Cho doan thang AB.§iem C cach deu hai diem A,B. Diem D cach deu hai diem A,B(D va C nam khac phia doi voi AB)
a) Chung minh rang: Tia CD la tia phan gia cua goc ACB
b) Ket qua cau a con dung khong neu C,D nam cung phia voi AB?
Cau 5: Trong cac khang dinh sau, khang dinh nao dung, khang dinh nao sai?
1.Ba diem phan biet la ba diem thang hang.
2.Voi ba diem phan biet luon co hai diem nam ve cung phia doi voi diem con lai.
3.Voi ba diem thang hang phan biet luon co hai diem nam khac phia voi diem con lai.
4.Voi ba diem A,B,C thang hang thi diem B luon nam giua hai diem A,C.
5.Co mot va chi mot duong thang di qua hai diem (phan biet) cho truoc.
6.Hai duong thang phan biet thi song song voi nhau.
7.Hai tia chung goc thi cung nam tren mot duong thang.
8.Hai tia chung goc thi doi nhau
9.Neu diem M nam giua diem A,B thi no la trung diem cua doan thang AB.
10.Neu MA=MB thi M la trung diem cua doan thang AB.
11.Neu MA+MB= AB va MA=MB thi M la trung diem cua doan thang AB.
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5. Dien de duoc phat bieu dung
a)Mot phan duong thang bi chia ra boi diem O cung voi diem O duoc goi la mot ...
b)Hinh tao boi diem O va mot phan duong thang chua tat ca cac diem nam cung phia la mot ...
c)Neu diem O nam tren duong thang xy thi diem O la goc chung cua
d)Hinh gom hai diem ... va tat ca cac diem nam giua ... duoc goi la doan thang RS. Hai diem ... duoc goi la hai mut cua doan thang RS.
e)Khi MP+MK=PK thi .........
f)Diem M la trung diem AB neu M ...... A, B va ..... cach deu ........
tren hai canh Ox va Oy cua goc nhon xOy dat cac doan thang AB va CD sao cho AB=CD. Diem A nam giua O va B , Diem C nam giua O va D , OA khac OC . Goi E va F lan luot la trung diem cua AC va BD . M la diem doi xung cua D qua E .
a, chung minh tam giac ECD = tam giac EAM
b, chung minh EF song song voi Ot va Ot la tia phan giac cua goc xOy
gọi I là trung điểm AD
xét tam giác ACD có EI là đường trung bình nên IE song song CD và bằng 1/2 CD
xét trường hợp 1 EF cắt OA tại K ko thuộc tia Ox và cắt Oy tại Q thuộc Oy
có EI song song CD nên IEF=FQD
tương tự ta có IN là đường trung bình tam giác ABD nên IF song song AB và bằng 1/2 AB
AB=CD nên IE=IF
tam giác IEF cân tại I
ta có IF song song AB nên IF song song OK
INK= KNI
IMN = NQD = OQK
nên tam giác OKQ cân tại O có Ot là phân giác góc ngoài tại O nên Ot song song KQ hay song song MN
trường hợp còn lại làm tương tị
chỗ Ot là phân giác ngoài ban tự chứng minh song song đi dễ mà
1) Cho hai doan thang AC.BD cat nhau tai I. Phat bieu nao sau day?
A) Goc BAC va DIC dong vi B) Goc ADB va CBD so le trong
C) Goc BAC va ACD so le trong D) Goc CAD va ACB so le trong
2) Cho tam giac ABC co BAC=90 do. Qua B dung duong thang b vuong goc voi AB va qua C dung duong thang c vuong goc voi AC. Phat bieu nao sau day la sai?
A) b va c cat nhau B) AB//c C) AC//b D) Ca A,B,C deu sai
3) Cho hai duong thang song song a,b. Mot duong thang c vuong goc voi ca hai duong thang a va b. Goi d la mot duong thang bat ky. Phat bieu nao sau day la dung?
A) Neu d khong co diem chung voi a thi cung khong co diem chung voi b
B) Neu d cat a thi d cung cat b
C) Neu d vuong goc voi a thi d song song voi c
D) Ca ba paht bieu tren deu dung.
4) Cho ba diem M,N,P khong thang hang. Phat bieu nao sau day sai?
A) Chi co mot duong thang di qua M va song song voi NP B) Co mot tam giac MNP
C) Chi co mot duong thang di qua M va vuong goc voi NP D) Tat ca deu sai
5) Cho biet hai duong trung truc cua hai doan thang AB va CDD cat nhau tai O. Trong cac cau sau, cau nao dung:
A) AB//CD B) AB\(\perp\)CD C) AB va CD cat nhau D) Tat ca deu sai
Câu 1: B
Câu 2: D
Câu 3: D
Câu 4: D
Câu 5: D
Bai 1
Cho tam giac nhon ABC , diem M thuoc canh BC , goi D la diem doi xung voi M qua AB , goi E la diem doi xung voi M qua AC. Goi I,K la giao diem cua DE voi AB va AC
a,CMR ; MA la tia fan giac cua goc IMK
b,Tim vi tri cua diem M de DE co do dai nho nhat
Bai 2
Cho hai diem A va B nam cung phia doi voi duong thang d.goi AH , BK la cac duong vuong goc ke tu A , B den d.Goi C la diem bat ki nam giua H va K
a,Ve diem A' doi xung voi A.cmr goc ACH = goc A'CH
b,Gia su goc ACH = goc BKC ,cmr khi do 3 diem A',C,B thang hang
c,Neu cach dung diem C nam giua H va K sao cho goc ACH = goc BKC
SACH CAC DANG TOAN VA PHUONG PHAP GIAI LOP 8
cho tam giac abc can tai a.tren duong thang vuong goc voi ac tai c lay diem d sao cho hai diem b,d nam khac phia doi voi duong thang ac.goi k la giao diem cua duong thang qua b vuong goc voi ab va duong thang qua trung diem m cua cd vuong goc voi ad.c/m kb=kd
cho hinh thang ABCD(AB//CD)
a)chung minh rang neu hai tia phan giac cua hai goc A va D cung di qua trung diem F cua canh ben BC thi canh ben AD bang tong hai canh day
b) chung minh rang neu AD=AB+CD thi tia phan giac cua hai goc A va B cat nhau tai trung diem cua canh ben BC
cho ΔABC vuong tai A va ABC=60
a, so sanh AB va AC
b, Tren BC lay D sao cho BD =AB. Qua D dung cac duong thang vuong goc voi BC cat tia doi AB tai E. CHung minh ΔABC=ΔDEB
c, goi H la giao diem cua ED va AC. chung minh BH la tia phan giac cua ABC
d,Qua B dung cac duong thang vuong goc voi AB cat duong thang ED tai K vhng minh ΔHBK deu
a: góc ACB=90 độ-60 độ=30 độ<góc ABC
nên AB<AC
b: Xét ΔABC vuông tại A và ΔDBE vuông tại D có
BA=BD
góc ABC chung
Do đó: ΔABC=ΔDBE
c: XétΔBAH vuông tại A và ΔBDH vuông tại D có
BH chung
BA=BD
Do đó: ΔBAH=ΔBDH
Suy ra: góc ABH=góc DBH
hay BH là phân giác của góc ABC
cho tam giac ABC deu. Tren tia doi cua tia AB lay diem D va tren tia doi cua tia AC lay diem E sao cho AD=AE. Goi M, N, H, Q theo thu tu la trung diem cua cac doan thang BE, AD, AC, AB.
CM: a) Tu giac BCDE la hinh thang can.
b) Tu giac CNEQ la hinh thang
c) Tren tia doi cua tia MN lay diem N' sao cho MN'=MN. Cm BN' vuong goc voi BD, EB=2MN.
d) Tam giac MNH la tam giac deu