Thiết kế bài giảng hình học 10 nâng cao (tập 2) phần 1

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


- Niu cdc cong thifc.
- Thuc hiin ^ ^ 7.
- Thifc Men 4 ^ 8.
- Thuc Men - ^ 9.
- Thuc Men 4 ^ 10.
c) Qud trinh thifc hien
• Neu cac cdng thiic
S - —ah^

•

— bhu - ~cM

(1)

— absinC = —acs'mB = —i»csinA ;
2

2
2
S=

(2)

abc

(3)

4R

S = pr :

(4)

S = ylp(p - a)(p - b)(p - c).

(5)

(Cdng thiic (5) ggi la cdng thdc He-rong).
• Thuc hien ^ C 7
Cho HS thao luan dl bai.
- TReo hinh 52 len bang.
- Sii dung cdng thirc
A

B

H

A

H
Hinh 52

B


GV thu'c hien thao tac nay trong 2'
Hoat ddng ciia giao vien
Cau hdi 1

Hoat ddng ciia hoc sinh
Ggi y tra Idi cau hdi 1

Hay tfnh h^ trong tam giac AHB

h^ = csinB

theo canh c va gdc B
Cau hoi 2

Ggi y tra Idi cau hdi 2

Thay vao cdng thiic 5 = -ah^ de
dugc cdng thiic (2)

S = —ali^ = —acsinB
1

"
1

•Thuc hien S ^ 8.
GV thu'c hien thao tac nay trong 2'
Hoat ddng cua giao vien
Cau hdi 1

Hoat ddng ciia hoc sinh
Ggi y tra Idi cau hdi 1

Hay tfnh sinC tu' dinh li sin
Cau hdi 2

sin C = — .
IR

Ggi y tra Idi cau hdi 2
Thay vao cdng thiic S = - ab sin C,
1
abc
2
S = —absmC =
de dugc cdng thirc (3)
2
AR

• Thuc hien ^

9 (h. 53)

Hinh 53

20


GV thu'c hien thao tac nay trong 2'
Hoat ddng cua hoc sinh

Hoat ddng ciia giao vien

Ggi y tra ldi cau hdi 1

Cau hdi 1
Hay tfnh dien tich cac tam giac
OBC, OCA, OAB.
Cau hdi 2

"^AAOS = r ^ ^ - ' ' 5

^^AOC=l:^^•'"•>

=~CB.r

^ACOB

Hay ap dung cdng thii'c (1) dl suy
Ggi y tra Idi cau hdi 2
ra cdng thiic (4).
S^-.r(CB

+ CA + AB) = pr.

• Thuc hien ^ ^ 10
GV thu'c hien thao tac nay trong 2'
Hoat ddng ciia giao vien

Hoat ddng cua hge sinh
Ggi y tra Idi cau hdi 1

Cau hdi 1

Hay tinh dien tich tam giac cd 3 S=6.
canh 3, 4, 5
Ggi y tra Idi cau hdi 2
Cau hdi 2
S= 84.
Hay tinh dien tfch tam giac cd 3
canh 13, 14,15 .
Cau hdi 3

Ggi y tra Idi cau hdi 3

Hay tinh dien tfch tam giac cd 3
S=1170.
canh 51, 52, 53 .

HOAT DONG 5
5. Giai tam giac va iing dung thue te
a) Mxic dich: Giiip HS van dung cac dinh li de giai toan vl tam giac.

21


b) Hudng thitc Men
- Thuc Men cdc vi du td 5 de'n 9
c) Qud trinh thuc Men
• Thuc hien vf du 5
- Cho HS thdo ludn bdi todn
- Vehinh 54

Hinh 54
»

Day la bai toan thuc te, GV hudng din hge sinh lam bai theo cac budc sau diy:
- Tinh gdc A;
- Ap dung dinh li ham sd sin, tfnh cac canh b va c.
- Chii y : nen dung may tfnh bd tdi de tfnh kit qua gin diing.
Kit qua
.
a.sinB
17,4.sin44''30'
,^^
a.sinC
17,4.sin64''
b=
=
% 12,9 c = —•—— =
sin A
sin71''30'
sin A

sin7l''30'

,^^
* 16,5.

• Thuc hien vi du 6
- Cho HS thao luan de bai.
- Ve hinh 55

Hinh 55

Diy la bai toan thuc tl, GV hudng din hge sinh lam bai theo cac budc sau day:
- Tinh canh c bing each ap dung dinh li ham sd cdsin;
- Ap dung dinh li ham sd cdsin, tfnh gdc A; tit dd suy ra gdc B.
22


- Chu y : nen diing miy tfnh bd tiii de tinh kit qua gin diing.
Kit qua
B « 180° - (101°2' + 47°20') = 31°38'.
• Thuc hien vf du 7.

A,^

- Cho HS thao luan dl bai.

J-^^'^^

- Ve hinh 56

5-==—

^ \

=—

—^C

Hinh 56

Day la bai toan thuc te, GV hudng din hge sinh lam bai theo cac budc sau day:
- Tinh gdc A dua vao dinh II ham sd cdsin;
- Ap dung dinh If ham sd sin, tinh cac gdc B va C.
- Chii y : nen diing may tfnh bd tiii dl tfnh kit qua gin diing.
Ket qud.
B ~ 28°38' ; C «180° - (117°49' + 28°38') = 33°33'.
• Thuc hien vi du 8
- Cho HS thao luan dl bai.
- Treo hinh 57.
A

1^''^°%

t
%

TC

B

Hinh 57

Day la bai toin thuc tl, GV hudng din bgc sinh lam bai theo cac budc sau diy;
- Tinh canh a dua vao dinh Ii ham so cdsin;
- Chii y : nen diing may tfnh bd tiii de tinh kit qua gin diing.
Kit qua:

a ^ 11 (km).