Giải thích các bước giải:
a.Gọi $AI$ là phân giác $\widehat{BAC}$
$\to\widehat{BAI}=\widehat{IAC}$
Mà $\hat B=\hat C\to \widehat{ABI}=\widehat{ACI}$
$\to \widehat{AIB}=180^o-\widehat{IAB}-\widehat{IBA}=180^o-\widehat{IAC}-\widehat{ICA}=\widehat{AIC}$
Xét $\Delta ABI,\Delta ACI$ có:
$\widehat{AIB}=\widehat{AIC}$
Chung $AI$
$\widehat{BAI}=\widehat{IAC}$
$\to\Delta ABI=\Delta ACI(g.c.g)$
$\to AB=AC$
Xét $\Delta ABD,\Delta ACE$ có:
Chung $\hat A$
$AB=AC$
$\widehat{ABD}=\dfrac12\widehat{ABC}=\dfrac12\widehat{ACB}=\widehat{ACE}$
$\to \Delta ABD=\Delta ACE(g.c.g)$
$\to BD=CE$
b.Từ câu a $\to AB=AC(đpcm)$
