Hình học 6 Vnen học kì I

t

E

C#mS I
gr. nr6u.

DIEM. DTTONG TIIANG
.*9A-*N--T[I4NG: TrA

ot]dxc

:.i

trixc.

oUdrvc

ruixc

DI QUA HAI or6la

MUC TIEU
Nhqn bitit dugc: eiem, duorg thing; di6m thu$c dunrig th6ng, di6m kh6ng'thu$c
dulng thang; dulng *tngdi qua hai di€m.

1. Thr.rc hiQn c5c hoqt dQng sau
a) Guan s*t,

-

Xem hinh

atBt$m xe6t

1.

Hinh

1

Em ndi vit ghi nhd : Ddu ch6m nho cua dAu brit (chi) trdn trang gidy,h1t c6t tr6n mflt
bdn (mat eiefl,..ld nhtng hinh 6nh ct:n diAm.


b) Dqc ki nQi dung sau

Vi du: O hinh

2 ta c6 ba di6m phdn biQt lA M, N, P.

c) LuyQn tqp, ghi vAo v&:

-

2.

Emvd (vdo vo) b6n diem b6t ki, dat t6n chring theo c6c chfi c6i ld A, B, C, D.
Em n6i;,,Trlnhinh c6 b6n di6m ld: tli6m A, dii5m B, ditlm C, di6m D".
Em vi6t:Trdnhinh c6 b6n <1i6m lir: A, B, C vd D.

Thrgc hiQn c5c hoqt dQng sau
a) Dgc vir

lim theo

-

Dung brit (chi) v4ch tr0n trang giSy theo m6p cua thu6c thing. Quan s6t n6t vC do dAu
birt tao ra.

-

Emn6ivdghinh6:

x

V6i bft vd thu6c thing ta vE dugc vpch thing. Vpch thing do dAu brit t?o ra tr6n
trang gi6y,hay ddng k6 tr€n trang gi6y,... cho ta hinh 6nh cua dudng thiing- Dudng
thing kh6ng bi si6i hqn vi hai ph{a.

*

Uleu di6n ducrng thing.
Ngudi ta thudng dung cht c6i thuirng, nhu d, b,...
CC Apt t6n cho duong thing (xem hinh 3).

Ta dtng v4ch thing

OO

Ilinh

3


b) Dgc ki nQi dung sau

c) LuyQn tfp, ghi vio vO

-

Xem hinh 5.
Cho bitit trong sd c6c tlitim M, N, di6m ndo thuQc hay kh6ng
thuQc ttudng thing a?

-

Di6nkihieu e hay Cthichhqpvdo 6tr6ng:

@

3. Thgc hiQn cic
a) Dgc vA

-

Nf a;UIa.

hoqt dQng sau

lim theo

Em vd (vdo vo) hai ditlm X, Y (phdn biQt). Sau d6 dtng

thu6c thing vd brit (chi) tl6 vE mQt dudng th6ag
hai tti6m X, Y 6y (xem hinh 6).

!ffiriil
Itffi*lEttr

Hinh 5

Em n6i vd ghi nha, Drdng thdng

ffii
=l
u

I
!

b) Dgc ki nQi dung sau

fr qua hai ifr.Om

ili

qua

Ilinh

6

X Y citn ituqc ggi ld itudnS thdng XY.


c) Luy$n t$p, ghi

v'mm or:cr

Xem hinh 8 vd di6n tu (hay sOl tt

i"t

hqp vdo ch6 ch6m (...):

-

O hinh 8 c6 ....... di6m 1d:....
di6m d6ng thoi thuQc hai dudng thing.

-

O hinh 8 c6....... tludng thing

li:

mi m5i

............

Hinh 8

HOAT DqNC LTJYEN TAP

.

#

.ffii

1.

,

:.:Yr]

..

Xem hinh 9 vi tr6 loi c5c

-

ciu h6i sau:

Di6m A thuQc nhirng duong thing ndo?
Di0m D kh6ng thuQc nhirng dudng thing ndo?
Nhirng dudng thing ndo di qua di6m C?

2. LuyQn tfp, ghi vdo v&

Hinh 9

a) VC (vdo vcr)

-

MQt ducrng thdng m;

Mgt di6m M kh6ng thuQc dudng thing m;
Mgt di6m N thuQc ducrng thing m.

b) Dlra vdo hinh vria v0 duoc trd loi c6c cdu h6i

-

C6 hay kh6ng nhirng di6m kh6c di6m N

mi

sau:

thuQc ducrng

thing m?

C6 hay kh6ng nhirng di6m khac tli6m M md kh6ng thuQc ducrng thing m?

3. Tri lli

cdu h6i

Hdy cho bi6t: Qua bdi ndy em dd hoc dugc nhirng ki6n thric ndo?

@


HOAT DqNG V,TN DUNG

Thqrc hdnh
tU6i ban g6p mQt to gi6y (tao thdnh ntip g6p), sau d6 trii phing to gi6y d6 ra, quan
nOp g6p c6 dugc. NCp g6p d6 girip em 1i6n tucrng dtln kitin thric gi vta hgc?

s6t

Quan s6t, tim hi6u

Quan

sht

bdu trdi d\m day sao vir lien tucmg d6n c6c di€m.

Quan s6t mQt sO bric tranh cdt. Qtatl6 hi6u thOm v6 vr€c: vdi cac di€m ta tao nAn cdc
hinh. N€u c6 th6, hdy dung brit ch5m ra mQt sO OiO* d6 tao ra (hay vO) mQt hinh
(ching h4n ph6c hop chin dung cira em).

Quan s6t (ho[c h6i ngudi 16n) dC hi6u vO c6ch mQt ngudi thg xdy dtng d0y d€ xdy
daqc cac hdng ggch. Qua t16 hi6u thOm vC tinh ch6t: Qua hai di€m xdc dinh duy
nhiit m\t dadng thdng.

HO&T OgruC,dM T$t, n*6 norrlC

LuyQn

tfp, ghi vio vo

VE (tr6n gi6y ho[c m6t d60

-

Mgt duong thing q;
MOt di6m P nim trOn ducrng thing q;

Mgt di6m T kh6ng thuQc ducrng thing q;
Dudng thing b di qua hai di6m P vd T.

Mgt di0m U kh6ng nim tr6n ducrng thing PT, d6ng thoi n6 khdng thuQc ducrng thing
q vd ducrng thing b kh6ng di qua di6m U.


2. Dgc th6m

Tim hiOu th6m (qua ngudi lon hay qua mang Internet) vd mdn hinh v6 tuy6n (TV) hay
mdn hinh m6y tinh xhchtay (Laptop), ee niOu th6m vA di€m dnh.

Thilyl figrr#*

mfi$n x$t vi* gtri

rfi$n kdr qu;i **gc fi*p c*a frpc sinft'

Rgre

$2. BA DIEM THANG HANG. DOAN THANG
MVC TIBU
NhAn biiit dugc: Ba di€m thing hing, ba tli6m kh6ng thing hdng; quan hQ gita ba
di6m thing hing; hai tlulng thing fiung nhau, hai dudmg thing cdt nhau, hai
tlu
th[ng song song; dopn thing.

gii5t c6ch vE: Ba di6m thing hing; dopn thing; hai dutmg thang cft nhau, hai
ducrng thing song solrg; doan thingcft dopn thdag, dopn thing cit dusng thing

HoAT o6HC KHCI O6ruC vA HiNH IHANH rurTTI IHUC

ffi##
1. Thr,rc hiQn c5c hogt dQng sau
m) &maru sl&t v*.t

-

l&m

th**

Xem hinh 10.
Dung thu6c thitg kir5m tra xem dudng thing YZ co di qua
di6m V kh6ng, dudng thing WX c6 di qua di6m V kh6ng?

)

x\z
w

\Y

\

Hinh 10


'

ll"'!+
r il.d*

i

n

ffik?sEF
!

;.#ilq*

iLrliff-r

k

h) Sqc kI nQi dung sau

I{hi ba diiSm citng thu6c mQt drong thang ta n6i chring thdng
Vi du: 6 hinh 11, ba di6m A, B, C thing hdng.
ffi

hdng. 'rii\'

Khi ba di€m kh6ng cilng thuQc mQt dadng thdngta n6i
chring khhng thdng hdng.

11

Vi du: 6 hinh l2,badi6m X, Y, Z k&6ng thSng hdng.
Trong ba di0m thing hang cd mQt vd chi m|t di€m
J

.-

7

. 1.;

.

1

t

nam gtaa hat dtem con lqt.

Khi d6, ta c6

":rr.

l.L-

xdY

thO n6i:

Ilinh

12

+ Hai didn A, C ndm citng phia dAt voi dilm B.
+ Hai didm B, C ndm cilng phia diii voi di€m A.
+ Hai di6m A, B niim khdc phia difi vai di€m C.
+ Didm'C niim gi&a hai di€m A, B.
- ___ ---":

i -"'"--

,;.E}6

k#

c) Luy$n t$p, ghi viio v&

-

Em n6i: O hinh 13 c6 ba di6m X, U, T kh6ng thing hing; ba di6m U, V, X thing
hhng, di6m X nim gifia hai di6m U vd V.

-

Xem hinh 13 vd cho bi6t:

T
o

+) c6c b0 ba di6m kh6ng thing hdng;
+) hai di6m nim cirng phia

AOI vOi

di6m V;

+) hai di6m nim kh6c phia

OOi vOl

di6m X.

U

x
Hinh

13

Fffi#

ffir't:

2.

.Y**

Thr,rc hiQn c6c hoqt dQng sau
a) Sqc vir linn theo

-

VC (vdo vcr) hai di6m X, Y (ph6n biQt). Dung thu6c
thing vi brit (chi) dC vE dopn thing XY (hinh 14).

34567

Ilinh

14


-

Emn6ivdghinh6:
+) Dogn thdng XY l^ hinh gdm crt diAm X, diAm Y vd
tiit cd ctic di6m nim gifra hai itiAmx, f (hinh 15).
+) Hai tli6m X, Y li hai tlfru mfit clfla tlo4n thnng XY.

x

Y

Hinh

15

b) Quan s6t, nhfln x6t, ghi nh&

A

B

' (c)

(b)

(a)

Hinh

16

- Quan sdt cbc hinh vE o hinh 16.
- Em n6i vd ghi nh6:

chr f:
Hai ducrng thing kh6ng tri,mg nhau cdn dugc ggi ld hai

duong

2B

thingphanbiet.Haiduongth5ngph6nbiQtho[cchic6mQt
di6m chung hoflc khdng c6 di6m chung

ndo.

Ar'

Hinh t7

Hinh 17 bi6u diSn: dadng thdng d ch doqn thdng AB.
Cdn hinh 18 bi6u di6n: dosn thdng MN ciit doqn thdng AB.

Em hdy vE hinh bi6u diSn

+) mQt tludng thing cit mQt dopn thing;
+) mQt t1o4n th&ng cat mQt ilo4n thing.

Hinh

18


d) tmy#m t$p,

-

gE-rI

v** v#

Em n6i: O hinh 19 c6

+) XW vd UV ld hai duong thing song song vdi nhau;
+) UT vd XW ld hai ducrng thing cit nhau;
+) TW vd TV ld hai ducrng thdng trung nhau;
+) ducrng thing TtJ cltdopn thSng XW;
+) dopn thing XW cit doan thing XU.

-

Hinh

19

Xem hinh 19 vd chi ra: hai duong thing c6t nhau; hai dudng thing trung nhau;
duong thing phdn biQt; ducrng thing c6t do4n thing; ilopn thing clt doqnthing.

HoAT noruc

lwtru rAp

#
1.

*) Em

-

vE vdo vo theo c6c diSn dpt sau:

Ba tlitim X, Y , Z thtnghdng vd di0m Y nim gita hai di6m

X

vit Z.

Ba ditim X, Z,rJ kJt}ng thing hdng.
Ba tlitim X, Y, T th6ng hdng vd di6m T nim gifia hai di6m X vd Y.

h) Dga vdo hinh vira v0 dugc cho bi6t:

-

cac b0 ba di6m

thing hdng;

cic b0 ba di6m kh6ng thing hdng;
J

.-

-.i
ili6m
nam gifta hai di6m khric;

,

hai di6m nim cung phia OOi vOi di€mZ;
hai di6m nim kh6c phia OOi vOi di6m Y.

*)VO b6n di6m M, N,P, Q, trong d6 chi c6 ba di6m M, N, P thing hdng.
- VO vd k6 t6n cdc do4n thing, c6 hai tlAu mrit trong s6 c6c <1i6m M, N, P, Q.

-

VC c6c tludng thing, mdi ducrng di qua hai trong sO c6c ditim M, N, P, Q. Khi d6, k6
tdn c6c ducrng thing phin bi6t.


2. ni6t ring T ld mQt di6m b6t ki cira do4n thing MN.

-

B?n An cho ring: Di€m

T

phdi trilng

Ban Binh khing dinh: Di€m
B?n Canh n6i: Ei€m

T

T

vcti di€m M.

phai tritng vcti di6m N.

phai ndm gitra hai di€m Mvd N.

Ban Dung n6i: Di€m T hojc tri.tng voi di€m M, hofic tritng vcti di€m N, hofic ndm gitta
hai di€m Mvd N.

Theo em, trong s6 c6c ban An, Binh, Cinh, Dung bpn n)o n6i chua tlirng? Gi6i thich tai
sao b4n Ay n6i chua dring.
3.

Trd loi cdu h6i
HEy cho bi6t: Qua bdi ndy em dd hoc duoc nhring ki6n thirc ndo?

Hoar DQNC vAN

DUNC

'1. Thgc hdnh
a) O6 bpn x6p dugc 5 viOn soi (hay vi6n bi) thdnh 2 hing, m6i hdng c6 dirng 3 viOn soi
(hay vi6n bi) thing hdng.
b) D6 b4n xtip dugc 9 vi6n soi (hay vi6n bi) thdnh 8 hirng, m6i heng c6 rlirng 3 vi6n soi
(hay vi6n bi) thing hdng.

2.

Quan s5t, tim hi6u

Quan

-

sht xung

quanh em vdchi ra hinh 6nh co 1i0n quan dtin:

cicdiOm thing hdng; di6m nim giira hai di6m kh6c;
dopn thing;

dudng thing song song, dudng thing cit nhau, dudng thing trung nhau; ducrng thing
phdn biQU

3.

ducrng

thing cit do4n thing; dopn thing cit do4n thing.

Trd choi "Thing hing".
Vt6i nh6m chuAn bi mQt s6 viOn soi (hay vi6n bi) vi k6 mQt s6 ducrng thing tr6n d6t @ay
td gi6y). D6n luqt ngudi choi s0 tung c6c vi6n soi l6n vung ddt da k6 c6c ducrng thing
t'
(hay trang gray c6 ddng k6), s6 vi6n soi cung thuQc mQt ddng k6 (hay thing hdng) ld s6
di6m nguditt6 c6. Sau mQt sO tuqt choi, ai c6 s6 di6m cao hcrn li ngudi thing cuQc.


HoAT oOmc

1.

LuyQn

dru tol, rrro nOruc

tfp, ghi vdo v&

*} Theo em trong cic

-

cdu sau d0y, cdu ndo thing? cdu ndo sai?

Hai duong thing song song ld hai tlulng thtngphdn biQt.
Hai tludng thdng cdt nhau ld hai dudng thingphdn biQt.
Hai dudng thing c6 di€m chung ld hai ducrng thingphdn biQt.

C

hi Xem hinh 20.

-

Tim di6m D trOn dulng thing m sao cho ba di6m C, A,
D thing hdng. Tim di6m E tr0n dudng thing n sao cho
ba tli6m B, A, E thing hdng.

Ve vd ggi tOn c5c ilo4n thing me hai dAu mrit

A
a

cria

B

Ilinh 20

chfng nim trong s6 c5c di6m: A, B, C, D, E.

Tim hi6u, dgc th6m
a) Tim hiOu th6m (qua ngudi 16n hoic Internet) v€ nhqt thqrc todn phdnhay nguyQt thqc
todn phdn(hinh 21). Qua d6 hi0u th6m vC hiqn tuqng thing hdng trong vu trg.

Ilinh 2l

b) Tim hi6u th6m (qua ngudi 16n) v0 c6ch dO mQt xs thu nglm ban trung dich. Qua d6
hiOu th6m vC ba di6m thing hdng trong kh6ng gian.
c) Quan s5t (hay h6i nguoi

cic

16n) de hi6u v6 c6ch ngudi thg

x6y dingddy dpi

dC

mep oba song song voi nhau.

Tttayieo gr;io refi$m :rdr va gfui rtf*$m kef q*l;i m*e f$p eara i*oe

€i

srrufa.

xdy dugc


$8. E0 oAt DO4N rH,ENc.
R.t2
TRLING DIEM CUA DOAN THANG

1.

cic hoqt d6ng
a) Dgc vi lim theo

Thr.rc hi6n

-

sau

Nhd lai xemtru6c t16y em d5 clo dO ddi rlopn thing nhu thti ndo?

Emn6ivdghinh6:
Od do dO ddi tlo4n thing AB (hinh 22), tadflt canh thu6c (c6 chia ttcrn vi) rli qua
hai tli6m A, B sao cho ttitim A trung v6i vpch sO 0, khi tI6 ni5u di6m B trung v6i

mQt vach (ching hpn vpch so to; thi ta n6i tloqn thing AB c6 dO ddi l0cm.

IDnh 22

@


b) Dgc kT nQi dung sau

Vi dp, vtri UV:3cm, PQ:5cm, RT:3cm, thi:
+ hai tloan thang IIV vd RT biing nhau $ay c6 ci,mg d0 ddi) vi ki hiQu ld w: RTi
+ dopn thing PQ ddi hon (hay cd d0 ddi lon hon) do4nthing UV vd ki hiQu H PQ > UV;
<
hay cdn n6i UV ngdn hon (hay c6 dO ddi nhd hon) PQ vd ki hiqu ld UV PQ.

+UV+PQ:3*5:8(cm)

c) LuyQn tfp, ghi

-

-

vio v&

Dirng thu6c do d0 ddi c6c tto4n thing: GH, HK, KL, LG,
GK, LH d hinh 23.

Tt d6, rli6n ki higu >,:

GH ........ HK; HK........GK; GL ........ HK; GK

Eo

t10

Hinh 23

hay < vdo ch6 ch6m (...) d6 c6 ktit qu6 tlirng: GH .....'..' LK;

"""' LH'

2. Thpc hiQn c6c hoqt dQng sau
a) Dgc vi lim theo
-

GH

MN

P

IDnh 24

ddi c5c ilo4n thing: MN, NP, MP & hinh 24'

+) Di6n dO dei c6c dopn thing vdo ch5 ch6m (...) : MN + NP

: ';",MP : ""' '

+) So s6nh MN + NP v6i MP. NCu nhQn x6t'

- vE ba ili€m thang hang A, B, C md di6m c nim gifia e

vd B. Do vd so sr{nh AC +

cB voi AB.


9) Dqc ki nQi dung sau

c) Luy,$n tfp, ghi vio vcr

-

Em

T 3cm U

n6i:6 hinh 25 c6 rli6m U nim gita

n6n TU + UV : TV. gi(it TU :

3cm,

hai
TV:

tt

L--------------------------J

6cm

6cm, suy ra

IJV:3cm.

Innh

So silnh TU vd UV.

d) Ogc ki ngi dung sau

e) Luygn

-

tfp, ghi vio v&

Do dO dni ci:r- cfuc tto4n thing SW, WJ, SJ, SF, FJ d hinh 27.
Tre loi cdc cdu h6i sau:

+) W c6 phai ld trung tti6m cua tloqn thing
+) F c6 phni

h

trung

c1ii5m

SJ hay

tfidng? Vi sao?

cria tloan thdng SJ hay kh6ng?

Vi

sao?

25

?cm


HOAT DONG LI.IYEN TAP

#

.:ilFi

1.

*] Dgc vd cho Uitit m5i ciu

sau day ld dring hay sai,

vi

sao?

- N6u M nim gif,a hai di6m A vd B thi M ld trung ditim cria do4n thing AB.
- Ntiu AM: MB thi M ld trung di,5m ctra do4n thing AB.
- Nifu AM + MB : AB thi M ld trung ditim cira dopn thing AB.
- N6u AM: MB vd AM + MB : AB thi M ld trung di6m cira dopn thing AB.
-

Ntiu

AM: MB : *
2

,f,i M ld trung di6m cua do4n thing AB.

- M5i do4n thing chi c6 mQt trung di6m.
- M6i diOm chi c6 th6 ld trung di6m cua mQt dopn thing.
- M vd N tuong rmg ld fung di6m ci.r. cdcdoAn th6ng AB vd CD thi M kh6ng thO trung vcri N.
*! ;1.* hinh 28.
ffiED

-

ei6t

BC:

DE. So s6nh d0 ddi hai dopn thing BE vd CD.

:

Bit5t BE CD vd A ld trung di6m cira do4n
diiSm cira do4n thdng BD kh6ng? Vi sao?

thing CE. Theo em, A c6 phii ld trung

2. Tri loi cdu hoi
Hdy cho bi6t: Qua

bii

ndy em d5 hqc dugc nhfing ki6n thric ndo?

HO&T IIqNC V+N DUN6

*"

" :.'
:@1,,

Er

1. Thr,rc hinh
1

Dung thu6c (c6 chia dcrn vi) OC do d0 ddi c6c
cAnh cia mflt bdn hgc thuQc nh6m cita em.
rcB

Hinh 28


h) So s6nh d0 ddi cria hai d6 vflt, nhu But chi vd Thuoc kd,... md em c6.
*) U6c lugng (theo bu6c ch6n ho[c theo vi6n g4chl6tn6n) chi6u ddi cira phdng hgc (hay
gian nhd) cira em.

2. Quan sdt, nhQn x6t
m] Quan s6t xung quanh em vd chi ra hinh dnh c6 1i6n quan d6n: nhtrng doqn th;ing biing
nhau; cac doan thdng ddi hon, ngdn hon; trung di€m doqn thdng.
kp}

So s6nh d0 ddi hai t16 vflt md em c6, ching han: so tlfia t10 c6 mQt d6i dei bing nhau.

*3 D6 ban:

-

Su dung sgi dey dC chia mQt v4t cimg (nhu thanh 96 hay mQt m6p bdn,...) thdnh hai
.).
phdn c6 d0 dei bSng nhau.

-

Mdn hinh ti vi c6 d4ng mQt hinh cht nhpt. Khi n6i ti vi 50 in-so thi ducrng ch6o cira
mdn hinh cua chi5c ti vi tl6 ddi khoing bao nhi0u cen-ti-met? (Bi6t ring mQt in-so
khoing 25,4 mi-li-mdt).
a?

HOAT I)QNG TIM TOl, MO RSNG

'.e.
rn . .fl"
..; #,1i
.k&#- {-

1.

r4

LuyQn

tfp, ghi vio vo

m) Theo em, c6c c6u sau tlAy dirng hay sai?

-

Ntiu A, M, B thing hdng thi AM + MB

*3)

Hinh 29 co

Vi

sao?

Hai tloqn thing c6 d0 ddi bing nhau thi bing nhau.

: AB.

N6u M c6ch rt6u A va B thi M ld trung ditim cira do4n thing AB.

BD:

l4cm;BC

: ED :

3cm vd A ld trung
Cho bitit dq dei cira doan thing CA.

A

Cho bii5t dq dei cira do4n thing BE.

2,

Ilinh

D
29

Tim hi6u, dgc th6m

Tim hi6u th6m (qua ngudi 16n hoflc
Internet)

a) Ve chr tqo oia cdn thdng biing (hay

cdn dia). Qua t16 hi6u th6m ,rd trurg
I

-.
cira do4n th[ng trong thgc ti0n.
di6m

Cdn thing

bing

Cin

tlTa


gitr thdng bdng
trAn day. Qua d6 hi6u th6m vd trung

fu) VC c6ch d6 m6t ngudi

di6m ctra tloan thing trong kh6ng gian.

#) VC c6ch do khoing c6ch (hay d6 dei)
trOn mflt dAt laga vdo thu6c chfi A, hay
thu6c ddy,...). Qua d6 hi6u th6m v0 c6ch
do chiriu ddi vi c6ng cp tto chiOu ddi
trong thgc ti6n.

Ttt6yl*A gi6ta nhan xed ya gft*

mdea*

ker

ryer;*

94. TrA. vE Do4N THX,Nc
tl

*

nr6r DO nAr

TIEU

gict c6c kh*i ni-€m: tia; hai tia tloi nhau; hai tia trung nhau; hai tia ph6n biQt.
gi6t cfch: v6rn$t tia, hai tia tl6i nhau, hai,tia trung nhau; ve doqn thing bi6t d6 dii; v6
' ,tryng ctidrq m$t tloan thdng; tia cit dogn thing ,tra c*tducrng thing.

HOAT oONG KH6I

1.

MU. C

fuge f$p f{da f?SC ssmfu"

o0luc v* nirun THANH KITN THUC

Thr,rc hiQn c5c hoqt d6ng sau

e] ffium* x*t w*

-

mha&n xe*t

Em n6i: O hinh 30 c6

0123456789
i
lla so

Tia gdc O

+) M6t tia s6;

no

+) MQt tia Pt;
+) C6c tia g6c O

Ntra tlucrng thing gdc O

li

Om vd On.

o

Hinh 30


Fn.i

E)'-;*

,tcT L:u""ftfr

#r.ii;i:{

t!;'ti..!

Vt6i Oicm fi6n dudmg thing chia dulng thing d6 thenh hai phAn. Vi du ditim O (o
hinh 30) chia duong thane mn thinh hai phAn ld Om vd On.

*

Hinh''g6m di6m A vi'm$t'phln ducrng thing bi
chia ra boi t1i6m A dugc gqi ld mdt tia g6c A
(hay con ggi li n*a itudng thdng g6c A).

Ta dung mOt vach thing
g6c tia

du-o.

Uieu diSn mQt tia,

c vE 16.

Vi du: Hinh 3l

*

AO

c6 c6c tia Ay,

Az, Av.

Hai tia chung g6c vd tpo thdnh m$t iludng thing
dugc ggi lir hai tia il6i nhau. Mdi di0m tr6n
dudng thlng ld g6c chung cira hai tia d6i nhau.

Vi du: Tr€n ducrng thing mn

15y mQt

Hinh

31

di6m O bat ki (hinh 30), c6 Om

vi On ld

hai tia dOi nhau.

Tia Az cdn ggi li tia
hai tia trilng nhau.

-

dB.

(hinh 32).
Hai tia Az vd AB ld

B

Ifinh

Hai tia khong trung nhau duoc ggi

li hai tia phin

32

biQt.

###
.1 -, ..

-

:

;":l i 'i ; I

,i'

;li:)

.r":, ij' :i

:l

Em noi: O hinh 33 co cdc tia gdc A ld Ax, Ay vd ld hai tia ddi nhau.

Hinh 33

-

bi6t: c6c tia g6c B; c6c tia d6i nhau; cic tia trung nhau; cdc tia
phdn bi6t; cdc tiakhdng d6i nhau.
Xem hinh 33

vdr cho

172.


d) Quan s*t

-

v* nh6rr x*t

Emn6ivdghinh6:

+) Ifinh 34 biAu didn ttogn thdng AB vd tia Ox cdt nhau.
+) Ifinh 35 bihu di6n itudng thdng mn vd tiaPt cdt nhsu.

Hinh 34

2.

Em hdy vE hinh bi6u diSn m6t tlopn thing
thing cit mQt tlo4n thing.

Hinh 35

cit mqt tia. VE hinh bi6u diSn mQt duong

Thr3c hiQn c6c hoqt dQng sau
a) Sge

-

v* l&n: the*

Em n6i, ldm theo vi ghi nh6: Dfit cgnh
thwbc (cd chia tton v!) theo tia Ox (hinh
j6) sao cho etiAm O tilng voi vgch 0. Tqa
itdu bfit (chi) theo mdp thrdc, kdo tb ilihm
O iIAn vgch 2, ggi thn ifiAm ryi vgch 2 ld M,
tu cd itoan

-

OM:2cm.

Itrnh 36

D6 ban kh6c (trong nh6m) theo c5ch tucrng tU vE dugc mQt do4n thing
tr6n mQt tia Hn.

HK: 7cm,

b) B+c v*r l*rm thea

-

Em n6i, ldm theo vd ghi nh6: Drtt compu
sao cho ctic mfii nhgn trilng voi cric ifrAm A
vd B (hinh 37). Gitr nguyAn compa ,ii d4t
sao cho mQt mfii nhgn cfta nd tring v6,i
tfihm C, mfri kiu thuQc tia Cx, cho ta diAm
D. Khi tili cri CD: AB.

-

Nhan xet Vdi compa ta cd th€ vd duqc tuAn
m\t tia m)t dosn thdng c6 dO ddi biing dQ
ddi cila m6t doan thiing cho traoc md
kh6ng cdn bi€t dO ddi cila chring.

C

Hinh 37

VE mQt do4n thing PQ. Ldm tuong tg nhu tr6n tlil vO dugc fiAniaYzmQtdo4n thing

UV:

PQ.


c) Dgc ki nQi dung sau

d) Luypn tfp, ghi

-

vio vcr
K

Em n6i: O hinh 39, tren tia Hx c6 HK < HL
n6n tli6m K nim gifia hai tli6m H vd L.
VC tia Ot. Tr0n tia Ot, vC c6c doan thSng

OM:

Ilinh 39
5cm vd

ON:

6cm;

+) Cho bi6t: Trong ba ttiOm O, M, N tti6m ndo nim gifla hai diOm cdn lpi?
+) VC tti6m T ld trung di6m cira ttopn thing ON.

Qt

]
\

1. a) Vo mQt ducmg thing uv vd mQt dii5m O e uv. L6y di6m M thuQc tia Ou. L5y diCm N
thuQc tia Ov. Xem hinh v0 d6 vd cho bitit:

-

citctiac6chungg6cM; cdctiadtiinhaug6cN; cbctiatrungnhau; cdctiaphdnbiQt.
trong ba di6m M, N, O di6m ndo nim gifia hai di6m cdn l4i?


b) TrOn tia Ox vE hai do4n thing OA : 3cm vlr OB : 6cm. VC tr6n tia Ox do4n thing
BC : AB, trong d5 di6m C kh6ng thuQc doan thing OB.
a) Xem hinh 40. Doc t6n:

-

nhirng tia cltdo4n thing BC;

-.-: nhfriig,dtt&rrg.

-':

nhtng tia

thing cft tia AB;

cdt ducrng thang DE.

b) VC do4n thdng AB : 7cm, r6i ve trung diOm M
cira tlopn thdng AB. N6i v6i b4n v6 c6ch md em vE
dugc trung di6m M ctra do4n thing AB.

.

.:, 1 ,

';

Hinh 40

,'r'

3. Tri loi c6u h6i
Hdy cho bitit: Qua bdi ndy em dd hgc dugc nhirng ki6n thric ndo?

Thr,rc hdrnh. Dtng compa (hay thudc chfr A) vd thu6c
thing d0 vC tr6n trang giSy (hay tr6n mflt d6l cac do4n thing
c6 ctng d0 dei.
2. Quan 35t xung quanh vd chi ra dugc nhimg hinh 6nh c6
1i0n quan d6n: tia; tia phdn bi€t; tia chung g6c; tia diSi nhau.

1.

LuyQn tQp, ghi

vio v&

-:,

-

,,.

'.

a) Trong c5c c6u sau ddy cdu nAo drlng, cdu ndo

-

sai? "

'"

Hai tia chung g6c ld hai'tia t16i nhau.
Di6m M nim gifra hai di6m A vd B thi cdctia AM, MB trung nhau.
Ntiu di6m M thuQc tia Ax thi Mx vd Ax ld hai tia trung nhau.


**] ThUc hi6n c6c hoat d6ng sau.

-

Ve trOn tia Qy do4n thing

QM: 6cm.

Ve trung di6m O ctra doan thing QM.

2. Tim hi6u, dgc th6m

Tim hi6u th6m (qua ngudi l6n hodc Internet)
a) VC tia sang vd img dung cua tia s5ng laze trong trinh diSn
nghQ thu4t.
*a)

VC c6ch do d9 ddi dopn thing tr6n mdt dat lAya vdo thu6c
cht A, hay thu6c xich,...). Qua d6 hiOu th6m vO mQt ung
dqrng cira do4n

thing bing nhau.

FFa#grc& grua* nft#m

gs. THUc HANI{

H*f v;* ghr

mfte$* kdle ryu;i

fuq* f$p eaia ftpe sfnfu.

rndxc cAv urixc

HANG. Do D0 DAI

MUC TIEU
Bii5t cdch gr6ng (ki6m ffa) ba c6y (hay cqc) thing hdng. giet c6ch do dQ diri tr6n

HOAT

S8N6

LUYEN

r+P

;F6

##H#

1.

D6

-

Xem hinh 41.

Hinh 4l

.,@,

mlt

ddt.


-

2.

D6 ban: Nguoi ta dd ldm thd ndo d0 x6p (hay dUng) duoc c6c cQt nhd (hay chc cgc tiOu)
thing hirng?

Th1rc hdnh xiSp theo hdng doc
a) Ghia nhdm
Lcrp tluqc chia thdnh c6c nh6m khoing
7-8 hgc sinh.
b) XSp

-

the* h*ng dpe

M6i nh6m thuc hdnh x6p theo mQt hdng
dgc (theo nghi thirc d6i).
Nh6m trucrng chinh d6n dO chcbantrong
nh6m dimg thing hdng (hinh 42).

Thay nhau ldm nh6m trucrng dO chinh
ddn c6c ban trong nh6m dimg thdnh

m6t hdng dgc, thing hdng.

-

Hinh 42

N6i v6i b4n vd c6ch kiOm tra sq thing hdng cira nh6m sau khi da dimg theo tlQi hinh
hdng doc.

thing hdng

Thr,rc hdnh tr6ng cdy (c5m cgc ti6u)

ai fruan s*t, nhfrn x*t

-

Hinh 43 bi6u diSn c5ch md nh6m ba em tr6ng (hay cim) dugc ba cdy (cgc ti6u) o c6c
vi tri A, B, C thing hdng.
THL|.

c HANHTRoNG

ru

cAyrnixc

nANc

ffiffi

-"A

Hinh 43

o


-

Emn6ivdghinh6:
OA

t6ng (hay ciim) ifu{c ba cgc fiAu Qi A, B, C thdng hdng ta ldm nhu sau:

+) Trmirc n& ciim ctic cgc ti\u (thdng ihbns
+) Tiiip theo, mQt bgn cdm cgc

dd| ryi ctic v! tri A
fiAu thdng itftng 6 v! tri C.
vdri mrtt

vd B.

+) Sau tt6, mQt bgn tt*ng 0 v! tr{ A ngiim vd ra hiQu ift bgn ttftng tgi v!
chinh suo cho cgc fiAu 0 A che liip cric cgc fiAu cd:m ryi B vd C.

tri

C

itiiu

b) Thlrc hdnh cf,rn cgc ti6u th$ng h&ng

-

ChuAn bi c6c cgc ti6u (dC cAm) vd ddy dgi (dC ki6m tra cgc duoc c6m thing dring so

v6i mqt ct6t).

-

Thgc hdnh tr6ng ba cdy (hay ba cgc ti6u) thing hdng (tr6n ddt,hay sdn trucrng).

cl Thr,rc hinh do khodng cich glilra hai di6mT tr$n mft ddt

'

Theo vi tri md nh6m

vla

chgn cdm 3 cgc ti6u A, B, C, hdy do c6c khoing cdch AC,

AB bing thudc (thu6c d6y, hoflc thu6c cht A, hoflc thu6c m6t,...).

-

Ghi ktft qui: AB

: ................m, BC: ................m;

i,; Thryc hdnh ,dm coc tiAu thiing hdng vrri hai tradng hqp:
AvdB; di€m C kh6ng 6 gitra hai di€m AvdB.

Chil

AC

:

................m.

di€m C o gitra hai di€m

m

q€E+

1
1

4. Tri lli

c6u h6i

Hdy cho bi6t: Qua bdi ndy em dd hoc dugc nhimg ki6n thitc ndo?

HOAT DQNC VAN DUNC

Quan s6t, tim hi6u
a) Quan

sf/-

,:
thang nang.

xung quanh em vd chirahinh 6nh c6 1i6n quan d6n nhftng cdy (hay c7c fiAu)

b) U6c lugng, sau do dung thudc thing do vlr cho bi6t chu vi ctra

lcrp hgc.


2. D6

-

DO bpn: X6p

duoc 10 vi6n soi (hay vi6n bi) thdnh 5 hdng, m5i heng c6 dirng 4 vi6n soi

(hay vi6n bi) thing hdng.

D6 b4n: Xi5p dugc 16 vi6n soi (hay vi6n bi) thdnh 10 hdng, m5i heng c6 dring 4 viOn
soi (hay vi6n bi) thing hdng.

-

HoAT D0NG TiM Tol, rvl*

n0nc

t?) fl,,,i:

.,r.'*#rl

Tim hi6u, dgc th6m
Tim hi6u th6m (qua ngudi l6n hoflc Internet)
m3

VO c6ch d6 ngudi thg xay dugc c6c hdng cQt nhd

*l:] VO

thing dirng vd thing hdng.

ngii* thiing vd do dO ddi trqrc tiep trong trdc dia.

Ffe;#yle# grf;** mtu$m xsif s{* gftr nl.*$rn fr*i5* ryara* P}S# S#S

@

*#e $rps seet$t"