Răspuns:
Explicație pas cu pas:
a. aplicam reciproca lui Thales
[tex]\frac{AM}{MB} =\frac{AN}{NC}[/tex]
[tex]\frac{2}{6} =\frac{5}{15} \\[/tex]
30=30 ⇒ MN║BC
b.
AN=AC-CN=10-8=2
[tex]\frac{AM}{MB} =\frac{AN}{NC}[/tex]
[tex]\frac{AM}{AM+MB} =\frac{AN}{AN+NC} \\\frac{AM}{AB} =\frac{AN}{AC} \\\frac{3}{15} =\frac{2}{10}[/tex]
30=30⇒MN║BC
c.
[tex]\frac{AM}{MB} =\frac{AN}{NC} \\\frac{6}{8} =\frac{10}{20}[/tex]
120≠80⇒MN∦BC
d. AN=AC-NC=30-24
[tex]\frac{AM}{AM+MB} =\frac{AN}{AN+NC} \\\frac{AM}{AB} =\frac{AN}{AC} \\\frac{4}{24} =\frac{6}{30}[/tex]
144≠120⇒MN∦BC
