Hạ EG vuông góc DC (G thuộc DC)
Ta có:
\(\widehat{FEG}+\widehat{AEM}=90^0\\ \widehat{MAE}+\widehat{AEM}=90^0\)
\(\rightarrow\widehat{FEG}=\widehat{MAE}\)
Xét \(\Delta ABM\) và \(\Delta EGF\) có:
\(EG=AB\left(=BC\right)\)
\(\widehat{FEG}=\widehat{MAB}\)
\(\rightarrow\Delta ABM=\Delta EGF\\ \rightarrow AM=EF\)
cho hinh vuong abcd, ac cat bd tai e, duong thnag qua a cat bc tai m , cat duong thang cd tai n,em cat bn tai k. chung minh ck vuong goc voi bn
cho tam giac abc vuong can (ab=ac). Qua C ve duong thang cat canh AB tai D. Tu B ve duong vuong goc voi CD tai I cat AC tai E. CMR AD=AE
cho hinh vuong abcd co ac cat bd tai o.m la diem bat ki thuoc canh ad(m khac d,a).tia bm cat duong thang cd tai n,om cat an tai i.C/m di vuong goc voi an
cho hinh vuong ABCD. Qua A ve hai duong thang vuong goc voi nhau lan luot cat BC tai P va R, cat Cd tai Q va S.
a, chung minh tam giac AQR va tam giac APS la cac tam giac can
b, QR cat PS tai H; M,N la trung diem cua QR va PS. chung minh tu giac AMHN la hinh chu nhat
c, chung minh P la truc tam
d, chung minh MN la duong trung truc cua AC
e, chung minh bon diem M, B,N,D thang han
cho tam giac ABC vuong tai A co AB=9cm BC=15cm tren tia doi cua tia AB lay diem D sao cho A la trung diem cua doan thang AB
a, tinh do dai canh AC va ss cac goc cua tam giac ABC
b, cm tam giac BCD can
c, goi E la trung diem cua canh CD ,BE cat AC o I .cm DI ik qua trung diem cua canh BC
(ve hinh )
De bai : Cho tam giac ABC co AB=9 cm,BC=12 cm,BC=15 cm
a,C/m tam giac ABC vuong
b,Duong phan giac cua goc B cat AC tai D . Tinh AD,DC
c,Duong cao AH cat BD tai I. Chung minh IH.BD=IA.IB
d,Chung minh tam giac AID can
bai 3 ; cho tam giac abc . tren canh ab lay diem m , tren canh ac lay diem n sao cho bm = cn . goi i la trung giem doan bn , goi k la trung diem doan cm , duong thang ik cat ab tai p , cat ac tai q . chung minh rang tam giac apq la tam giac can .
Cho tam giac ABC co dien tich 126cm^2.Tren AB lay D sao cho AD=DB, tren Bc lay E sao cho BE=2EC.Tren AC lay CF=3FA.Cac doan thang CD, BF AE lan luot cat nhau tai M,N,P.Tinh SMNP vong 15 violympic toan
bai 7 : cho tam giac abc vuong tai a , duong trung tuyen am . goi d la trung diem cua ab , e la diem doi xung voi m qua d .
a ) chung minh e doi xung voi m qua ab .
b) cac tu giac aemc, aebm la hinh gi . chung minh .
c ) cho bc = 4 cm . tinh chu vi tu giac aebm.
d ) tam giac vuong abc can co them dieu kien gi de aebm la hinh vuong .
