We have The triangle ABCand we always hve AB + AC>BC, how can we prove it?

Answer 1

Draw a line from A perpendicular to BC. Let E be the intersection between this line and BC => BE + EC = BC
We have:
AB>BE (1)
and AC>EC (2)
(1)+(2) => AB + AC > BE +EC
AB + AC > BC

Answer 2

this is simply a requirement of distance between two objects. for a rigorous proof, you could use contradiction and show that if you assume that AB +AC <= BC the sum of the angles is not 180 degrees.