Giải thích các bước giải:

Gọi $DP\cap AB=E$

$\to \widehat{EHB}=\widehat{EAD}(=90^o)$

$\to \Delta EHB\sim\Delta EAD(g.g)$

$\to \dfrac{EH}{EA}=\dfrac{EB}{ED}$

$\to \Delta EBD\sim\Delta EHA(cgc)$

$\to \widehat{EBD}=\widehat{EHA}$

$\to \widehat{AHD}=180^o-\widehat{AHE}=180^o-\widehat{DBE}=\widehat{ABD}=45^o$

Gọi $DH\cap MN=F$

$\to \widehat{FNP}=\widehat{FHM}(=90^o)$

$\to \Delta FHM\sim\Delta FNP(g.g)$

$\to \dfrac{FH}{FN}=\dfrac{FM}{FP}$

$\to \Delta FHN\sim\Delta FMP(c.g.c)$

$\to \widehat{FHN}=\widehat{FMP}=\widehat{NMP}=45^o$

$\to \widehat{FHN}=\widehat{AHD}$

$\to A, H, N$ thẳng hàng