cho tam giac ABC B=60 tren tia doi BC lay diem E sao cho BE=BA . qua B ve 1 duong thang song song AE cat AC o F a] chung minh BE la phan giac cua goc ABC b] Qua A ve mot duong thang vuong goc BF cat BC tai D .Chung minh tam giac ABC deu c] goi Ax la tia doi cua AB . Chung minh goc CAx =goc CDF d] chung minh AF=FC
tam giac ABC co canh BC la canh lon nhat . Tren canh BC lay diem D va E sao choa BD=BA va CE=CA . Tia phan giac cua goc B cat AE tai M; tia phan giac cua goc C cat AD tai N. Chung ming rang tia phan giac cua goc BAC vuong goc voi MN
cho tam giac abc co goc b = goc c, tia phan giac cua goc a cat bc tai d
1. chung minh tam giac adb = tam giac adc
2. chung minh ad vuong goc voi bc
3. tren tia doi cua tia da lay diem m sao cho da = dm, chung minh ab // cm
cho tam giac abc co goc c+90 do=goca ve ah vuong goc bc duong thang vuong goc voi ab tai a cat bc tai d goi m la giao diem cua cac tia phan giac goc bah va adh chung minh goc bah=2c chung minh mavuong goc ac
CHO TAM GIAC ABC CO AD LA PHAN GIAC CUA GOC A (D THUOC BC). KE DEVUONG GOC VOI AB, KE DF VUONG GOC VOI AC
a, CHUNG MINH TAM GIAC AED= TAM GIAC AFD
b, TIA FD CAT TIA AB TAI P, TIA ED CAT TIA AC TAI Q. CHUNG MINH AP=AQ
c, TIA AD CAT PQ TAI M. CHUNG MINH AM LA DUONG TRUNG TRUC CUA DOAN THANG PQ
d, CHO GOC BAC=50 DO. TINH SO DO GOC APQ VA GOC AQP
cho tam giac ABC. Goi M la trung diem BC va AM la tia phan giac cua goc A. Ve MI vuong goc AB, MH vuong goc AC. Chung minh rang:
a, MI = MH
b, Tam giac ABC can
c, Cho AB = 17 cm, AM = 15 cm. Tinh BC
d, Tren tia doi cua tia BC lay diem D, tren tia doi cua tia CB lay diem E sao cho BD = CE. Chung minh: tam giac AED can
Cho tam giac ABC vuong tai A. Tia phan giac cua goc ABC cat AC tai D, E la diem tren canh BC sao cho BE = BA. DE vuong goc voi BC
a) Chung minh rang tam giac ABD = tam giac EBD
b) Chung minh rang DE vuong goc voi BC
cho tam giac ABC co goc a nhon M la trung diem cua BC tren tia doi cua tia MA lay diem D sao cho MA=MD chung minh BAM=CDM chung minh AC=AD tren nua mat phang Bo AB ko chua C ve tia Ax vuong goc AB tren nua mat phang bo AC ko chua B ve tia Ay vuong goc AC tren tia Ax lay Diem P sao cho AP=AB tren tia Ay lay diem Q sao cho AQ=AC chung minh tam giac ABQ= tam giac APC goi giao diem cua DA va PQ la K chung minh AK vuong goc PQ
1)cho tam giac ABC co goc A <90 độ ve tia Ax vuong goc voi AB(Ax va AC cung nam trong nua mat phang bo la duong thang AB) tren tia Ax lay diem d sao cho AD=AB.Ve tia Ay vuong goc voi AC(Ay va AB cung nam trong 1 nua mat phang bờ la doan thang AC )tren tia Ay lay diemE sao cho Ae=Ac.Goi M la trung diem cua canh BC .Chung minh rang
a)AM=1/2DE
b)AM vuong goc voi DE
2)cho tam giac ABCgoi M,N lan luot la trung diem cua AB va AC .Chung minh rang MN//BCva MN=1/2 BC
3)cho tam giac ABC vuong tai A , AH vuong goc voi BC. Biet HC-HB=AB.Chung minh rang BC = 2AB
4)tim so nguyen x,y sao cho:x-2xy+y=0
5)cho tam giac ABC co goc A = 60 độ . Chung minh BC.BC=AB.AB+AC.AC-AB.AC