a)Xét \(\Delta ABC\)và \(\Delta HBA\)có:
\(\widehat{BAC}=\widehat{BHA}\)(=\(90^0\))
\(\widehat{B}\)chung
=>\(\Delta ABC\)~\(\Delta HBA\)(g.g)
=>\(\dfrac{AB}{HB}=\dfrac{BC}{AB}\)
=>\(AB^2=HB.BC\)
CHO TAM GIAC ABC VUONG TAI A ,CO AB=12,AC=16 .KE DUONG CAO AH
A,CUNG MINH TAM GIAC HAB DONG DANG VOI TAM GIAC ABC
B, TINH DO DAI DOAN THANG BC,AH
C,GOI AD LA DUONG PHAN GIAC CUA BAC ,DE LA DUONG PHAN GIAC CUA ADB.DUONG THNAG VUONG GOC VOI DE TAI D ,CAT ACANH AC O F.CHUNG MINH EA/EB*DB/DC*FC/FA=1
Cho tam giac ABC vuong tai A ( AB<AC) ve duong cao AH (H thuoc BC)
A) cm tam giac ABH dong dang tam giac CBA suy ra AB binh =BH.BC
B) Cho AB =6cm , AC=8cm. Tinh BC .Tren canh BC lay diem E sao cho CE=4cm, cm BE binh =BH.HC
C) Tinh dien tich tam giac ABH
D) Duong phan giac cua goc AHB cat AB tai D duong phan giac cua goc AHC cat AC tai F duong thanh DF cat AH tai I va cat CB tai K. Cm DI .FK=DK.FI
cho tam giac abc vuong tai a, co ab=3 cm ac=4 cm, duong phan giac ad. duong vuong goc voi dc cat ac tai e
a) cmr tam giac abc va tam giac dec dong dang
b) tinh do dai cac doan thang bc,bd
c) tinh do dai ad
d) tinh dien tich tam giac abc va dien tich tu giac abde
Cho tam giac ABC vuong tai A (AB<AC) ve duong cao AH (H thuoc BC)
A)cm tam giac ABH~tam giac CBA suy ra AB binh =BH.BC
B)cho AB=6cm, AC=8cm . Tinh BC.Tren canh BC lay diem E sao cho CE=4cm, cm BE binh=BH.HC
C) tinh dien tich tam giac ABH
D) Duong phan giac cua goc AHB cat AB tai D, duong phan giac cua goc AHC cat AC tai F, duong thang DF cat AH tai I va cat CB tai K.cm DI.FK=DK.FI
CHO TAM GIAC ABC VUONG TAI A ,BIET AB=9,AC=12 .TIA PHAN GAC CUA BAC CAT CANH BC TAI DIEM D .TU D KE DUONG THANG VUONG GOC VOI AC ,DUONG THANG NAY CAT AC TAI E.
A,TAM GIAC CEB DOGN DANG VOI TAM GIAC CAB
B,TINH CD/DEC,TINH S TAM GIAC ABD
CAN GAP GIUP MK VOI
cho tam giac ABC vuong tai A ( AB>AC). AM la duon trung tuyen. Ke duong thang vuong goc AM tai M lan luot cat AB tai E, cat AC tai F. CMR
a. Tam giac MBE dong dang tam giac MFC
b. AE.AB= AC. AF
c. Duong cao AH cua tam giac ABC cat EF tai I. CMR \(\dfrac{S_{ABC}}{S_{AFE}}\)=\(\left(\dfrac{AM}{AI}\right)^2\)
cho tam giac abc co goc a=120 do, phan giac ad. duong phan giac goc ngoai tai x cat duong thang ab tai k. goi e la giao diem cua dk va ac. tinh goc bed
Cho tam giac ABC nhon, co AM la trung tuyen. Duong thang xy qua A va vuong goc AM. Duong thang qua B vuong goc AC cat xy tai D. Tren Ax lay E: AD=AE. Chung minh CE vuong goc AB
cho tam giac ABC vuong o A, duong cao AH. Ke HD vuong goc AB ,HE vuong goc AC (D thuoc AB , E thuoc AC ) . Goi O la giao diem cua AH va DE
a)CM:AH=DE
b)goi P va Q lan luot la trung diem cua AH,DE. CM tu giac DEQP la hinh thang vuong
c) CM :O la truc tam cua tam giac ABQ
CM: dien tich tam giac ABC bang 2 lan dien tich tu giac DEQP