Question

In trapzul ABCD cu AB || CD si AC intersectat cu BD ={O} , se iau punctele M apartine (AO) si N apartine (BO) astfel incat AM/MO = 2/3 si BN/BO = 2/5. Aratati ca MN || DC. Va rog mult ajutati.ma e urgent!
Multumesc !

Answer 1

In triunghiul AOB:
$\frac{AM}{MO}=\frac{2}{3}=\ \textgreater \ \frac{AM}{AM+MO}=\frac{2}{2+3} =\ \textgreater \ \frac{AM}{AO}=\frac{2}{5}$
Dar si BN/BO = 2/5.
=> AM/AO=BN/BO => reciproca teoremei lui Thales => MN || AB
Dar AB || CD => MN || CD.