Question

ABCD-trapez
AB||CD, AB>CD
AC intersectat cu BD ={O}
M apartine AO
N apartine BO
AM/MO=2/3
BN/BO=2/5
Demonstreaza ca MN||DC
Am facut si desen.

Answer 1

Răspuns:

Explicație pas cu pas:

Vom demonstra prin reciproca lui Thales

$\frac{BN}{BO}=\frac{2}{5} \\\frac{BN}{BO-BN}=\frac{2}{5-2} \\\\\frac{BN}{NO}=\frac{2}{3}$

$\frac{AM}{MO} =\frac{2}{3}$

Observam ca cele 2 rapoarte sunt egale ⇒din Thales ca MN║AB

dar AB║CD⇒ MN║CD