1.
ΔABC~ΔDEF de unde rezulta ca vom forma un raport de asemanare:
[tex] \frac{AB}{DE} = \frac{BC}{EF}= \frac{AC}{DF} [/tex]
Acum ca am format raportul,inlocuim:
[tex] \frac{8}{6} = \frac{BC}{9} = \frac{AC}{12} \\\\
=\ \textgreater \ BC= \frac{9*8}{6} =\ \textgreater \ BC=12 cm\\\\
[/tex]
Am aflat BC-ul,acum aflam AC din proportia:
[tex] \frac{BC}{9} = \frac{AC}{12} =\ \textgreater \ \frac{12}{9} = \frac{AC}{12} =\ \textgreater \ AC= \frac{12*12}{9} =\ \textgreater \ AC= \frac{48}{3} =\ \textgreater \ AC=16cm[/tex]
2. Daca triunghiul ABC este asemenea DEF iar AB-16 cm AC-14cm BC-18 si DE-28cm calculati DE SI EF.
ΔABC~ΔDEF
=>[tex] \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}\ \textless \ =\ \textgreater \ \frac{16}{28} = \frac{18}{EF} = \frac{14}{DF} \\\\
=\ \textgreater \ EF= \frac{18*28}{16} =\ \textgreater \ EF=31,5\\\\
=\ \textgreater \ DF= \frac{14*31,5}{18} =\ \textgreater \ DF=24,5[/tex]
