Question

In △ABC the points M and N belong to the sides

AC and AB respectively. AM/MC = AN/NB = 2/3 .
Prove that MN∥BC. Find MN, if BC=20. Please help!!!

Answer 1

since AM/AC = AN/AB = 2/5,

then ∆ABC similar to ∆ANM.

since ∆ABC ~ ∆ANM,

then MN || BC.

by similarity

MN = BC•2/5 = 8