Răspuns:
Explicație pas cu pas:
a.
[tex]\frac{AM}{MB} =\frac{1}{6} \\\frac{AN}{AC} =\frac{1}{7}[/tex]
in a doua facem proportie derivata si obtinem:
[tex]\frac{AN}{AC-AN} =\frac{1}{7-1} \\\frac{AN}{NC} =\frac{1}{6}[/tex]
Observam ca [tex]\frac{AM}{MB}=\frac{AN}{NC} =\frac{1}{6}[/tex]⇒Reciproca Teoremei Thales ca MN║BC
b.
[tex]\frac{AM}{MB}=\frac{2}{5} \\\frac{NC}{AC} =\frac{5}{7}[/tex]
Lucram la a doua prin proportii derivate si vom avea
[tex]\frac{AC}{NC}=\frac{7}{5} \\\frac{AC-NC}{NC} =\frac{7-5}{5} \\\frac{AN}{NC} =\frac{2}{5}[/tex]
Observam ca [tex]\frac{AM}{MB}=\frac{AN}{NC} =\frac{2}{5}[/tex]⇒Reciproca Teoremei Thales ca MN║BC
