B Hdy tim tren a diem M, tren b diem N soo cho AM + M N -I- NB be nhd't
(hudng ddn - Ldy A ' ddi xung vdl A qua a Ndi A'B cdt b tqi N tu N dyng N M vudng gdc vdl a (M thudc a). Cdc diem M thudc a, N thudc b Id cac diem cdn fim). Neu a,b khdng song song vdl nhou ta cd bdi todn 7 sou:
Hinh 6
El
...••••M N
Hinh 5
a
Bdi todn 7: Cho gdc xOy vd mdt diem A cd djnh ndm trong gdc dd. Hdy fim tren Ox, Oy cdc diem M,N soo cho A M -i- M N -i- NA nhd nhdt.
Tu dd; todn / t o cd the cd ngay cdch gidi cua bdi fodn 8 sou:
Bdi todn 8: Cho C tam gidc nhqn ABC
vd mdt diem I cd djnh tren cqnh BC fim tren AB, AC cdc diem M, N soo cho chu vi tom gidc IMN
Id nhd nhdt.
Vd neu khdng cd djnh diem I tren cqnh BC to cd bdi todn khd sou:
Bd; todn 9: Cho tom gidc ABC nhqn fim tren cdc cqnh AB, AC, BC cdc diem M, N, I soo cho Chu vl tom gidc MNI Id nhd nhdt (M, N, I Id chdn 3 dudng coo cuo tom gidc ABC).
*••
Vdl he thdng bdi tdp tren, GV ddn ddt tu bdi todn CO bdn den bdi todn ndng coo, fim tdi vd xdy dyng cdc bdi todn khd md cdch gidl bdi sou hodn todn cd the duqc suy ro tu cdch gidi bdi todn trudc dd. Vdl cdc he thdng bdi top tuong ty, khi gidng dqy ne'u GV bie't cdch khai thdc vd tdp cho HS thdi quen khoi thdc mqt cdch hieu qud thi rd rdng myc dich cua dqy hqc Id dqy cho HS phuong phdp tu hqc ty fim tdi vd khdm phd hodn todn cd the dot duoc. 1^
^ 9
Tdng muc luc...
(Tiip theo trang 71)
Bien pliap \&\ac piiuc kho l(han ve CSVC va Itiiet bi GD a trudng MN Muimg Phang huyen Dien Bien.,.
Ren luyen Kinang song cho HS - mot each tiep can ve chat luong, hieu gua GD Khac phuc benh thanh tich trong giao duc a cac nha taiong hien nay GlAO DUC NUOC NGOAl
Su nqhiep phat trien GD cua tinh Xaynhabuli trong 33 nam qua (1975-2008)
Sir lien quan cua l<hai niem Id nang song den khai niem xoa mil cha o o mot sd ni/dc tren the gid Mdt sd kinh nghiem phai then GD khdng chinh quy cua Thai Lan
Quy che mdi ve xet tuyen vao cac tnJtmg DH a Lien bang Nga nam 2009 va net ve quan diem GD cua truang DHTH Calgary (Canada) GD Phan Lan vS md hinh nha trudng tu chu
Tim hi& chuong trinh va SGK Sinh hoc cua Australia
Ti/tudnq \ii chien luoc GD cua nha GD Thai Nguyen Bdi (Tmng Qudc) CT nghiep vu SP cho GV tuong lai 0 mdi sd nudc tren the qidi
Nanq luc cua ddi ngQ quan li trong chinh phu Hoa Ki va bai h x kinh nghidm cho cac nha quan li GD Vidt Nam Quan niSm va tidu chi ve GDMN chat luong cao d bang New Jersey (Hoa ki)
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Vd Van Tdi Michelle Zjhra
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