Giải thích các bước giải:
a.Xét $\Delta AIC,\Delta DIB$ có:
$IA=ID$
$\widehat{AIC}=\widehat{BID}$
$IB=IC$
$\to\Delta AIC=\Delta BID(c.g.c)$
b.Từ câu a $\to\widehat{IAC}=\widehat{IDB}\to AC//DB$
c.Ta có $AH\perp BC, DK\perp BC\to AH//DK$
Xét $\Delta AIH,\Delta DIK$ có:
$\widehat{HAI}=\widehat{IDK}$ vì $AH//DK$
$IA=ID$
$\widehat{AIH}=\widehat{DIK}$
$\to\Delta AIH=\Delta DIK(g.c.g)\to AH=DK$
d.Xét $\Delta ADN,\Delta DAM$ có:
$\widehat{MAD}=\widehat{ADN}$ vì $AH//DK$
Chung $AD$
$\widehat{DAN}=\widehat{ADM}$ vì $AC//DB$
$\to\Delta ADN=\Delta DAM(g.c.g)$
$\to AN=DM$
Xét $\Delta AIN,\Delta DIM$ có:
$IA=ID$
$\widehat{IAN}=\widehat{IDM}$ vì $AC//DB$
$AN=DM$
$\to\Delta AIN=\Delta DIM(c.g.c)$
$\to\widehat{AIN}=\widehat{DIM}$
$\to M,I,N$ thẳng hàng
