— /
- Trong mdt tam gidc, 3 trung tuyen ddng quy tai trpng tam G, cdch dinh
2I?> mdi trung tuyen
- Trong tam gidc 3 dudng cao ddng quy tai 0 (gpi la true tam)
- Mdt sd ket qua trong tam gidc
vudng
a^ = b^+c^
^ - ^ + —
h^ b" c
cos'« + cos P = '^
{a;P la gdc giira cac canh vdi canh
huyen)
Tir dien
•
- Sd mat phang tao thdnh Id 4 -Dinh
-Mat
-Gdc nhi dien giira hai mat - Dien tieh mat
- The tich tii dien
- Trong mdt tir dien, 4 trung tuyen ddng
quy tai trpng tam G, each dinh VA mdi
trung tuyen
- Trong tir dien 4 dudng cao khdng ddng
quy
- Mdt so kit qud trong tir dien cd gdc tam dien 3 mat vudng
S'(ABC)=S'(OAC)+S^(OAB) +S'(OBC)
1 1 1 1
— 1 1
OH' 0/ OB' oc'
cos'«-^cos'/^ + cosV = i
{a\P\y Id gdc giira cdc mat ben vdi mat
huyen)
Vl du2: Mdt so bai toan cd tac dung bdi dudng, phat trien kha nang so sanh va
tuong tu hda cua ngudi hgc trong hoat dgng giai toan
BaU. Cho hinh chdp S.ABCD co day la hinh chir nhat. Chirng minh rang
" 2 + cP' ' = <:R '+ SD • ^^^ ^^^ ^°^" ^^^^ ^^ ^^^^ ^^ "^^ P^^' ^° "^^^ ^^°
^ -* —*
2SO^^ OA'^'^ OC^ Id hodn todn cd the viet dupe ve phdi nhu sau:
2SO^ "*" OB^ '^ OD^ ^^ ^^ ^^ ^^^ ^^^ ^^ dmg tim ra hudng gidi quyet Bdi 2: Cho tir dien ABCD vd mdt dilm M ndm trong tam gidc BCD
a. Dung dudng thang qua M song song vdi hai mat phang (ABC ) vd (ABD).
Gid su dudng nay cat mat phang (ACD) tai B'. CM rdng AB', BM vd CD
ddng quy
b Chung minh ^ = ^ ^ ( ^ ^ ^
^ BA dt{BCD)
c. Tuomg tu, dudng thang song song vdi hai mat phang (ACB) vd (ACD) ke tir M eat (ABD) tai C vd dudng thang song song vdi hai mat phang (ADC) vd
(ADB) ke tir M cdt (ABC) tai D'. Chimg minh rdng ^ + ^ + ^ ^ 1
fS/i y^A. LJ/i
Ldi gidi y b la co sd. Id tien de cho viec gidi quyet y c. Tuy nhien.,hpe
sinh khdng thi sir dung binh ve de viet d\xqz cdc ty so-—-;-—- md phdi dua
tren kit qud da chimg minh dupe ciia y b ciing vdi thao tdc tu duy so sdnh,
, . f , X ^ MC dt(MBD) MD' dt(MBC) ^ . , '- A^ A - u
tirong tu mm co the duoc — = - ^ ; ^ = ^ ^ • Ch. can den day hpc
sinh dl dang giai quyet dugc bai toan
Vi du3: Mgt so bai toan cd ldi giai tuong tu ddi hoi hgc sinh phai nam dugc
phuong phap chung dl giai nhimg bai toan do
Bai toan cd ldi giai tuong tu nhau la rat phong phu va da dang. Ta c6 the
kl den nhirng bai toan diln hinh cd thuat toan giai dugc trinh bay trong tai lieu
sach giao khoa nhu la: giai phuang trinh bac nhat, bac hai mgt an, giai he phuang trinh bac nhat mgt in, tim hai s6 khi biet tong va hieu hoac la tim hai
khdng thupc dang dien hinh nhung van cd dilm tuomg dong nhau trong phuang phap giai nhu la:
f ^
* Mot so bai todn ve phucmg trinh sau day:
- ( 2 - V3)'' + ( 2 + V 3 f = 1 4
- (V7T4V3 r ^ " + ( V 7 - 4 V 3 r ' ' - 4
- ( 5 - 721)"+ 7.(5+ 721)" = 2'^^ - 8"+ 18" = 2.(27)"
- 5 " + 1 2 " =13"
* * Mdt sd bdi todn ve tinh dien tich
Bdi 1: Mdt thira rudng hinh thang ed dien tich 200m^. Day ldn gap 3 ldn day nhd. Dien tieh thira rudng Id 200m . Ngudi ta chia thira rudng thdnh 4 phdn cho 4 gia dinh trdng rau an bang cdch cang day theo hai dudng cheo, Tinh
dien tich mdi phdn dupe chia?
Bdi 2: Cho tam gidc ABC cd dien tich 1200m^ Tren canh AB ta lay diem N,
tren canh AC lay dilm M sao cho BN=-AB vd AM =MC, BM cdt CN tai 0. 3
Tim dien tieh tam gidc BOC?
Bai 3: Cho tam giac ABC, tren AB va AC lay lan Iugt 2 diem M va N sao cho AM gap ddi BM. CN bang - AN. Hai doan thing BN va CM cit nhau tai 0.
Ndi AO keo dai cit BC tai P?
a. Tinh dien tich tam giac ABC bilt dien tich tam giac BOC bang 12cm^
b. Xac dinh ty sd cua hai doan thing PC va PB?