a, Vì M là trung điểm BC => MC = MB
Xét △ABM và △ECM
Có: AM = ME (gt)
BMA = CME (đối đỉnh)
BM = CM (gt)
=> △ABM = △ECM (c.g.c)
b, Vì △ABM = △ECM (cmt)
=> AB = CE (2 cạnh tương ứng)
c, Vì △ABM = △ECM (cmt)
=> ABM = MCE (2 góc tương ứng)
Mà 2 góc này nằm ở vị trí so le trong
=> AC // BE (dhnb)
cho tam giac ABC tren tia doi cua tia AB lay diem D sao cho AC= AD. tren tia doi cua tia AC lay diem E sao cho AE=AB
a) chung minh tam giac ADE= tam giac ACB
b)goi M la trung diem cua BE chung minh tam giac ABM bang tam giac AEM
c) duong thang AM cat CD tai N. Chung minh AN vuong goc CD
Cho tam giac ABC co 3 goc nhon , AB = AC . Goi M la trung diem cua BC
a) Chung minh tam giac ABM = tam giac ACM
b) Tren tia doi tia MA lay diem E sao cho MA = ME . Chung minh AC // BE
c) ke BH vuong goc AC tai H . CK vuong goc Be tai K . Chung minh goc ABH = goc ECK
Cho tam giac ABC can tai A. Goi M la trung diem cua AC. Tren tia doi cua tia MB lay diem D sao cho DM=BM
a. Chung minh tam giac BMC bang tam giac DMA. Suy ra AD // BC
b. Chung minh tam giac ACD la tam giac can
c. Tren tia doi cua tia CA lay E sao cho CA =CE. Chung minh DC di qua trung diem I cua BE
Cho tam giac ABC , AB = AC . M la trung diem cua BC
a) Chung minh tam giac ABM = tam giac ACM.
b) Tren tia doi tia MA lay die mD sao cho MD = MA . Chung minh AB // CD
Cho tam giac ABC vuong tai A co AB=AC . Goi D la trung diem cua AC . Tren tia doi cua tia DB lay diem E sao cho DB=DE
a) Chung minh : tam giac ADB=tam giac CDE
b) Tren tia doi cua tia AB lay diem I sao cho AD = AI. chung minh : tam giac CDE = tam giac AIC
c) chung minh CI vuong goc EB
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
Cho tam giac ABC co AB<AC. M la trung diem cua BC. Tren tia doi cua tia AM lay D sao cho AM=MD.
a) Chung minh tam giac ABM = tam giac DCM
b) Chung minh BD\\AC
c) Qua A ve duong thang no cat BD tai E. Chung minh B la trung diem cua ED
Cho tam giac ABC , AB < AC . AE la tia phan giac cua goc BAC (E thuoc BC) . Tren canh AC lay diem M sao cho AM=AB
a) Chung minh tam giac ABE = tam giac AME
b) AE cat BM tai diem I . Chung minh I la rung diem cua BM
c) Tren tia doi cua tia EM lay diem N sao cho EN=EC. Chung minh tam giac ENB = tam giac ECM
d) Chung minh K,B,M thang hang
Cho tam giac ABC , AB < AC . AE la tia phan giac cua goc BAC (E thuoc BC) . Tren canh AC lay diem M sao cho AM=AB
a) Chung minh tam giac ABE = tam giac AME
b) AE cat BM tai diem I . Chung minh I la rung diem cua BM
c) Tren tia doi cua tia EM lay diem N sao cho EN=EC. Chung minh tam giac ENB = tam giac ECM
d) Chung minh K,B,M thang hang
