Teorema lui Thales spune asa:
Daca o dreapta este paralela cu o latura a unui triunghi,
atunci aceasta determina segmente proportionale pe celelalte 2 laturi.
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[tex]\displaystyle\bf\\a)\\\\\frac{AM}{MB}=\frac{~~4^{(2}}{10}=\frac{2}{5}\\\\\frac{AN}{NC}=\frac{~~6^{(3}}{15}=\frac{2}{5}\\\\\implies\frac{AM}{MB}=\frac{AN}{NC}=\frac{2}{5}\\\\\implies~MN\Big|\Big|BC\\\\\\\\ b)\\\\MB=9~cm\\\\AM=AB-MB=15-9=6~cm\\\\\frac{AM}{MB}=\frac{~~6^{(3}}{9}=\frac{2}{3}\\\\\frac{AN}{NC}=\frac{2}{3}\\\\\implies\frac{AM}{MB}=\frac{AN}{NC}=\frac{2}{3}\\\\\implies~MN\Big|\Big|BC[/tex]
Răspuns:
Explicație pas cu pas:
Reciproca lui Thales ; daca AM/MB=AN/NC ⇒MN║BC ; 4/10=6/15=2/5 ; B) AM=15-9=6 ;6/9=2/3 ; MN║BC