a) Xét \(\Delta ABE\) và \(\Delta ACD\) có:
AB = AC (gt)
\(\widehat{A}\left(chung\right)\)
AE = AD (gt)
Do đó: \(\Delta ABE=\Delta ACD\left(c-g-c\right)\)
=> BE = CD (hai cạnh tương ứng)
b) Vì \(\Delta ABE=\Delta ACD\left(cmt\right)\)
=> \(\widehat{ABE}=\widehat{ACD}\) (hai cạnh tương ứng)
=> \(\widehat{AEB}=\widehat{ADC}\) (hai cạnh tương ứng)
Ta có: AB = AC; AD = AE
mà : DB = AB - AD
CE = AC - AE
=> DB = CE
Xét \(\Delta BOD\) và \(\Delta COE\) có:
\(\widehat{DBO}=\widehat{ECO}\left(\widehat{ABE}=\widehat{ACD}\right)\)
DB = CE (cmt)
\(\widehat{BDO}=\widehat{CEO}\left(\widehat{ADC}=\widehat{AEB}\right)\)
Do đó: \(\Delta BOD=\Delta COE\left(g-c-g\right)\)