Nu stiu daca ai nevoie si de desen. Iata rezolvarea:
Verificam rapoartele: [tex] \frac{DG}{DE} [/tex] si [tex] \frac{DH}{DF} [/tex]
a) [tex] \frac{DG}{DE} = \frac{1,5}{7} = \frac{15}{70} = \frac{3}{14} [/tex]
[tex] \frac{DH}{DF} = \frac{3}{14} [/tex]
Deci rapoartele fiind egale, rezulta ca GH || EF.
b) [tex] \frac{DG}{DE} = \frac{2,5}{4} = \frac{25}{40} = \frac{5}{8} [/tex]
[tex] \frac{DH}{DF} = \frac{2,75}{4,5} = \frac{275}{450} = \frac{11}{18} [/tex]
Rapoartele nu sunt egale, deci GH nu este paralel cu EF.
c) [tex] \frac{DH}{DF} = \frac{1/28}{5/12} = \frac{12}{28*5} = \frac{3}{35} [/tex]
[tex] \frac{DG}{DE} = \frac{1/5}{7/3} = \frac{3}{5*7} = \frac{3}{35} [/tex]
Rapoartele sunt egale, deci GH || EF.
