Tài liệu Thiết kế bài giảng hình học nâng cao lớp 10 -tập 2

IRAN VINH HINH HOC TAP HAI • II NHA XUAT BAN HA NOI ^ • TRAN VINH THIET KE BAI GIANG I l I M l IKN J NANG CAO - TAP HAI NHA XUAT BAN HA NOI LflflNOIDAU Bit diu tii nam hoc 2006 - 2007, hai bo sach giio khoa toan moi : Co ban va Nang cao da duoc su dung tren toan quoc Viec thay sich luon gin liin v6i viec ddi mofi phuong phap day hoc. Bo sach Thiet ke bai giang Toan 10 - nang cao ra ddi nhim phuc vu viec ddi moi do. Bo sach dugc bien soan dua tren cac chuong, muc cua sach giao khoa, bam sit noi dung ciia sich giio khoa, tijr do hinh thanh nen cau true mot bai giang theo chuong trinh m6i: Lay hoc sinh lam trung tam va hd trg ciia cac phuong tien day hoc hien dai. Phin dai sd gdm 2 tap. Tap T. gdm cic chuong 1, chuong II va chuong 111. Tap 2 : gdm cac chuong IV, chuong V va chuong VI. Phan hinh hge gdm 2 tap. Tap 1: gdm chuong I va bai 1, bai 2 chuong II. Tap 2: phan con lai Mdi chuong dugc thiet ke cong phu, dua ra cac cau hoi va tinh huong thu vi. Trong cac boat dgng chiing toi co' ging chia lam 2 pljin:' Phin cCia giao vien (GV) va phin ciia hge sinh (HS), 6 mdi phin co cac cau hoi chi tilt va hudfng din tra ldi. Thuc hien xong mdi boat dgng, la da thuc hien xong mgt don vi kiln thiic hoac cung co' don vi kie'n thiic do. Sau mdi bai hge chiing toi co .dita vao phin cau hoi trie nghiem khach quan nhim dl HS tu dinh gii dugc miic do nhin thiic va miic do tie'p thu kiln thiic ciia minh. Sau mdi bai chiing toi cd ging co nhiing phin bd sung kiln thiic danh cho GV vaHS khi gioi. Phan phu luc trong dai so. la phan danh cho giao vien, nhim sii dung cac phin mem cua toan hge lam chii kien thiic, lam chu cac con so cin tinh toan. tir do neu len dugc each day moi chii dgng va sang tao. Day la bg sach hay. dugc tap the tie gia bien soan cong phu, iing dung nhiiu thanh tuu khoa hge moi trong tinh toan va day bgc. Chiing toi hy ygng dap iing dugc nhu cau cua giao vien toan trong viec ddi moi phuong phap day bgc. Trong qua trinh bien soan, khong the tranh khoi nhiing sai sot, mong ban dgc cam thong va chia se. Chiing toi chan thanh cam on su gop y ciia cac ban. Tac gia Chi/dNq II HUdNG CUA HAI VEC TO VA LfNG DUNGCtiep theo) TICH V O §3. He thu'c liidng t r o n g t a m giac (tiet 5, 6, 7, 8) 1. MUCTIEU 1. Kien thurc HS nim dugc: Dinh li cosin, dinh li sin trong tam giac va cac he qua. Cac cong thiic tinh do dai trung tuyin va dien tich tam giac. Hge sinh van dung dugc cac cong thiic tren de giai cac bai toan chung minh va tinh toan co lien quan din do dai trung tuyin, dien tich, chieu cao ciia tam giac. 2. KT nang • Van dung thanh thao dinh li cosin va dinh li sin de tinh cac goc, cac canh chua bie't ciia tam giic khi da biet ba canh hoac hai canh va goc xen giira, hoac mgt canh va hai goc kl. 3. Thai do • Lien he dugc voi nhiiu van dl co trong thuc te , nhat la trong do dac. • Co nhiiu sang tao trong hinh bgc. • Nhan thirc to't hon trong tu duy hinh hge. n. CHUAN BI CUA GV VA H6 ' 1. Chuan bi cua GV: 1. GV: Chuin bi mgt so' cac vi du da hge a lop 9 de dat cau hoi. 2. Chuin bi mgt so' hinh sin d nha vao giay hoac vao ban meca de chiiu neu co miy chiiu: Tur hmh 44 de'n hinh 58. Chuin bi phin mau. Ngoai ra con phai ve sin mgt so' hinh 6i hudng din bgc sinh thuc hien cac" 2. Chuan bi cua HS : • Dgc bai ki d nha, co the dat ra cac cau hdi vl mgt van 6e ma em chua hieu. • Chuin bi tdt mdt so cdng cu de ve hinh. m. PHAN P H O I THCDI LUONG Bdi ndy chia ldm 4 tiet'. Tiet 1: tit ddu den het phdn 2 (dinh li sin); Tiet 2 . Mtic 3, 4 Tiet 3. Muc 5(gidi tam gide) Tiet 4. On tap IV. TIEN TDINH DAY HOC n. KiCMTRn Bi^lCU GV: Kiem tra bdi cd trong 5' Cau hoi 1. •Cho tam giac vudng ABC, vudng tai A, BC = a 5 = 60''. a) Tinh cic gia tri lugng giic cua cic gdc trong tam giic. b)Tinh AB.BC; AB.CB; AB.CA Cau hdi 2. Cho tam giic ABC, A(l ; 1), B(-2; -1), C(3; -2). a) Tinh cac gdc trong tam giac; b) Tinh AB.BC; AB.CB; AB.CA . B. iini M 6 I nOATDONGl L Dinh li cosin trong tam giac a) Muc dich: Giiip HS biit dugc dinh 11 cdsin va biit van dung nd trong giai toan. b) Hudng thifc hien - Ddt van de. - Thue hiin - Thite Men -^f 1. - Niu dinh li odsin. - Thuc hiin / \ 2. - Thue hiin J ^ 3. - Hudng ddn HS ldm vi du 1 trang 54 SGK, vi du 2 trang 55. - Niu chii y quan trgng. . c) Qud trinh thifc Men • Dat vin dl GV ve hinh 44 len bang. ^ C Hmh 44 - Cho mdt HS phit bieu dinh li Py - ta - go cho hinh 44: BC^ = AC^ AB' - Phin tich fiC = AC - A6. Tir do ta cd BC =(AC-AB)^=AC + AB^-2AC.AB = AC^+Jf^ • Thuc hien ?1 GV: Thi/c hien thao tac nay trong 2' Hoat dong cua giao vien Cau hoi 1 Hoat dgng ciia hoc sinh Ggi y tra ldi cau hoi 1 Trong chiing minh tren, A vudng Vi A vudng , nen AC L AB, hay dugc su dung trong budc nao? Z6.AC = 0 Cau hoi 2 Ggi y tra Idi cau hoi 2 NIu bd di gia thiet A vudng thi Khdng diing. kit luan tren cdn diing hay khdng? • Thuc hien ^ C 1 GV: Thu'c hien thao tac nay trong 5' Hoat dgng ciia giao vien Cau hoi 1 Hoat dgng cua hoc sinh Ggi y tra Idi cau hoi 1 Hay phan tich BC theo AB vh 'BC = Jc. Ggi y tra Idi cau hoi 2 Cau hoi 2 Hay tinh BC . Cau hoi 3 'BC = JC JC-JB. = (AC - Afi)2 +~AB -IAC.JB. Goi y tra Idi cau hoi 3 Hay ip dung dinh nghia tich vd hudng cua hai vecto trong trudng AB.AC = AB.AC cos A hgp nay. Ggi y tra Idi cau hoi 3 Cau hoi 4 Kit luan. a 2 = b2 + e2 - IbecosA • Neu dinh li cdsin Djnh li Trong tam gide ABC, vdi BC = a. CA = b, AB = c, ta co a^ = b^ +c^ - IbccosA lac cosB ; ; b^ = a^ + c' c^ = a^ +b^ - lab cos C. • Thuc hien -^f 2 GV Cho nhieu hoc sinh phat bieu roi dtia ra nhan xet tC/ng phat bieu cua hpc sinh. Sau do dua ra phat bieu chi'nh thCic: Dinh li cd the phdt bieu nhu sau : Trong mgt tam gide, binh phifong mgt cgnh bang tdng cdc binh phifong ciia hai cgnli kia, trif hai ldn tich ciia chung vd cosin eiia gdc xen giita hai cgnh do. • Thuc hien ?2 GV: Thu'c hien thao tac nay trong 2' Hoat dgng ciia giao vien Cau hoi 1 Hay ap dung dinh li cdsin vao tam giac vudng ABC. Hoat ddng ciia hge sinh Ggi y tra Idi cau hoi 1 a'^ = b^ + c^ - IbccosA Vi A vudng , nen cosA = 0, do 66 a^=b'+c^ Cau hoi 2 Day la dinh li quen thudc nao? • Thuc hien 7/%, 3 GV: Thirc hien thao tac nay trong 2' Ggi y tra Idi cau hoi 2 Dinh li Py - ta - go Hoat ddng ciia giao vien Hoat ddng cua hoc sinh Cau hoi 1 Ggi y tra Idi cau hdi 1 Tit a^ = Z?^ + c^ - IbccosA hay tinh cos A. Cau hdi 2 9 7 Tir 6 =a tinh cos B. Cau hdi 3 b, 2 +, 2c -a2 cos A = 'Ibc Ggi y tra ldi cau hdi 2 9 +c -2accos5hay cosB = . lac Ggi y tra Idi cau hdi 3 Tit c^ = a^ +b^ - lab cos C. hay tinh cos C. ^ a'+b^-c^ 2ab GV cho HS phit bieu : He qua b, 2 + c2 cos A = Ibc cosB = a^+b^-e^ lab • Thuc hien Vi du 1. Trang 54 SGK. cosC = - GV treo hinh 45 len bang - Ggi mdt HS phit biiu dinh li cdsin cho canh BC. Ap dung tinh ta dugc kit qua : a = Vl300 « 36 (hai li). Hinh 45 10 a^+e^-b^ lac Ddy Id mgt bdi todn thuc ti', GV ddn ddt hge sinh mo td bdi todn thdnh bdi todn trong tam gide ABC, vdi ^ = 60*^. GV ddn dat HS gidi bdi todn theo cdc bifde sau: - Vehinh; -Tinh cgnh BC; - Dung mdy tinh bd tiii delay ki't qua gdn diing. • Thuc hien vi du 2. - Cho HS ve hinh 46 Hinh 46 Cho HS dua ra cdng thiic tinh cos A. Tut dd tinh cos A = b^+c^ 24^ + 23^ - 7^ a Ibc 0,9565. 2.24.23 Diing miy tinh bd tiii ta tinh dugc A « 16°58'. • Neu chu y: Hudng din HS thuc hanh ngay cic bai tap tren. Neu su dung may tinh bd tiii (MTBT) dl tinh gdc A khi biet cos A = 0,9565 ta cd thi lam nhu sau 1) Dd'i vdi MTBT CASIO/x-220 hoac/x-500A thi an 0.9565 SHIFT cos SHIFT Ol'' . Kit qui : A =* 16°58'. 2) Dd'i vdi MTBT CASIO/x-500MS thi in SHIFT cos 0.9565 0 O' ? 5 Kit qua : A ~ 16"58'. 11 HOAT DONG 2 2. Djnh li sin trong tam giac a) Muc dich: Giiip HS biit dugc dinh li sin va biet van dung nd trong giai toan. b) Hudng thuc hien - Ddt vdn de. - Thifc hiin -^^ 4. - Niu dinh li sin. - Thuc hiin vi du 3. - Neu chit y.- Thifc hien vi du 4. c) Qud trinh thitc hien • Dat vin dl GV ve hinh 47 . - Cho HS thao luan cac van dl sau Hinh 47 NIu gdc A vudng (h. 47) thi a = lR\k dl thiy a = lRsmA, b ^ IRsinB , c = IRs'mC . (1) • Thuc hien w 4 (De chiing minh cac cdng thii'c (1)) Ve hinh 48 len bang. a) b) Hinh 48 12 GV Thu'c hien thao tac nay trong 4' Hoat ddng ciia hge sinh Hoat ddng cua giao vien Ggi y tra ldi cau hdi 1 Cau hdi 1 Khi nao thi hai gdc cd sin bing Khi hai gdc bing nhau hoac bii nhau. nhau? Cau hdi 2 Ggi y tra Idi cau hdi 2 cd Ha gdc nay bing nhau hoac bii nhau. Hai gdc : BAC va BA^ quan he vdi nhau nhu the nao? Vay sin BAC = sinA4T Cau hdi 3 Ggi y tra ldi cau hdi 3 Tinh sinfiXx" sixiBA CBA' =— . IR Til' dd ta cd s i n A = — IR • Neu dinh li Vdi mgi tam giac ABC, ta cd a b c sin A sinB sinC = 1R, trong do R Id bdn kinh dudng tron ngogi tii'p tam giac ABC. GV: Thu'c hien thao tac nay trong 4' Hoat ddng ciia giao vien Cau hdi 1 Hay tinh a theo R va sin A. Cau hdi 2 Hay tinh b theo R va sinB. Hoat ddng ciia hoc sinh Ggi y tra Idi cau hdi 1 a = 2RsinA. Ggi y tra Idi cau hdi 2 b= 2RsinB. Cau hdi 3 Ggi y tra Idi cau hdi 3 Hay tinh c theo R va sinC. c= 2RsinC. • Thuc hien vi du 3. Cho^ HS thao luan dl bai. Treo hinh 49 len bang. Hinh 49 Day la bai toan thuc te, GV nen hudng din hge sinh trd vl bai toan quen thudc theo cac budc sau: - Tinh gdc A trong tam giac ABC. - Tinh gdc C trong tam giac ABC. - Tinh gdc B trong tam giac ABC. - Tinh gdc AC trong tam giac ABC. - Tinh gdc CH trong tam giac vudng AHC. - Diing may tinh bd tiii de tinh kit qua gin diing. CH = AC • Neu chii y. 14 169,4 134,7 (m). , , . , 70.sinl05''30' ^. . ^, Neu sii dung MTBT de ti'nh bieu thuc b = thi ta co the sinl4°30' lim nhu sau 1) Dd'i vdi MTBT CASIO/x-220 hoac/x-500A thi an [(... 105 o,,, 30 o,,, ...)] 0 EJ sin 14 o,., 30 o,., ...)] [il.Kltqua:Z? « 269,4. 2) Dd'i vdi MTBT CASIO/x-500MS thi an 70 0 [sin] 105 0 ^ 30 0 ^ 0 |sin| 14 O''' 30 Oi'y 0. Kit qua:b ~ 269,4. • Thuc hien vi du 4. Bdi todn dugc gidi theo cdc budc sau: - Ap dung dinh li sin dl tinh sinA, sinB, sinC. . . a sinA = — , IR . b smB -—, IR . c sine = — . IR - Cdng cac kit qua lai. sini4 - 2 sin 5 + sinC — (a -lb IR + c) = — ( 4 - 10 + 6) = 0 IR ffOATDONC3 3. Tdng binh phuong hai canh va do dai dudng trung tuyen cua tam giac a) Mtic dich: Giiip HS bie't dugc do ddi dudng trung tuyin trong tam giac. b) Hudng thirc hien - Gidi bdi todn 1. - Thifc hiin ' ^ t 5. 15 - Gidi bdi todn 2 - Thifc hiin 1 ^ 6. - Gidi bdi todn 3. c) Qud trinh thitc hien • Giai bai toan 1 - Neu bai toan, cho HS thao luan de bai - Goi mdt HS ve hinh 50 Hinh 50 • Thuc hien [?3j CVThiic hien thao tac nay trong 4' Hoat ddng ciia giao vien Cau hdi 1 Ggi y tra Idi cau hdi 1 Khi m = — thi tam giac ABC cd 2 tinh chat dac biet gi khdng? Cau hdi 2 2 Hoat ddng cua hoc sinh Tam giac ABC vudng tai A. • Ggi y tra Idi cau hdi 2 2 AB + AC bdng bao nhiiu ? AB'^ + AC^ = a l • Thuc'hien 4yf 5 (Dl giai bai toan 1) CVThi/c hien thao tac nay trong 4' Hoat ddng ciia giao vien 16 Hoat ddng ciia hoc sinh r Ggi y tra ldi cau hdi 1 Cau hdi 1 Dat Ai = A/ + /fi, tfnh AB^. AB^ = A I - + IB^ + 2 A 7 7 5 Ggi y tra Idi cau hdi 2 Cau hdi 2 Dat AC = A/ + 7c, tinh AC^. AC^ = AI^ + ic^ + 2 A 7 7 C Ggi y tra Idi cau hdi 2 Cau hdi 3 A5%AC^= 2 AI^ + 2IC^ + Tinh JB +Jc . 2 A 7 ( 7 C + 7 B ) = 2 A 1 ' + 2IC^ 2 AB^ + AC^ =ln? +—. 2 ^ • Giai bai toan 2 - Cho HS neu va thao luan vl bai toan - Goi mdt HS ve hinh 51. - Ap dung bai toin 1: ta tfnh MP^ + MQ^ theo a va k. ,2 Ket qua: Ml 2 = . 2 4 • Thuc hien^%^ 6 GV: Thi/c hien thao tac nay trong 4' 2-TKBGHH10-NC-T2 17 Hoat ddng ciia giao vien Hoat ddng eiia hge sinh Cau hdi 1 Ggi y tra Idi cau hdi 1 Hay nhan xet ve (*). VI trai ciia (*) ludn khdng am. Cau hoi 2 Ggi y tra Idi cau hdi 2 Hay bien luan (*). NIu k < - ^ , khdng cd diem M nao V2 thoa man; Neu k = -7=r thi M trung I; V2 Neu K > 2a thi M chay tren dudng trdn -f7>- • • Giai bai toan 3. - Cho HS Thao luan bai toan. - Van dung bai toan 1. - Kit qua: a 4 m '"a = a^+b^ 2 a +c 4 2 m^ = HOAT DONG 4 4. Dien tich tam giac a) Mtic dich: Giiip HS van dung cac dinh II vl dien tfch tam giic dl giai toan vl tam giac. b) Hudng thitc hien 18