21.
a) AN = AB + BN = 3+1 = 4cm
Comparăm ΔABC cu ΔAMN:
[tex]\it \begin{cases}\it \widehat{BAC}=\widehat{MAN}=90^o\\ \\ AB=AM=3\ cm\\ \\ AC=AN=4\ cm\end{cases} \stackrel{c.c.}{\Longrightarrow}\ \Delta ABC\equiv \Delta AMN \Rightarrow BC=MN[/tex]
b) Știm că, în două triunghiuri congruente la laturi congruente
se opun unghiuri congruente.
[tex]\it \left.\begin{aligned}\Delta AMN\equiv\Delta ABC\\ \\.\ \ \ \ \ \ [AM] \equiv [AB] \end{aligned}\right\}\ \Rightarrow \widehat{MNA}\equiv \widehat{BCA}[/tex]
[tex]\it c) \left.\begin{aligned}\Delta AMN\equiv\Delta ABC\\ \\.\ \ \ \ \ \ [AN] \equiv [AC] \end{aligned}\right\}\ \Rightarrow \widehat{AMN}\equiv \widehat{ABC}[/tex]
