Tit: 20Tn bi: H THC LNG TRONG TAM GIC.I, Mc tiu bi dy.1, V kin thc:- Hiu r v nm chc nh l c sin, nh l sin trong tam gic cng h qu ca nh l.2, V k nng:- Vn dng l c sin, nh l sin trong tam gic tnh cc cnh,cc gc cha bit ca mt tam gic trong cc trng hp.- Bc u bit vn dng vo gii cc bi ton thc t.3, V t duy:- Pht trin kh nng t duy logic. - Hiu c nh l biu th mi quan h gia cc i lng cnh v gc trong tam gic, t tnh c cc yu t cn li.4, V thi :- Nghim tc, t gic, tch cc trong hc tp.- Ham hc, cn c v chnh xc, l vic c khoa hc.- Bit vn dng vo gii cc bi ton thc t.II, Chun b phng tin dy hc1, Thc tin:- HS c kin thc v h thc lng trong tam gic vung.2, Phng tin:a. Gio vin: - Gio n, SGK, SGV, ...- Hnh v gi m yu cu cn c l c sin trong tam gic.b. Hc sinh: - Kin thc v h thc lng trong tam gic vung.- SGK, v ghi, dng hc tp, my tnh Casio fx 500A hoc fx 500MS..3, Phng php:III, Tin trnh bi dy v cc hot ng.A, Cc hot ng dy hc:HOT NG 1:Kim tra bi c:HOT NG 2:Dy:nh l c sin trong tam gic.HOT NG 3:Cng c nidungnh lv p dng.HOT NG 4:Hng dn hc sinh s dng MTBT tnh cc GTLG,tra gc khi bit GTLG ca gc.HOT NG 5:Hng dn hc sinh hc nh:B, Tin trnh bi dy:HOT NG 1: (5).1, Kim tra bi c: Hot ng ca GV Hot ng ca HSCu hi 1: Pht biu nh l Pythago trong tam gic vung.p dng: Cho tam gic vung ABC (A=900) bit AB = 4m, 3C = 3m. Tnh di cnh huyn BC?.Cu hi 2: Cho tam gic vung ABC (A=900). Tnh ( )2? AB AC uuur uuur.p n 1: Trong tam gic vung ABC vi A=900) Ta c: AB2 + AC2 = BC2.p dng: Ta c: BC2= AB2 + AC2= 25 nn BC = 5.p n 2: Ta c: 2 222 22 2( ) 2. .2 . . 90AB AC AB AB AC ACAB AC AB AC cosAB AC + + +ouuur uuur uuur uuur uuur uuur2, Dy bi mi:HOT NG 2: (22).1. NH L C SIN TRONG TAM GIC.Hot ng ca GV Hot ng ca HS?. Trong tam gic ABC s o ca gc gia hai vc t( , ) AB ACuuur uuur l s o ca gc no?.?. Tnh ( )2? AB AC uuur uuur?. Ta bit( )BC AB AC uuur uuur uuur, Vy BC2 s c tnh theo cng thc no? Kt lun: Nh vy chng ta c L s o ca gc A.Ta c: ( )2 222 22 2( ) 2. .2 . . ,2 . .cos .AB AC AB AB AC ACAB AC AB AC cos AB ACAB AC AB AC A + + + uuur uuur uuur uuur uuur uuuruuur uuurTa c:2 2 22 . .cos . BC AB AC AB AC A + cng thc tnh bnh phng dica mt cnh khi bit di hai cnh kia v gc xen gia chng. Chng ta gi cng thc ny l:nh l c sin trong tam gic.Yu cu HS pht biu nh l c sin trong tam gic.GV pht biu chnh xc nh l bng li, Ghi ND nh l trn bng.?. T L, Nu ta mun tnh di ca mt cnh trong tam gic th cn bit nhng yu t no??. Nu A 90 o ta c cng thc no??. T L c sin vit cng thc tnh:cos , cos , cos theo ,? , A B C a b cnh l: HS suy ngh v tr li.NuA 90 o ta c cng thc2 2 2 (DL Pythago) BC AB AC +HOT NG 3: (10).3, Cng c ton bi:CNG C NIDUNGNH LV P DNG.Hot ng ca GV Hot ng ca HSPhn lp hc ra 4 nhm (theo tng t).Giao BT cho cc nhm:Nhn nhim v.Tm hiu bi, cch gii.Thc hin gii v ca i din bo co cho nhm ca mnh.Cc nhm cn li nghe bo co ca cc nhm khc cho kin v xut PP gii khc ( Nu c).Trong tam gic ABC, vi , , AB c BC a CA b , ta c:2 2 22 2 22 2 22. . .cos2. . .cos2. . .cosa b c b c Ab c a c a Bc a b a b C + + + 2 2 22 2 22 2 2cos2cos2cos2b c aAbcc a bBcaa b cCab+++Nhm 1,3:Bi 1: Cho tam gic ABC c:60 A o,AB = 40 (km)v AC = 30 (km).Tnh AC = ?.Nhm 2,4:Bi 2: Cc cnh ca tam gic ABC l:7, 24, 23 a b c .Tnh gc A = ?.Li gii.Bi 1: p dng nh l c sin vo tam gic ABC.Ta c: 2 2 22 . .cos . BC AB AC AB AC A + Nn: 230 40 2.30.40.cos 60900 1600 1200 1300.1300 10. 13aa + + oBi 2: p dng h qu ca nh l c sin vo tam gic ABC. Ta c: 2 2 2 2 2 224 23 7cos2 2.24.23cos 0.9565.b c aAbcA+ + Suy ra: 0 'A 16 58 HOT NG 4:(6) HNG DN HS S DNG MTBT CASIO.Hot ng ca GV Hot ng ca HSHng dn:1. Tnh cc GTLG ca mt gc:2. Tra gc bit GTLG ca gc:Ch nghe, hiu.Thc hnh theo hng dn ca GV.p dng:a. Tnh cos 75037=?. b. Tm : bit cos = 0.7518HOT NG 5: (2).4, Hng dn hc sinh hc nh:- Yu cu HS v nh n bi c: Nm vng ND L, h qu v ngha thc tin. Xem li cc Bi tp gii.- Lm cc BT: 15, 16, 17, 18 Trang 64, 65 SGK HH10.- c trc bi mi: Phn 2+3 Trang 55 58 SGK HH10.Tit: 21Tn bi: H THC LNG TRONG TAM GIC (TIP).I, Mc tiu bi dy.1, V kin thc:- Hiu r v nm chc nh l sin trong tam gic v cng thc trung tuyn.2, V k nng:- Vn dng l c sin, nh l sin, cng thc trung tuyn trong tam gic tnh cc cnh, cc gc cha bit ca mt tam gic trong cc trng hp.- Bc u bit vn dng vo gii cc bi ton thc t.3, V t duy:- Pht trin kh nng t duy logic. 4, V thi :- Nghim tc, t gic, tch cc trong hc tp.- Ham hc, cn c v chnh xc, l vic c khoa hc.II, Chun b phng tin dy hc1, Thc tin:2, Phng tin:a. Gio vin: - Gio n, SGK, SGV, ...b. Hc sinh: - Kin thc c lin quan.- SGK, v ghi, dng hc tp.3, Phng php:III, Tin trnh bi dy v cc hot ng.A, Cc hot ng dy hc:HOT NG 1: Kim tra bi c.HOT NG 2: Dy nh l sinHOT NG 3: V d thc t vn dng nh l sin trong tam gic.HOT NG 4: Cng thc tnh di ng trung tuyn.HOT NG 5: V d p dngHOT NG 6: Cng c bi dy.B, Tin trnh bi dy:HOT NG 1: (3)1, Kim tra bi c:Hot ng ca GV Hot ng ca HSCu hi:Pht biu ND nh l c sin v h qu.Tr li:nh l:Trong tam gic ABC, vi , , AB c BC a CA b , ta c:2 2 22 2 22 2 22. . .cos2. . .cos2. . .cosa b c b c Ab c a c a Bc a b a b C + + + H qu: Trong tam gic ABC, vi , , AB c BC a CA b , ta c:2 2 22 2 22 2 2cos2cos2cos2b c aAbcc a bBcaa b cCab+++2, Dy bi mi:HOT NG 2:2. NH L SIN TRONG TAM GIC.Hot ng ca GV Hot ng ca HSNu bi ton.Yu cu HS thc hin.Cho tam gic ABC, vi , , AB c BC a CA b ni tip ng trn (O;R).Hy tnh a, b, c theo R v A, B, C.HD HD xt hai trng hp: A 90 & A 90 . o o?. Nu ta k ng knh BA ca ng trn, Em c nhn xt g v s o cahai gc A v A?? Vy: sin sin ' A A ?.Nhn nhim v.Tm hiu bi, cch gii.Li giiTrng hp:A 90 o.Ta c a=2R.Vy: a= 2R.sinA b= 2R.sinB c= 2R.sinCTrng hp:A 90 o.Trong tam gic vung ABC ta c kt qu no?2 .sin ' 2 .sin 2 .sin .BC R A R Aa R A | ` . ,Bng cch tng t khi ta k cc ng knh ca ng trn t cc nh A v C ta c cc kt qu no?Nh vy: Nu tam gic ABC, vi , , AB c BC a CA b ni tip ng trn (O;R), Th ta lun c:2 .sin . a R A 2 .sin . b R B 2 .sin . c R C y chnh l kt qu ca nh l sin trong tam gic.Cho HS pht biu L.GV chnh xc v ghi bng.K ng knh BA ca (O;R). Ta c:sin sin ' A A .Trong tam gic vung ABC ta c:2 .sin ' 2 .sin2 .sin .BC R A R Aa R A Tng t ta c:2 .sin . b R B v2 .sin . c R C HOT NG 3: V D THC T VN DNG NH L SIN TRONG TAM GIC.V d 3: T hai v tr A v B ca mt to nh ngi ta quan st nh C ca ngn ni (Hnh 49- SGK HH10 trang 56). Bit rng cao AB = 70m,phng nhn AC to vi mt phng ngang mt gc 300,phng nhn BC to vi mt phng ngang mt gc 15030. Hi ngn ni cao bao nhiu so vi mt t. Hot ng ca GV Hot ng ca HSNu bi ton, treo hnh v.Yu cu HS thc hin.?. Hy xc nh s o ca cc gc trong tam gic ABC?.Nhn nhim v, quan st hnh v.Tm hiu bi, cch gii.Li giiT gi thit, ta suy ra tam gic ABC c:60 , 105 30', 70.180 ( ) 14 30'.CAB ABC cC A B + o oo onh l:Vi mi tam gic ABC, Ta c: 2 .sin sin sina b cRA B C Trong R l bn knh ca ng trn ngoi tip tam gic ABC.Theo nh l sin ta c ta c c iu g?.Vy ngn ni cao bao nhiu so vi mt t?.Theo nh l sin ta c:sin,sin sin sinb c c Bhay bB C C Do : 70.sin105 30'269, 4( )sin14 30'AC b m ooHOT NG 4:3. TNG BNH PHNG HAI CNH V DI NG TRUNG TUYN.Hot ng ca GV Hot ng ca HSNu bi ton 1.Cho tam gic ABC, gi , ,a b cm m ml di cc ng trung tuyn ln lt tng ng vi cc cnh , , AB c BC a CA b Chng minh cc cng thc sau y,Gi l cng thc trung tuyn.2 2 222 4ab c am+ ; 2 2 222 4ba c bm+ 2 2 222 4cb a cm+ HD v Yu cu HS thc hin.Yu cu HS v nh chng minh cc cng thc cn li.Nhn nhim v.Tm hiu bi, cch gii.Chng minh:Ta c:( )( )2 2 22 2 2( );( )=2 .1=2 . 2AB AM MB AC AM MCAB AM MB AM MBAC AM MC AM MC + + + ++ +uuur uuuur uuur uuur uuuur uuuruuuur uuuruuuur uuurCng (1) Vi (2) theo v, ta c:22 2 22 2 22+ = 2 22+2 4BCAB AC AMAB AC BCAM| ` + . , Hay 2 2 222 4ab c am+ Chng minh tng t ta c c cc cng thc cn li.HOT NG 5: V D P DNG Hot ng ca GV Hot ng ca HSNu bi ton 2.Cho hai im phn bit P v Q. Tm tp hp cc im M sao cho 2 2 2MP MQ k + trong k l mt s cho trc.Nhn nhim v.Tm hiu bi, cch gii.HS thc hin gii.HD gii ti lp, GV nhn xt nh gi.HOT NG 6:3, Cng c ton bi:- Nhc li ni dung L Sin, cng thc tnh di trung tuyn v PP vn dng.- Cng c cho HS PP gii bi ton tp hp im.4, Hng dn hc sinh hc nh:- n bi c.- Gii cc bi tp tng ng trong SGK.Tit: 23Tn bi: H THC LNG TRONG TAM GIC (TIP).I, Mc tiu bi dy.1, V kin thc:- 2, V k nng:- 3, V t duy:- Pht trin kh nng t duy logic. 4, V thi :- Nghim tc, t gic, tch cc trong hc tp.- Ham hc, cn c v chnh xc, l vic c khoa hc.II, Chun b phng tin dy hc1, Thc tin:- 2, Phng tin:a. Gio vin: - Gio n, SGK, SGV, ...b. Hc sinh: - Kin thc c lin quan.- SGK, v ghi, dng hc tp.3, Phng php:III, Tin trnh bi dy v cc hot ng.A, Cc hot ng dy hc:HOT NG 1:HOT NG 2:HOT NG 3:HOT NG 4:B, Tin trnh bi dy:HOT NG 1: (3)1, Kim tra bi c:Hot ng ca GV Hot ng ca HS2, Dy bi mi:HOT NG 2:2. NG L SIN TRONG TAM GIC.Hot ng ca GV Hot ng ca HSHOT NG 3: Hot ng ca GV Hot ng ca HSHOT NG 4:3. TNG BNH PHNG HAI CNH V DI NG TRUNG TUYN.Hot ng ca GV Hot ng ca HSHOT NG 5:Hot ng ca GV Hot ng ca HS3, Cng c ton bi:HOT NG 6:4, Hng dn hc sinh hc nh:Tit: 25Tn bi: N TP HC K I.I, Mc tiu bi dy.1, V kin thc:- Vc t v cc php ton v vc t.- H trc to - to trn h trc to .- Tch v hng v p dng.- nh l C sin v nh l Sin .2, V k nng:- Vn dng kin thc l thuyt c bn gii ton.3, V t duy:- Pht trin kh nng t duy logic. 4, V thi :- Nghim tc, t gic, tch cc trong hc tp.- Ham hc, cn c v chnh xc, l vic c khoa hc.II, Chun b phng tin dy hc1, Thc tin:- Kin thc hc trong KH 1.2, Phng tin:a. Gio vin: - Gio n, SGK, SGV, ...b. Hc sinh: - Kin thc c lin quan.- SGK, v ghi, dng hc tp.3, Phng php:III, Tin trnh bi dy v cc hot ng.A, Cc hot ng dy hc:HOT NG 1+2: n tp v vc t.HOT NG 3+4: H trc to - to trn h trc to .HOT NG 5: Cng c bi dyB, Tin trnh bi dy:1, Kim tra bi c.2, Dy bi mi:HOT NG 1 (12): n tp v vc t.Hot ng ca GV Hot ng ca HSBi 2. Gi G l trng tm ca tam gic ABC. ly trn ba cnhBC, CA, AB ba im tng ngA1, B1 , C1 sao cho:1 1 11 1 1AC BA CBk (k 1)C B A C B A . Chng minh rng G cng l trng tm tam gic A1B1 C1. BCAC1A1B1MGG1Gi tr liGi G1 l trng tm tam gicA1B1 C1. ta chng minhG v G1 trng nhau hay chng minh cho1BG BG uuur uuuurtBA a; BC b uuur ruuur rTa i tnh : BGuuur ( ) ( )2 2 1 1BG BM a b a b3 3 2 3 ] + + ] ]uuur uuur r r r r1 1 1 1BG BA A G +uuuur uuuur uuuuur m ( )1 1 1 1 1 11 1 1 11 1 1 1 1 11A G A C A B3A C BC BA (1 k)a kbA B A C C B (1 k) b k(a b) + + + + uuuuur uuuur uuuuruuuur uuuur uuuur r ruuuur uuuur uuuur r r r( ) ( )( )( )1 11 1A G 1 k a k b 1 k b k a b1 1a (1 3k) b a b3 3BG BG G G ] + + ] ] + + ] uuuuur r r r r rr r r ruuur uuuurHOT NG 2 (7): HOT NG 3: (15)BI TP 14 (SGK HH 10 T52).Trong mt phng to cho tam gic ABCc cc nh A(-4;1), B(2;4), C(2;-2).a. Tnh chu vi v din tch ca tam gic ABC.b. Tm to trng tm G, trc tm H v tm ng trn ngoitip I ca tam gic ABC, Hy kim tra tnh thng hng ca ba im G, H, I.Hot ng ca GV Hot ng ca HSGiao bi tp cho HS.Treo hnh v sn.Phn tch bi gip HS tm c PP gii BT.Yu cu HS gii phn a, .? Nu H l trc tm ca tam gic, khi ta phi c k no? Yu cu HS thc hin, GV gim st.Nhn bi, tm hiu yu cu bi v xc nh PP gii.Thc hin gii BT.Li giia. HS t gii.b. To trng tm G. G(0;1) Gi H l trc tm tam gic, khi ta phi c: ( ). 0 *. 0HA BC HA BCHB ACHB AC ' ' uuur uuuruuur uuurGi s H(x;y) ta c: Hot ng ca GV Hot ng ca HSBi 4. Cho t gic ABCD.1. Xc nh im O sao cho OB 4 OC 2 OD. + uuur uuur uuur2. Tm cc im M tho mn h thc:MB 4 MC 2 MD | 3 MA| + uuur uuur uuuur uuuurABCDIGEO(d)HGi tr li ( )( )OB 4 OC 2 OD.OB 4OB 4BC 2OB 2BD3OB 2 BD BC 2BC3OB 2CD 2BC3OB 2 CD CB3OB 4CIOB CI+ + + + + uuur uuur uuuruuur uuur uuur uuur uuuruuur uuur uuur uuuruuur uuur uuuruuur uuur uuuruuur uuruuur uur(V i I l trung im ca BD)4 =3Vy O l nh th t ca hnh bnh hnh BIEO viOB CIuuur uur4 =3? Nu I ltm ng trn ngoi tip tam gic, khi ta phi c k no? Yu cu HS thc hin, GV gim st.?. Vi ba im G, H, I tm c, bng cch no ta chng t c chng thng hng? ( ) ( )( ) ( )4; 1 , 2; 40; 6 , 6; 3AH x y BH x yBC AC+ uuur uuuruuur uuurThay vo (*) ta c h pt: 11 022 01y xx yy ' ' vy 1;12H| ` . ,. Gi I ltm ng trn ngoi tip tam gic, khi ta c:( ) **IA IBIB IC'Gi s I(x; y) ta c: (**)( ) ( ) ( ) ( )( ) ( ) ( ) ( )2 2 2 22 2 2 24 1 2 42 4 2 2x y x yx y x y+ + + ' + + +141xy ' vy 1,14I| ` . ,Ta c 1 1;0 , ;02 4GH GI| ` | ` . , . ,uuur uurDo2 GH GI uuur uur nn ba im G, H, I thng hng. HOT NG 4: (8)V d 2:Trong mp to Oxy cho hai im M(-2;2) v N(4;1).a. Tm trn trc Ox im P cch u hai im M v N.b. Tnh c sin ca gc MON.Hot ng ca GV Hot ng ca HSGiao yu cu bi ton cho HS.? ViP Ox to ca P c xc nh nh th no? ?. Tnh cc khong cch MP, NP??. Vy MP=NP khi p tho mn k no?? Vy p= ?, To ca P ?.Tm hiu yu cu bi ton.Thc hin gii:Li giia. V P thuc Ox nn P c to (p;0),Khi :?. Nhc li cng thc tnh gc gia hai vc t?, p dng. ( ) ( )2 22 22 22 2 4 1312 9 .4MP NP MP NPp pp p + + + Vy 3;04P| ` . ,.b. Ta c( ) ( ) 2; 2 , 4;1 OM ON uuuur uuur. Vy:cos cos( , )2.4 2.1 38. 17 34MON OM ON + uuuur uuurHOT NG 6: (2)3, Cng c ton bi:- Nhc li cho HS nm vng cc PP gii bi tp.4, Hng dn hc sinh hc nh:- Chun b tt cho hi kim tra HK 1.