Thiết kế bài giảng hình học 10 nâng cao (tập 1) phần 1

TRAN VINH JI1 HINH HOC TAP M O T ^ NHA XUAT BAN DAI HOC SU PHAM TRAN VINH ^ ^ s, THIET KE BAI GIANG HINH HOC -^ /v NANG CAO - TAP MOT NHA XUAT BAN OAI HOC SLT PHAM L0I NOI DAU Bat d^u tir nam hoc 2006 - 2007, hai bo sach giao khoa toan mdi : Co ban va Nang cao da duoc su dung tren toan qudc Viec thay sach luon gkn lien v6i viec ddi mdi phuong phap day hoc Bo sach Thiet ke bai giang Toan 10 - nang cao doi nham phuc vu viec ddi mdfi Bo sach duoc bien soan dua tren cac chuong, mitc ciia sach giao khoa, bam sat noi dung cua sach giao khoa, tir hinh nen cau triic mot bai giang theo chuong trinh m6i: Lay hpc sinh lam trung tam va hd trp cua cac phuong tien day hpc hien dai Phan dai sd gom tap Tap 1: gdm cac chuong I, chuong II va chuong III Tap : gdm cac chuong IV, chuong V va chuong VI Phan hinh hpc gdm tap Tap 1: gdm chuong I va bai 1, bai chucmg II Tap 2: phan lai Mdi chuong dupe thiet ke cong phu, dua cac cau hdi va tinh hudng thii vi Trong cac hoat dong chung toi cd gang chia lam phan: Phan ciia giao vien (GV) va phan ciia hpc sinh (HS), df mdi phan co cac cau hoi chi tiet va hudng din tra ldi Thuc hien xong mdi hoat dong, la da thuc hien xong mot don vi kien thiic hoac ciing cd don vi kien thiic Sau mdi bai hpc chiing toi co dua vao ph^n cau hpi trie nghiem khach quan nham de HS tu danh gia dupe miic dp nhan thiic va miic dp tiep thu kien thiic cua minh Sau mdi bai chiing toi cd gang co nhirng phki bd sung kien thiic danh cho GV va HS kha gioi Phan phu luc dai sd, la phan danh cho giao vien, nham sii dung cac phdn mdm ciia toan hpc lam chu kidn thiic, lam chu cac c«n sd can tinh toan tir neu len dupe each day moi chii dong va sang tao Day la bp sach hay, dupe tap the tac gia bien soan cong phu, iing dung nhidu tuu khoa hpc mdi tinh toan va day hpc Chiing toi hy vpng dap iing dupe nhu cau ciia giao vien toan viec ddi mdi phuong phap day hpc Trong qua trinh bien soan, khong the tranh khoi nhung sai sot, mong ban dpc cam thong va chia se Chiing toi chan cam on su gop y cua cac ban ac gia Chi/oiMq I VECTO PHAN NHONG VXN E CUA CHLfONG I NOI DUNG Chuong I nham cung ca'p cho hpc sinh nhirng kien thiic co ban vd vecto, cac phep toan vd vecto va cac tinh chat cua vecto Hpc xong chuang yeu cau hpc sinh nam viing nhirng van dd sau: Dinh nghia vecto: Gia ciia vecto, hai vecto cimg phuong, hai vecto cung hudng, hai vecto ngupc hudfng Hai vec to bang nhau, vecto-khong Tdng cua hai vecto: Quy tac hinh binh hanh va Quy tac ba diem Hieu cua hai vecto Tich cua vecto va mot sd Toa dp trung diem, toa dp vecto, toa dp trpng tam, dp dai vecto va dp dai doan thang II MUC TIEU Kien thijrc Nam dupe toan bp kidn thiic co ban chuong da neu tren - Hieu khai niem vecto - Hidu y nghia cac phep toan vd vecto - Bidt dupe phep toan cua mot vecto va mot sd thuc - Nam dupe toa dp ciia vecto, toa dp cua diem, toa dp trung diem va toa dp trpng tam KT nang - Xac dinh nhanh mot vecto bidt mdt doan thang - Xac dinh dupe dp dai vectP - Chirng minh ba didm thang hang dua vao vecto - Tfnh dupe dp dai dudfng trung tuyen, chu vi tam giac, Thai - Hpc xong chuong hpc sinh se lien he dupe vdi nhieu van de thuc te sinh dong Lien he dupe vdi nhiing va'n 6i hinh hpc da hpc b ldp dudi, md mdt each nhin mdi vd hinh hpc, tir dd cac em cd the tu minh sang tao nhiing bai toan hoac nhung dang toan mdi >^ PHAN CAC BAI SOAN §1 Cac dinh nghia (tiet 1, 2) - ^ ^ j I MUC TlfiU Kien thurc HS nam dupfc: HS hieu khai niem vecta, vectcf-khdng, dp dai vecta, hai vecta cilng phuong, hai vecta cung hudng, hai vecta bang HS biet duoc vecta-khong ciing phuong va cung hudng vdi mpi vecta HS biet chiing minh hai vecta bang ; biet xac dinh mot vecta bang vecta cho trudc va cd diem dau cho trudc KT nang • Xac dinh nhanh chdng dupe vecto biet mot doan thang • Xac dinh dupe hai vecto ciing chidu, hai vecto ngupc chidu • Xac dinh dupe hai vecto bang Thai • Lien he dupe vdi nhidu van 6i cd thuc te vdi van dd vecta • Cd mdi lien h6 chat che giua vecto va doan thang • Cd nhidu sang tao hinh hpc II CHUAN BI CUA GV VA HS Chuan bi cua GV: - Hinh ve 1, trang SGK - Tranh ve gidi thieu lire vat li - Thudc ke, phaii mau, Chuan bi ciia HS : - Dpc bai kl a nha, cd the dat cac cau hoi \ e mot van de ma em chua hieu in PHAN PHOI THOI LUQNG Tiet 1: Tiir dau den het muc Tiet 2: Phan lai va hudng dan bai tap IV TEN TDiNH DAY HOC n DAT VA'N D€ Cau hoi Tren mot doan dudng AB (ta gia sir day la mot doan thang) Ban Thao di tir A den B ban Hidn di tir B den A a) Quang dudng hai ban di cd bang khdng? b) Hudng di ciia hai ban cd ciing khdng? GV cho HS tra ldi va hirdng den khai niem vecta Cau hoi Hai dtd di tren hai doan dudng thang song song vdi (a) Hai dtd ludn ludn di cimg chidu (b) Hai dtd ludn di ngupc chieu (c) Hai dtd cd the di ciing chieu, cd thd ngupc chidu (d) Ca ba kdt luan tren deu sai Hay chpn khang dinh diing Cdu hdi Ggi y trd ldi edu hdi Hay ket thiic viec chiing minh tinh 3AB + 3BC = A'B + BC chat bdng each dung quy tdc ba diem = A'C' = 3AC • GV neu chii y quan 1) Do tinh cha't 1, ta cd (-k)d = (-1 k)d = (-l)(kd) = -(kd) Bdi vay ca hai vecto (-k)d va -(kd) dau cd the viet dcfn gian la -ka 2) Vecto — cd the viet la n Chang han - ed the vie't la— n ' 3 • Cho HS giai bai toan 1, nhdm ren luyen ki nang ve tfch ciia vecto vdi mdt sd - Treo hinh 22 len bang - Cho HS phan tich: MA = MI + IA va MB = Ml + IB - Gpi mdt HS thuc hien IA + IB - Riit ke't luan bai toan Hinh 22 GVco the chung minh bang each khac : dung D cho AMBD la hinh binh hanh Theo quy tdc hinh binh hanh ta cd: MA + M5 = MD = 2M/ • Thuc hien - ^ trang 20 SGK GV : Thirc hien thao tac 5' (GV ve hinh 23 SGK len bang) 57 Hoat ddng cua GV Hoat ddng cua HS Ggi y trd ldi cdu hdi Cdu hdi Tuong tu bai toan 1, hay bieu thi MA = MG + GA cac vecto MA, MB va MC qua MB = MG + GB cac vecto MG, GA, GB vaGC MC = MG + GC Ggi y trd ldi cdu hdi Cdu hdi Tinh long MA + MB + MC MA+ MB + MC = 3MG + GA + GB + GC Ggi y trd ldi cdu hdi Cdu hdi Ke't luan MA+ MB + MC =3MG HOAT DONG 3 Dieu kien de hai vectd cung phiTdng a) Muc dich: Giiip HS td tinh chdt trin rut dieu kiin de hai vecto cung phuong, hai vecto cung chieu b) Hudng thuc Men Thuc Men [?jj trang 21 SGK vd rdt kii ludn ve hai vecto cdng phuong - Thuc Men [ ? ^ trang 21 SGK vd riit kii ludn ve ba diem thdng hdng - Cho HS ldm bdi todn nhdm khdc sdu kii'n thifc c) Qud trinh thuc hien GV treo hinh 24 58 1 i i j • i i — > • ; •si \ if TT TT j i : / I c X i > V < Hinh 24 • Thuc hien [?lj trang 21 SGK va rut ke't luan ve hai vecta cung phuang GV thirc hien thao tac 5' Hoat ddng cua HS Hoat ddng cua GV Gen y trd ldi edu hdi Cdu hdi Hay tim cac sd k cho b = kd Cdu hdi Hay tim cac so m cho c =md Ggi y trd ldi edu hdi m= -— Gtyi y trd ldi cdu hdi Cdu hdi Hay tim cac sd n cho b = nc Cdu hdi n= — Ggi y trd ldi cdu hdi Hay tim cac so p cho x = pU Cdu hdi p = -3 Ggi y trd ldi cdu hdi Hay tim cac sd q cho y = qu q= - Tong quat 59 Vecto b ciing phifOng vdi vecto a (a ^Q) vd chi ed sd k ehob-kd • Thuc hien [^2] trang 21 SGK va rut ke't luan ve ba diem thang hang GV cd the trd ldi ngay: Vi neua = 0, thi Vk, ka luon cung phuong vdi mgi vecta Nhung khdng cd sd k ndo de b = ^.0 vdi b^i) Dieu kien de ba diem thdng hang Dieu kiin cdn vd du diba diem phdn biit A, B, C thdng hdng Id cd sd k cho AB = kAC GM cho HS chCmg minh khing dinh tren • Cho HS lam bai toan nham khac sau kien thurc - Treo hinh 25 len bang Hinh 25 cau a) - Ve dudng kinh AD - Chumg minh BH // DC BD // CH, tir suy AH = 207 Caub) -Phan tich OI^-(OB + OC) vaAH = 10I -Tirddnitra: 0H = 0A + 0B + 0C cau c) - Riit 077 = 30G - Ket luan 60 HOAT DONG 4 Bleu thi mot vectd theo hai vectd khong cung phUdng a) Mtic dich: Giiip HSdi di'n dinh li quan trgng, phuc vu cho phuong phdp tog sau ndy b) Hudng thuc Men: - Ddt vdn di - Niu dinh li trang 22 SGK -Hudng ddn HS chifng minh dinh li c) Qud trinh thuc Men • Dat van de GV cho hoc sinh lam bai tap sau: Cho hinh binh hanh ABCD Dat AB = a, AD =^ b Ggi M, N Ian luat la cac trung di^m cua BC va CD a) Hay,bieu dien AC qua a vab b) Hay bieu dien AM qua a va b c) Hay bieu dien A A^ qua a va b A GV thirc hien thao tac 5' Hoat ddng cua GV Cdu hdi Hay bieu dien AC qua a vab Hoat ddng ciia HS Ggi y trd ldi cdu hdi Theo quy tdc hinh binh hanh ta cd: 61 AC = AB + AD = a + b Cdu hdi Ggi y trd ldi cdu hdi Hay bieu dien AM qua a vab AM=AD+DC+CM AM=AB+BM Tit 66 ta cd AM = a + — b Cdu hdi Ggi y trd ldi cdu hdi Hay bieu dien AN qua a sab AN=AD+DN AN=AB+BC+CN Txx 66 ta c6 AN = -a + b • Ta cd dinh h sau day Dinh li Cho hai vecto khdng cdng phuong a vab Khi dd mgi vecto x deu cd the bieu thi dugc mgt edch nhdt qua hai vecto a vd b, nghia la cd nhd't cap sdm vd n cho x = md + nb • De chumg minh dinh Ii can cac thao tac - GV treo hinh 26 SGK len bang - Dat cac cau hdi sau: HI Cac cap vecto OA vaOA' ; ^ va 05*' cd quan he nhu the nao? H2 Hay bieu dian OX qua OA' vaOfi' H3 Hay bieu dien x qua a vab H4 Chiing minh su bieu dien dd la nhat 62 O h B B' Hinh 26 TOM T ^ Bfll HOC Tich cua vecta vdi sd thuc k la mdt vecto, ki hieu la ka , dupe xac dinh nhu sau • Na'u k > thi vecto ka ciing hudng vdi vecto ; Ne'u k < thi vecto ka ngupc hudng vdi vecto ; • Dp dai vecto ka bdngUI | | Phep la'y tich cua mdt vecto vdi mdt sd gpi la phep nhan vecto vdi so (hoac phep nhan sd vdi vecto) Vdi hai vecto ba't ki 5, ^ va mpi sd thuc k, I, ta cd • k(l a) = (kl)d ; • (k+i)d = kd + id ; • k(d + b) = kd + kb ; k(d-b) = kd-kb ; • kd = va chi ^ = hoac = Vecto b ciing phuang vdi vecto (d^O) va chi cd sd k cho b = kd 63 Dieu kien can va du de ba diem phan biet A, B, C thang hang la cd sd k cho 'AB^k'XC Cho hai vecto khdng ciing phuong a vab Khi dd mpi vecto x deu cd the bieu thi dupe mdt each nhat qua hai vecto va fc, nghia la cd nhat cap sd m va n cho x = md + nb HOAT DONG naOTNG DflN Bfll TflP SGK a) Muc dich: Giiip HS khdc sdu kii'n thdc vd ki ndng ve tich cua vecto vdi mdt sd - Van dung dugc kii'n thde dd viec gidi todn b) Hudng thuc Men - Chiia tgi ldp cdc bdi tap: 21 din bdi 25 Cdc bdi tap cdn lgi hudng ddn ve nhd c) Qud trinh thuc Men Bai 21 Hoat ddng ciia GV Hoat ddng cua HS Ggi y trd ldi edu hdi Cdu hdi Theo quy tdc hinh binh hanh hay Theo quy tdc hinh binh hanh ta cd: dung OA +aB Dung D cho OADB la hinh binh hanh Khi dd OA + OB = OD Cdu hdi Theo quy tdc ba diem OA - OB 64 Ggi y trd ldi cdu hdi hay dung 'OA-'OB =BA Cdu hdi Ggi y trd ldi edu hoi Theo quy tdc hinh binh hanh hay Dung OA ' = 30 A, 0B' = 40B, dung 3OA + tie'p theo ta dung D' cho OA'D'B' la hinh binh hanh, til dd ta cd 30A +40B =0D' Trd ldi 0A + | = lOA-O^I = \BA\ =aV2 ; |30A + | = 5a ; — OA + , 5 V54T V6073 a ; 'AoA-'-OB 28 a Bai 22 Hoat ddng ciia HS Hoat ddng ciia GV Ggi y trd ldi cdu hdi Cdu hdi Hay xac dinh m, n cho: OM = mOA +n0B , Cdu hdi Hay xac dinh m, n cho: MyV = mOA +nOB ; Cdu hdi Ta cd OM - — OA, dd m =— ,n-i) 1 Goi y trd ldi cdu hdi Tacd MN = -AB = OA + -OB, 1 d o d d m = — ,n = — 1 Ggi y trd ldi cdu hdi Hay xac dinh m, n cho: Ta cd AN^mOA AN=-AO+-AB^-AO+-OB, 1 5.TKBGHiNHH9C10/1(NC) +nOB 65 dd m = - , n = Cdu hdi Hay xac dinh m, n cho: Ggi y trd ldi cdu hdi Ta cd MB =m OA +n OB MB^MO + OB = OA dd m + OB, —, n= 1 Bai 23 Hoat ddng cua HS Hoat ddng ciia GV Cdu hdi Hay phan tich 2MA^ theo Ggi y trd ldi edu hdi 1MN = MC + MD MD va MC Cdu hdi Hay phan tfch MD iaeo MA Ggi y trd ldi cdu hdi MD = MA + AD va AD Cdu hdi Hay phan tich MC theo MB Ggi y trd ldi cdu hdi MC = MB + BC va C Cdu hdi Tir dd riit ke't luan Ggi y trd ldi cdu hdi 1MN = MC + MD^MA =AC+BD 66 + AC + MB + BD Bai 24 GV hudng ddn cdu a) Hoat ddng cua HS Hoat ddng cua GV Ggi y trd ldi cdu hdi Cdu hdi Gpi E la trung diem AB, hay GA+GB=1GE tinh: GA + GB Cdu hdi Ggi y trd ldi cdu hdi Hay tinh GA + GB + GC 1GE+GC=0 suy GA+GB+GC= G la trpng tam Bai 25 Hoat ddng ciia GV Cdu hdi Hay bieu thi AB theo a vab Cdu hdi Hay lam tuong tu dd'i vdi cac vecto cdn lai Hoat ddng cua HS Ggi y trd ldi cdu hdi jB JG + GB^-a + b Ggi y trd ldi cdu hdi GC = -d-b; BC = -d-lb GA = ld + b Bai 26 Hudng ddn Ap dung true tie'p bai 24 Bai 27 Hudng ddn De chiing minh hai tam giac PRT va QSU cd ciing trpng tam, theo bai toan 26, ta cdn chu:ng minh :YQ + ~RS + flJ = That vay, ta cd : 67 PQ + RS + TU=-(AC + CE + EA) = Bai 28 Hudng ddn a) Lay mdt diem O xac dinh nao dd, ta cd : GA+GB+GC+GD=OA-OG+OB-OG+OC-OG+OD-OG= = 0A + 0B + 0C + 0D-40G ,TrT Bdi vay ne'u GA + GB + GC+ GD ^0 thi OG = -(OA + OB + OC+ 0D) Vay diem G dupe xac dinh Gia su cd diem G' cho G'A + G'B + G'C+ G'D = Suv GA + GB + GC + GD = G'A + G'B + G'C + G'D[...]... deu) MQT SO CAG H O I TRAC NGHIEM Cau 1 Cho ngii giac ABODE Sd cac vecto khac 0 cd diem ddu va diem cudi la cac dinh cua ngu giac bang (a) 25 (b)20 (c) 16 (d) 10 Trd ldi Phuong an (b) diing Cau 2 Cho luc giac ddu ABCDEF Sd cac vecto ciing phuang vdi OC (O la tam cua luc giac deu) cd diem dau va diem cudi la cac dinh ciia liic giac bang (a) 10 (b )12 (c )13 (d) 14 Trd ldi Phuong an (b) dung Cau 3 Cho... hien - ^ 1 (trang 11 SGK) GV thiTc hien thao tac nay trong 3' 25 Hoat dong cua GV Cdu hdi 1 Hoat ddng ciia HS Ggi y trd ldi cdu hdi 1 Hay xac dinh JB + CB Tur B dung5£ - CB Khi 66 : JB + CB = Cdu hdi 2 JE Ggi y trd ldi cdu hdi 2 Hay xac dinh : ^ + SC La vecta AC • Thuc hien - ^ 2 (trang 11 SGK) GV thyc hien thao tac nay trong 3' Hoat ddng cua GV Hoat dong cua HS Ggi y trd ldi cdu hdi 1 Cdu hdi 1 AB =... Men \ ?1\ trang 12 SGK - Cho HS ldm bdi todn 1 -Thue hiin "pr 5 trang 12 SGK - Cho HS ldm bdi todn 2, bdi todn 3 -Thuc Men ^ trang 13 SGK - Niu ghi nhd - Neu chii y c) Qud trinh thuc Men • Neu hai quy tac: GV dat van de cho hoc sinh neu hai quy tac do, c6 suf dung hai hinh 12 va 13 SGK Vdi ba diem ba't ki M, A^, P, ta cd MN+ NP = MP Hinh 12 Neu OABC la hinh binh hanh thi ta cd ^ + 0C = 0B Hinh 13 • Thuc... HOAT DONG 1 1 Dinh nghTa tong cua hai vectd a) Muc dich: HS nam vd thuc Men duge phep cgng hai vecto dua tren hai quy tdc: - quy tdc ha diem; - quy tdc hinh binh hdnh b) Hudng thuc Men - Thue Men | ? l | trang 10 SGK, sii dung ede hinh 8, 9 de di de'n khdi niim tong hai vecto - Niu dinh nghia phep cgng hai vecto, sif dung hinh 10 - Cung cdvd khac sdu khdi niem : Thue hiin ' p r / vd '^ffi trang 11 SGK... todn 26 + BC b) Hudng thuc Men - Thuc Men ^ 3vd^4, sif dung hinh 11 , trang 11 SGK - Niu tinh chdt - Chu y quan trgng c) Qud trinh thuc Men • Thuc hien#^ 3 GV thirc hien thao tac nay trong 3' Cho hinh binh hanh ABCD Diing hinh nay dd kiem ehiing W^ 3 Hoat dong cua HS Hoat dong ciia GV Ggi y trd ldi cdu hdi 1 Cdu hdi 1 Hdy chifng to AB+ 1BC ^B^+ 'AB JB + ~BC = JC; BC-^AB = AD + DC = AC Cdu hdi 2 Ggi... thirc hien thao tac nay trong 3' Hoat dong ciia GV Cdu hdi 1 Hay chi ra diem A Hoat dong cua HS Goi y trd ldi cdu hdi 1 Qua 0 dung dudng thing A // d (d la gia cua a), tren A la'y A sao cho OA ciing hudng vdi a, va OA = a Cdu hdi 2 Cd bao nhieu diem A nhu vay ? 2- TKBGHiNHHQC10 /1 (NC) • Ggi y trd ldi cdu hdi 2 Cd mot diem A nhu vSy 17 TOM m B^i hpc 1 Vecta la mdt doan thang cd hudng, nghia la trong hai... cua cac vecto tren vdi chieu cao ciia tam giac deu ABC? Cho hoc sinh tra ldi va GV nhan xet • Cho HS lam bai toan 3 trang 13 SGK ^ -Sit dung hinh 15 SGK Tinh MA + AM = MM = 0 - Sir dung AM = MB -Tinh GA + GB = GC' = CG Hinh 15 TinhGA + GB + GC • Thuc hien [?3j trang 13 SGK GV thirc hien thao tac nay trong 3' Hoat dong cua GV Cdu hdi 1 Hoat dong cua HS Ggi y trd ldi cdu hdi 1 Em cd nhan xet gi ve dp dai... GV Cdu hdi 1 Hay chi ra cac cap vecto nao bang nhau? Cdu hdi 2 Hoat dong cua HS Ggi y trd ldi cdu hdi 1 AB va DC ; AD va BC ; Ggi y trd ldi cdu hdi 2 Hai vecta AB va CD cd bang nhau AB va CD khdng bang nhau vi khdng? vi sao? chiing ngupc hudng 16 • Thuc hien thao tac ^ 1 (trang 7 SGK) GV thirc hien thao tac nay trong 3' Hoat dong ciia HS Hoat dong ciia GV Ggi y trd ldi cdu hdi 1 Cdu hdi 1 Hay chi ra... vecto, sif dung hinh 10 - Cung cdvd khac sdu khdi niem : Thue hiin ' p r / vd '^ffi trang 11 SGK c) Qud trinh thuc Men • Thuc hien ?1 A' A / 1^ A M' Hinh 8 24 f /• • • / \( 1) GV thiTc hien thao tac nay trong 3' Hoat dong ciia HS Hoat dong cua GV Ggi y trd ldi cdu hdi 1 Cdu hdi 1 vat cd the dupe tinh tien chi mdt lan de tir Ta cd the tinh tien vat theo vecto vi tri (I) den vi tri (III) hay khdng ? Neu cd... 3.TKBGHiNHHpC10 /1( NC) -'-' GV gpi y HS lam theo each khac Bai? Hoat ddng ciia GV Hoat dong cua HS Ggi y trd ldi cdu hdi 1 Cdu hdi 1 Td giac ABCD cd AB = DC la La hinh binh hanh hinh gi? Cdu hdi 2 Ggi y trd ldi cdu hdi 2 Neu them dieu kien \AB\ = \BC\ thi tii giac ABCD la hinh gi? Hinh thoi vi nd la hinh binh hanh cd hai canh lien tiep bang nhau Bai 8 GV chifa cdu a) Hoat ddng ciia GV Cdu hdi 1 Hay xac ... trang 10 SGK, sii dung ede hinh 8, de di de'n khdi niim tong hai vecto - Niu dinh nghia phep cgng hai vecto, sif dung hinh 10 - Cung cdvd khac sdu khdi niem : Thue hiin ' p r / vd '^ffi trang 11 ... hdi Hay xac dinh tinh diing sai cua Tac6 AB + BC = AC do66 khangdinh 15 + ^1 AB BC la khang dinh diing Bai 10 Hoat ddng cua GV Cdu hdi Hay dien vao d trdng Hoat dong cua HS Ggi... c6 suf dung hai hinh 12 va 13 SGK Vdi ba diem ba't ki M, A^, P, ta cd MN+ NP = MP Hinh 12 Neu OABC la hinh binh hanh thi ta cd ^ + 0C = 0B Hinh 13 • Thuc hien ?2 trang 12 SGK GV thirc hien