Question

Exercitiul acesta, dau coroana. Va rog

Answer 1

   

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.

.  

$\displaystyle\bf\\a)\\\\\frac{AM}{MB}=\frac{~~4^{(2}}{10}=\frac{2}{5}\\\\\frac{AN}{NC}=\frac{~~6^{(3}}{15}=\frac{2}{5}\\\\\implies\frac{AM}{MB}=\frac{AN}{NC}=\frac{2}{5}\\\\\implies~MN\Big|\Big|BC\\\\\\\\ b)\\\\MB=9~cm\\\\AM=AB-MB=15-9=6~cm\\\\\frac{AM}{MB}=\frac{~~6^{(3}}{9}=\frac{2}{3}\\\\\frac{AN}{NC}=\frac{2}{3}\\\\\implies\frac{AM}{MB}=\frac{AN}{NC}=\frac{2}{3}\\\\\implies~MN\Big|\Big|BC$

 

Answer 2

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